Fractions of wholes and equivalent fractions
By the end of this chapter you will be able to
- Name and write a fraction from a picture of equal parts
- Find a fraction of a set or an amount
- Place a fraction on a 0 to 1 number line
- Find an equivalent fraction by multiplying or dividing top and bottom
You should already know
- Halves and quarters of shapes and amounts (Level 3, chapter 8)
- Times tables and division (chapters 4 to 6)
Where this leads
- Time to the minute (chapter 8)
Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Recognise and show, using diagrams, a fraction with a small denominator (F1), Recognise, find and write fractions of a set of objects and of a quantity, unit and non-unit (F2), Recognise fractions as numbers on a number line (F3), Recognise and show equivalent fractions with small denominators, for example 1/2 = 2/4 = 4/8 (F4).
Exercise P Do you remember?
Non-calculatorMethod. Count in threes eight times, or use the 3 facts.
- Count in threes. Each count adds 3.3, 6, 9, 12, 15, 18, 21, 24
- The last number we said is the answer. We counted eight groups of 3.3 × 8 = 24
- Write the answer. This is the total.24
Check. Check: 24 ÷ 3 = 8.
Watch out. Learn the 3 facts in order.
Method. Divide the total by the number of groups.
- Count the groups. There are 4 groups.4 groups
- Share the counters. Each group gets the same number.16 ÷ 4 = 4
- Write the answer. This is how many are in each group.4
Check. Check: 4 × 4 = 16.
Watch out. The number of groups is the divisor.
Method. Count in sixes four times, or use the 6 facts.
- Count in sixes. Each count adds 6.6, 12, 18, 24
- The last number we said is the answer. We counted four groups of 6.6 × 4 = 24
- Write the answer. This is the total.24
Check. Check: 24 ÷ 6 = 4.
Watch out. Multiplication works in any order.
Method. Take away the tens.
- Take 40 from 100. Think of 100 as 10 tens and take away 4 tens.100 - 40 = 60
- Write the answer. This is what is left.60
Check. Check: 60 + 40 = 100.
Watch out. Take away the tens first.
Method. Count in nines four times, or use the 9 pattern.
- Count in nines. Each count adds 9.9, 18, 27, 36
- The last number we said is the answer. We counted four groups of 9.4 × 9 = 36
- Write the answer. This is the total. Its digits add to 9.36
Check. Check: 3 + 6 = 9.
Watch out. The digits of a 9 fact add to 9.
Fractions of a whole
A fraction shows some of the equal parts of a whole. The bottom number is the number of equal parts. The top number is the number of parts we are looking at.
For example, 3/8 means 3 parts out of 8 equal parts.
Key ideas
- Bottom number: how many equal parts the whole has.
- Top number: how many of the parts are shaded.
- The parts must be equal to count as a fraction.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.8 equal parts
- Count the shaded parts. The top number is the number of shaded parts.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/8
Check. Check: 3 + 5 = 8, so 5 parts are not shaded.
Watch out. The bottom number counts all the equal parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The circle is split into 4 equal slices.4 equal parts
- Count the shaded parts. Three slices are shaded.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/4
Check. Check: 3 + 1 = 4, so 1 slice is not shaded.
Watch out. Each slice is one equal part.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into 8 equal parts.8 equal parts
- Find the number of parts chosen. These are the parts we count on the top.5 parts
- Write the fraction. Parts chosen over total parts.5/8
Check. Check: 5 of the 8 parts is 5/8.
Watch out. The top number is the number of parts chosen.
Watch out
Watch out. Count all the equal parts for the bottom number, not only the shaded parts. In 3/8, 3 is shaded and 8 is all the parts.
Exam tip
Grown-up tip. Ask: “How many equal parts are there in all? How many are shaded?” Let the child draw a bar and shade 3 of 8.
