Step-by-step Maths Level 4 Fractions of wholes and equivalent fractions: check-up and practice test questions

Method. A fraction is the number of shaded parts over the number of equal parts.

1. Count the equal parts in the whole. The bottom number is the number of equal parts.
   10 equal parts
2. Count the shaded parts. The top number is the number of shaded parts.
   2 shaded parts
3. 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.

1. Count the equal parts from 0 to 1. The line is split into this many equal parts.
   3 equal parts
2. Count the parts from 0 to the dot. The dot is after this many parts.
   1 parts
3. 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.

1. Count the equal parts from 0 to 1. The line is split into this many equal parts.
   2 equal parts
2. Count the parts from 0 to the dot. The dot is after this many parts.
   1 parts
3. 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.

1. Divide 30 into 10 equal parts. The bottom number tells us how many equal parts to make.
   30 ÷ 10 = 3
2. Take 6 of the parts. The top number tells us how many parts to take.
   6 × 3 = 18
3. 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.

1. Find the number of equal parts in the whole. The whole is split into this many equal parts.
   4 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   3 parts
3. 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.

1. Look at the first bar. It has shaded parts out of equal parts.
   3 shaded of 4
2. Look at the second bar. It has twice as many parts, and twice as many shaded.
   6 shaded of 8
3. 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.

1. Find the number of equal parts in the whole. The whole is split into this many equal parts.
   10 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   2 parts
3. 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.

1. Divide 10 into 2 equal parts. The bottom number tells us how many equal parts to make.
   10 ÷ 2 = 5
2. Take 1 of the parts. The top number tells us how many parts to take.
   1 × 5 = 5
3. 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.

1. Divide 18 into 3 equal parts. The bottom number tells us how many equal parts to make.
   18 ÷ 3 = 6
2. Take 2 of the parts. The top number tells us how many parts to take.
   2 × 6 = 12
3. 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.

1. Share 40 into 4 equal groups. Each group is one equal part of the set.
   40 ÷ 4 = 10
2. Count 2 of the groups. The shaded part is the top number of groups.
   2 × 10 = 20
3. 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.

Method. Count the equal parts from 0 to 1, then count how many parts there are to the dot.

1. Count the equal parts from 0 to 1. The line is split into this many equal parts.
   3 equal parts
2. Count the parts from 0 to the dot. The dot is after this many parts.
   2 parts
3. 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.

1. Find the number of equal parts in the whole. The whole is split into this many equal parts.
   4 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   1 parts
3. 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.

1. Multiply the top number by 2. Do the same to the top and the bottom.
   1 × 2 = 2
2. Multiply the bottom number by 2. The fraction keeps the same value.
   4 × 2 = 8
3. 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.

1. Count the equal parts in the whole. The bottom number is the number of equal parts.
   10 equal parts
2. Count the shaded parts. The top number is the number of shaded parts.
   5 shaded parts
3. 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.

1. Look at the first bar. It has shaded parts out of equal parts.
   1 shaded of 4
2. Look at the second bar. It has twice as many parts, and twice as many shaded.
   2 shaded of 8
3. 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.

1. Find the number of equal parts in the whole. The whole is split into this many equal parts.
   3 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   1 parts
3. 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.

1. Count the equal parts in the whole. The bottom number is the number of equal parts.
   2 equal parts
2. Count the shaded parts. The top number is the number of shaded parts.
   1 shaded parts
3. 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.

1. Find the number of equal parts in the whole. The whole is split into this many equal parts.
   3 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   1 parts
3. 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.

1. Count the equal parts from 0 to 1. The line is split into this many equal parts.
   10 equal parts
2. Count the parts from 0 to the dot. The dot is after this many parts.
   6 parts
3. 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.

1. Count the equal parts in the whole. The bottom number is the number of equal parts.
   10 equal parts
2. Count the shaded parts. The top number is the number of shaded parts.
   4 shaded parts
3. 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.