Exercise 7A Practice: fractions of a whole
Non-calculatorMethod. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.4 equal parts
- Count the shaded parts. The top number is the number of shaded parts.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/4
Check. Check: 3 + 1 = 4, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.4 equal parts
- Count the shaded parts. The top number is the number of shaded parts.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/4
Check. Check: 3 + 1 = 4, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.5 shaded parts
- Write the fraction. Shaded parts over the total number of parts.5/10
Check. Check: 5 + 5 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.2 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/2
Check. Check: 1 + 1 = 2, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.7 shaded parts
- Write the fraction. Shaded parts over the total number of parts.7/10
Check. Check: 7 + 3 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.9 shaded parts
- Write the fraction. Shaded parts over the total number of parts.9/10
Check. Check: 9 + 1 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.5 equal parts
- Count the shaded parts. The top number is the number of shaded parts.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/5
Check. Check: 3 + 2 = 5, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.5 equal parts
- Count the shaded parts. The top number is the number of shaded parts.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/5
Check. Check: 3 + 2 = 5, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.5 shaded parts
- Write the fraction. Shaded parts over the total number of parts.5/10
Check. Check: 5 + 5 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.8 equal parts
- Count the shaded parts. The top number is the number of shaded parts.7 shaded parts
- Write the fraction. Shaded parts over the total number of parts.7/8
Check. Check: 7 + 1 = 8, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.8 equal parts
- Count the shaded parts. The top number is the number of shaded parts.7 shaded parts
- Write the fraction. Shaded parts over the total number of parts.7/8
Check. Check: 7 + 1 = 8, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.3 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/3
Check. Check: 1 + 2 = 3, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.8 equal parts
- Count the shaded parts. The top number is the number of shaded parts.5 shaded parts
- Write the fraction. Shaded parts over the total number of parts.5/8
Check. Check: 5 + 3 = 8, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.4 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/4
Check. Check: 1 + 3 = 4, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.2 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/2
Check. Check: 1 + 1 = 2, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.4 equal parts
- Count the shaded parts. The top number is the number of shaded parts.2 shaded parts
- Write the fraction. Shaded parts over the total number of parts.2/4
Check. Check: 2 + 2 = 4, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Writing fractions from a picture or a description
Write a fraction from words as well as pictures. "Five out of eight equal cubes" is written 5/8.
The whole must be split into equal parts before you write the fraction.
Key ideas
- Parts chosen on top; total equal parts on the bottom.
- Read words like out of as a fraction.
- Check the top is not more than the bottom.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into 8 equal parts.8 equal parts
- Find the number of parts chosen. These are the parts we count on the top.5 parts
- Write the fraction. Parts chosen over total parts.5/8
Check. Check: 5 of the 8 parts is 5/8.
Watch out. The top number is the number of parts chosen.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The circle is split into 4 equal slices.4 equal parts
- Count the shaded parts. Three slices are shaded.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/4
Check. Check: 3 + 1 = 4, so 1 slice is not shaded.
Watch out. Each slice is one equal part.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.8 equal parts
- Count the shaded parts. The top number is the number of shaded parts.3 shaded parts
- Write the fraction. Shaded parts over the total number of parts.3/8
Check. Check: 3 + 5 = 8, so 5 parts are not shaded.
Watch out. The bottom number counts all the equal parts.
Watch out
Watch out. 3/8 and 8/3 are different. The top number is the parts we count; the bottom is the total number of equal parts.
Exam tip
Grown-up tip. Ask the child to say the fraction in words, such as “three eighths”, before writing it.
Exercise 7B Practice: writing fractions
Non-calculatorMethod. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.10 equal parts
- Find the number of parts chosen. These are the parts we count on the top.9 parts
- Write the fraction. Parts chosen over total parts.9/10
Check. Check: 9 of the 10 parts is 9/10.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.4 equal parts
- Count the shaded parts. The top number is the number of shaded parts.2 shaded parts
- Write the fraction. Shaded parts over the total number of parts.2/4
Check. Check: 2 + 2 = 4, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.3 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/3
Check. Check: 1 of the 3 parts is 1/3.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.10 equal parts
- Find the number of parts chosen. These are the parts we count on the top.5 parts
- Write the fraction. Parts chosen over total parts.5/10
Check. Check: 5 of the 10 parts is 5/10.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.8 equal parts
- Find the number of parts chosen. These are the parts we count on the top.3 parts
- Write the fraction. Parts chosen over total parts.3/8
Check. Check: 3 of the 8 parts is 3/8.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.3 equal parts
- Count the shaded parts. The top number is the number of shaded parts.2 shaded parts
- Write the fraction. Shaded parts over the total number of parts.2/3
Check. Check: 2 + 1 = 3, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.3 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/3
Check. Check: 1 of the 3 parts is 1/3.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.3 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/3
Check. Check: 1 of the 3 parts is 1/3.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.5 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/5
Check. Check: 1 + 4 = 5, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.5 equal parts
- Find the number of parts chosen. These are the parts we count on the top.2 parts
- Write the fraction. Parts chosen over total parts.2/5
Check. Check: 2 of the 5 parts is 2/5.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.8 equal parts
- Find the number of parts chosen. These are the parts we count on the top.6 parts
- Write the fraction. Parts chosen over total parts.6/8
Check. Check: 6 of the 8 parts is 6/8.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.2 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/2
Check. Check: 1 of the 2 parts is 1/2.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.8 equal parts
- Count the shaded parts. The top number is the number of shaded parts.4 shaded parts
- Write the fraction. Shaded parts over the total number of parts.4/8
Check. Check: 4 + 4 = 8, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.5 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/5
Check. Check: 1 + 4 = 5, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.8 equal parts
- Find the number of parts chosen. These are the parts we count on the top.7 parts
- Write the fraction. Parts chosen over total parts.7/8
Check. Check: 7 of the 8 parts is 7/8.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.5 equal parts
- Find the number of parts chosen. These are the parts we count on the top.4 parts
- Write the fraction. Parts chosen over total parts.4/5
Check. Check: 4 of the 5 parts is 4/5.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Finding a fraction of a set or an amount
To find a fraction of an amount, first divide by the bottom number to find one equal part. Then multiply by the top number.
For 3/4 of 20: 20 divided by 4 is 5, and 3 times 5 is 15.
Key ideas
- Divide by the bottom number to find one equal part.
- Multiply by the top number to find the fraction.
- A unit fraction (top number 1) is one equal part.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 20 into 4 equal parts. The bottom number tells us how many equal parts to make.20 ÷ 4 = 5
- Take 3 of the parts. The top number tells us how many parts to take.3 × 5 = 15
- Write the answer. This is the fraction of the amount.15
Check. Check: 5 + 5 + 5 = 15, and the last part is 5.
Watch out. Divide by the bottom number first, then multiply by the top.
Method. Find one equal part by dividing by the bottom number.
- Divide 35 into 5 equal parts. Each equal part is one fifth.35 ÷ 5 = 7
- Take 1 of the parts. The top number is 1, so take one part.1 × 7 = 7
- Write the answer. This is one fifth of the amount.7
Check. Check: 7 × 5 = 35.
Watch out. A unit fraction takes one of the equal parts.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 16 into 8 equal parts. Each part is one eighth.16 ÷ 8 = 2
- Take 3 of the parts. Three parts are shaded.3 × 2 = 6
- Write the answer. This is three eighths of the amount.6
Check. Check: 2 + 2 + 2 = 6, and 5 parts are left: 5 × 2 = 10, and 6 + 10 = 16.
Watch out. Divide by the bottom number, then multiply by the top.
Watch out
Watch out. 3/4 of 20 is 15, not 5. Find one quarter (5), then take three quarters: 3 × 5 = 15.
Exam tip
Grown-up tip. Ask: “What is one equal part? How many of those parts are we taking?”
Exercise 7C Practice: fractions of amounts
Non-calculatorMethod. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 45 into 5 equal parts. The bottom number tells us how many equal parts to make.45 ÷ 5 = 9
- Take 3 of the parts. The top number tells us how many parts to take.3 × 9 = 27
- Write the answer. This is the fraction of the amount.27
Check. Check: 2 parts are left and 18 is left over, so 27 + 18 = 45.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 32 into 8 equal parts. The bottom number tells us how many equal parts to make.32 ÷ 8 = 4
- Take 2 of the parts. The top number tells us how many parts to take.2 × 4 = 8
- Write the answer. This is the fraction of the amount.8
Check. Check: 6 parts are left and 24 is left over, so 8 + 24 = 32.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 56 into 8 equal parts. The bottom number tells us how many equal parts to make.56 ÷ 8 = 7
- Take 6 of the parts. The top number tells us how many parts to take.6 × 7 = 42
- Write the answer. This is the fraction of the amount.42
Check. Check: 2 parts are left and 14 is left over, so 42 + 14 = 56.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part, then multiply it by the top number.
- Share 24 into 8 equal groups. Each group is one equal part of the set.24 ÷ 8 = 3
- Count 3 of the groups. The shaded part is the top number of groups.3 × 3 = 9
- Write the answer. This is how many are shaded.9
Check. Check: 9 of the 24 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part, then multiply it by the top number.
- Share 12 into 4 equal groups. Each group is one equal part of the set.12 ÷ 4 = 3
- Count 3 of the groups. The shaded part is the top number of groups.3 × 3 = 9
- Write the answer. This is how many are shaded.9
Check. Check: 9 of the 12 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part, then multiply it by the top number.
- Share 40 into 5 equal groups. Each group is one equal part of the set.40 ÷ 5 = 8
- Count 2 of the groups. The shaded part is the top number of groups.2 × 8 = 16
- Write the answer. This is how many are shaded.16
Check. Check: 16 of the 40 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 21 into 3 equal parts. The bottom number tells us how many equal parts to make.21 ÷ 3 = 7
- Take 2 of the parts. The top number tells us how many parts to take.2 × 7 = 14
- Write the answer. This is the fraction of the amount.14
Check. Check: 1 parts are left and 7 is left over, so 14 + 7 = 21.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 60 into 10 equal parts. The bottom number tells us how many equal parts to make.60 ÷ 10 = 6
- Take 6 of the parts. The top number tells us how many parts to take.6 × 6 = 36
- Write the answer. This is the fraction of the amount.36
Check. Check: 4 parts are left and 24 is left over, so 36 + 24 = 60.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part, then multiply it by the top number.
- Share 28 into 4 equal groups. Each group is one equal part of the set.28 ÷ 4 = 7
- Count 3 of the groups. The shaded part is the top number of groups.3 × 7 = 21
- Write the answer. This is how many are shaded.21
Check. Check: 21 of the 28 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part, then multiply it by the top number.
- Share 40 into 8 equal groups. Each group is one equal part of the set.40 ÷ 8 = 5
- Count 6 of the groups. The shaded part is the top number of groups.6 × 5 = 30
- Write the answer. This is how many are shaded.30
Check. Check: 30 of the 40 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 35 into 5 equal parts. The bottom number tells us how many equal parts to make.35 ÷ 5 = 7
- Take 2 of the parts. The top number tells us how many parts to take.2 × 7 = 14
- Write the answer. This is the fraction of the amount.14
Check. Check: 3 parts are left and 21 is left over, so 14 + 21 = 35.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 72 into 8 equal parts. The bottom number tells us how many equal parts to make.72 ÷ 8 = 9
- Take 4 of the parts. The top number tells us how many parts to take.4 × 9 = 36
- Write the answer. This is the fraction of the amount.36
Check. Check: 4 parts are left and 36 is left over, so 36 + 36 = 72.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part, then multiply it by the top number.
- Share 36 into 4 equal groups. Each group is one equal part of the set.36 ÷ 4 = 9
- Count 3 of the groups. The shaded part is the top number of groups.3 × 9 = 27
- Write the answer. This is how many are shaded.27
Check. Check: 27 of the 36 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part, then multiply it by the top number.
- Share 15 into 5 equal groups. Each group is one equal part of the set.15 ÷ 5 = 3
- Count 1 of the groups. The shaded part is the top number of groups.1 × 3 = 3
- Write the answer. This is how many are shaded.3
Check. Check: 3 of the 15 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 40 into 10 equal parts. The bottom number tells us how many equal parts to make.40 ÷ 10 = 4
- Take 6 of the parts. The top number tells us how many parts to take.6 × 4 = 24
- Write the answer. This is the fraction of the amount.24
Check. Check: 4 parts are left and 16 is left over, so 24 + 16 = 40.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part, then multiply it by the top number.
- Share 25 into 5 equal groups. Each group is one equal part of the set.25 ÷ 5 = 5
- Count 3 of the groups. The shaded part is the top number of groups.3 × 5 = 15
- Write the answer. This is how many are shaded.15
Check. Check: 15 of the 25 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Equivalent fractions
Equivalent fractions are the same amount, written with different numbers. 1/2 = 2/4 = 4/8.
To find an equal fraction, multiply the top and bottom by the same number. To simplify, divide both by the same number.
Key ideas
- Do the same to the top and the bottom.
- Equal fractions are the same amount of the whole.
- Double, or halve, the top and bottom together.
Method. Equivalent fractions: multiply the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.1 × 2 = 2
- Multiply the bottom number by 2. The fraction keeps the same value.2 × 2 = 4
- Write the missing number. This is the bottom number of the equal fraction.4
Check. Check: 2/4 and 1/2 are the same part of a whole.
Watch out. Do the same to the top and the bottom.
Method. Equivalent fractions: multiply the top and bottom by the same number.
- Multiply the top number by 2. Double the top number.2 × 2 = 4
- Multiply the bottom number by 2. Double the bottom number too.5 × 2 = 10
- Write the missing number. This is the bottom number of the equal fraction.10
Check. Check: 4/10 and 2/5 are equal.
Watch out. Double the top and the bottom together.
Method. Equivalent fractions: divide the top and bottom by the same number.
- Divide the top number by 2. Halve the top number.6 ÷ 2 = 3
- Divide the bottom number by 2. Halve the bottom number too.8 ÷ 2 = 4
- Write the missing number. This is the top number of the simpler fraction.3
Check. Check: 3/4 and 6/8 are equal.
Watch out. Halve the top and the bottom together.
Watch out
Watch out. Doubling only the top gives 4/5, which is not 2/5. Double both the top and the bottom.
Exam tip
Grown-up tip. Shade 1/2 of a bar, then the same amount on a bar split into 4. Ask: “How many parts are shaded now?”
Exercise 7D Practice: equivalent fractions
Non-calculatorMethod. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.6 ÷ 2 = 3
- Divide the bottom number by 2. The fraction keeps the same value.10 ÷ 2 = 5
- Write the missing number. This is the top number of the simpler fraction.3
Check. Check: 6/10 and 3/5 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.2 shaded of 3
- Look at the second bar. It has twice as many parts, and twice as many shaded.4 shaded of 6
- Write the missing number. The bottom number is the total parts in the second bar.6
Check. Check: 4/6 is the same as 2/3.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 3. Do the same to the top and the bottom.1 × 3 = 3
- Multiply the bottom number by 3. The fraction keeps the same value.2 × 3 = 6
- Write the missing number. This is the bottom number of the equal fraction.6
Check. Check: 1/2 and 3/6 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.6 ÷ 2 = 3
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/6 and 1/3 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.1 × 2 = 2
- Multiply the bottom number by 2. The fraction keeps the same value.2 × 2 = 4
- Write the missing number. This is the bottom number of the equal fraction.4
Check. Check: 1/2 and 2/4 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 3. Divide the top and the bottom by the same number.3 ÷ 3 = 1
- Divide the bottom number by 3. The fraction keeps the same value.6 ÷ 3 = 2
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 3/6 and 1/2 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.10 ÷ 2 = 5
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/10 and 1/5 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.3 shaded of 4
- Look at the second bar. It has twice as many parts, and twice as many shaded.6 shaded of 8
- Write the missing number. The bottom number is the total parts in the second bar.8
Check. Check: 6/8 is the same as 3/4.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 3. Do the same to the top and the bottom.1 × 3 = 3
- Multiply the bottom number by 3. The fraction keeps the same value.4 × 3 = 12
- Write the missing number. This is the bottom number of the equal fraction.12
Check. Check: 1/4 and 3/12 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.4 ÷ 2 = 2
- Divide the bottom number by 2. The fraction keeps the same value.6 ÷ 2 = 3
- Write the missing number. This is the top number of the simpler fraction.2
Check. Check: 4/6 and 2/3 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.1 shaded of 2
- Look at the second bar. It has twice as many parts, and twice as many shaded.2 shaded of 4
- Write the missing number. The bottom number is the total parts in the second bar.4
Check. Check: 2/4 is the same as 1/2.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.4 ÷ 2 = 2
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/4 and 1/2 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.2 × 2 = 4
- Multiply the bottom number by 2. The fraction keeps the same value.3 × 2 = 6
- Write the missing number. This is the bottom number of the equal fraction.6
Check. Check: 2/3 and 4/6 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 3. Divide the top and the bottom by the same number.6 ÷ 3 = 2
- Divide the bottom number by 3. The fraction keeps the same value.9 ÷ 3 = 3
- Write the missing number. This is the top number of the simpler fraction.2
Check. Check: 6/9 and 2/3 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.2 × 2 = 4
- Multiply the bottom number by 2. The fraction keeps the same value.5 × 2 = 10
- Write the missing number. This is the bottom number of the equal fraction.10
Check. Check: 2/5 and 4/10 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.4 × 2 = 8
- Multiply the bottom number by 2. The fraction keeps the same value.5 × 2 = 10
- Write the missing number. This is the bottom number of the equal fraction.10
Check. Check: 4/5 and 8/10 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Fractions on a 0 to 1 number line
A fraction is a number. On a line from 0 to 1, a fraction is the distance from 0 to 1 in equal jumps.
Count the equal parts from 0 to 1. Count the jumps to the dot. The fraction is the number of jumps over the number of parts.
Key ideas
- A fraction is a number between 0 and 1.
- The bottom number is the number of equal jumps from 0 to 1.
- Count the jumps from 0 to the point.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into 4 equal parts.4 equal parts
- Count the parts from 0 to the dot. The dot is after 3 parts.3 parts
- Write the fraction. Parts from 0 over the total parts.3/4
Check. Check: 3 parts out of 4 is the same distance as the dot from 0.
Watch out. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count the parts to the dot.
- Count the equal parts from 0 to 1. The line has 2 equal parts.2 equal parts
- Count the parts from 0 to the dot. The dot is after 1 part.1 part
- Write the fraction. Parts from 0 over the total parts.1/2
Check. Check: 1/2 is halfway between 0 and 1.
Watch out. Halfway along a 0 to 1 line is one half.
Method. Count the equal parts from 0 to 1, then count the parts to the dot.
- Count the equal parts from 0 to 1. The line has 3 equal parts.3 equal parts
- Count the parts from 0 to the dot. The dot is after 2 parts.2 parts
- Write the fraction. Parts from 0 over the total parts.2/3
Check. Check: 2/3 is more than 1/2 and less than 1.
Watch out. Count the jumps, not the marks.
Watch out
Watch out. 1/4 is closer to 0 than 1/2 is. The more parts a line has, the smaller each part is.
Exam tip
Grown-up tip. Draw a line from 0 to 1 on paper, split it into 4 equal parts, and ask the child to mark 3/4.
Exercise 7E Practice: fractions on a number line
Non-calculatorMethod. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.4 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/4
Check. Check: 1 parts out of 4 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.5 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.3 parts
- Write the fraction. Parts from 0 over the total parts.3/5
Check. Check: 3 parts out of 5 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.8 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.6 parts
- Write the fraction. Parts from 0 over the total parts.6/8
Check. Check: 6 parts out of 8 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.10 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.4 parts
- Write the fraction. Parts from 0 over the total parts.4/10
Check. Check: 4 parts out of 10 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.10 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/10
Check. Check: 1 parts out of 10 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.5 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.2 parts
- Write the fraction. Parts from 0 over the total parts.2/5
Check. Check: 2 parts out of 5 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.4 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/4
Check. Check: 1 parts out of 4 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.3 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/3
Check. Check: 1 parts out of 3 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.2 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/2
Check. Check: 1 parts out of 2 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.10 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.5 parts
- Write the fraction. Parts from 0 over the total parts.5/10
Check. Check: 5 parts out of 10 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.10 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.5 parts
- Write the fraction. Parts from 0 over the total parts.5/10
Check. Check: 5 parts out of 10 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.8 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.2 parts
- Write the fraction. Parts from 0 over the total parts.2/8
Check. Check: 2 parts out of 8 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.10 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.4 parts
- Write the fraction. Parts from 0 over the total parts.4/10
Check. Check: 4 parts out of 10 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.4 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.2 parts
- Write the fraction. Parts from 0 over the total parts.2/4
Check. Check: 2 parts out of 4 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.4 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.3 parts
- Write the fraction. Parts from 0 over the total parts.3/4
Check. Check: 3 parts out of 4 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.2 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/2
Check. Check: 1 parts out of 2 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Chapter summary
| Skill | Method |
|---|---|
| A fraction of a whole | Top = parts shaded; bottom = equal parts in the whole |
| Writing fractions | Parts chosen over total equal parts |
| Fraction of an amount | Divide by the bottom number, then multiply by the top number |
| Equivalent fractions | Multiply or divide the top and bottom by the same number |
| Number line | Count the equal jumps from 0 to 1; the fraction is jumps over parts |
Can you…?
- I can say what fraction of a shape is shaded
- I can write a fraction from a picture or a description
- I can find a fraction of a set or an amount
- I can show that fractions such as 1/2, 2/4 and 4/8 are equal
- I can place a simple fraction on a 0 to 1 number line
Key terms
- numerator
- the top number of a fraction: the parts we count
- denominator
- the bottom number of a fraction: the number of equal parts
- equivalent
- equal in value, though written with different numbers
- unit fraction
- a fraction with 1 on top, such as 1/5
Exercise 7Z Check-up
Non-calculatorMethod. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.2 shaded parts
- Write the fraction. Shaded parts over the total number of parts.2/10
Check. Check: 2 + 8 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.3 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/3
Check. Check: 1 parts out of 3 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.2 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.1 parts
- Write the fraction. Parts from 0 over the total parts.1/2
Check. Check: 1 parts out of 2 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 30 into 10 equal parts. The bottom number tells us how many equal parts to make.30 ÷ 10 = 3
- Take 6 of the parts. The top number tells us how many parts to take.6 × 3 = 18
- Write the answer. This is the fraction of the amount.18
Check. Check: 4 parts are left and 12 is left over, so 18 + 12 = 30.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.4 equal parts
- Find the number of parts chosen. These are the parts we count on the top.3 parts
- Write the fraction. Parts chosen over total parts.3/4
Check. Check: 3 of the 4 parts is 3/4.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.3 shaded of 4
- Look at the second bar. It has twice as many parts, and twice as many shaded.6 shaded of 8
- Write the missing number. The bottom number is the total parts in the second bar.8
Check. Check: 6/8 is the same as 3/4.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.10 equal parts
- Find the number of parts chosen. These are the parts we count on the top.2 parts
- Write the fraction. Parts chosen over total parts.2/10
Check. Check: 2 of the 10 parts is 2/10.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 10 into 2 equal parts. The bottom number tells us how many equal parts to make.10 ÷ 2 = 5
- Take 1 of the parts. The top number tells us how many parts to take.1 × 5 = 5
- Write the answer. This is the fraction of the amount.5
Check. Check: 1 parts are left and 5 is left over, so 5 + 5 = 10.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 18 into 3 equal parts. The bottom number tells us how many equal parts to make.18 ÷ 3 = 6
- Take 2 of the parts. The top number tells us how many parts to take.2 × 6 = 12
- Write the answer. This is the fraction of the amount.12
Check. Check: 1 parts are left and 6 is left over, so 12 + 6 = 18.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. Find one equal part, then multiply it by the top number.
- Share 40 into 4 equal groups. Each group is one equal part of the set.40 ÷ 4 = 10
- Count 2 of the groups. The shaded part is the top number of groups.2 × 10 = 20
- Write the answer. This is how many are shaded.20
Check. Check: 20 of the 40 are shaded.
Watch out. The shaded part is always a fraction of the total set, not of the bottom number.
Total 19 marks. Allow about 19 minutes.
Exercise 7X Practice test questions
Non-calculatorMethod. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.3 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.2 parts
- Write the fraction. Parts from 0 over the total parts.2/3
Check. Check: 2 parts out of 3 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.4 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/4
Check. Check: 1 of the 4 parts is 1/4.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.1 × 2 = 2
- Multiply the bottom number by 2. The fraction keeps the same value.4 × 2 = 8
- Write the missing number. This is the bottom number of the equal fraction.8
Check. Check: 1/4 and 2/8 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.5 shaded parts
- Write the fraction. Shaded parts over the total number of parts.5/10
Check. Check: 5 + 5 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.1 shaded of 4
- Look at the second bar. It has twice as many parts, and twice as many shaded.2 shaded of 8
- Write the missing number. The bottom number is the total parts in the second bar.8
Check. Check: 2/8 is the same as 1/4.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.3 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/3
Check. Check: 1 of the 3 parts is 1/3.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.2 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/2
Check. Check: 1 + 1 = 2, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.3 equal parts
- Find the number of parts chosen. These are the parts we count on the top.1 parts
- Write the fraction. Parts chosen over total parts.1/3
Check. Check: 1 of the 3 parts is 1/3.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.
- Count the equal parts from 0 to 1. The line is split into this many equal parts.10 equal parts
- Count the parts from 0 to the dot. The dot is after this many parts.6 parts
- Write the fraction. Parts from 0 over the total parts.6/10
Check. Check: 6 parts out of 10 is the same distance as the dot from 0.
Watch out. The number line is split into equal parts. Count the jumps, not the marks.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.10 equal parts
- Count the shaded parts. The top number is the number of shaded parts.4 shaded parts
- Write the fraction. Shaded parts over the total number of parts.4/10
Check. Check: 4 + 6 = 10, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.