Year 4: Tenths and hundredths
Part of the Year 4 fractions chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Tenths and hundredths
When we cut a whole into 10 equal parts, each part is one tenth, written 1/10. Here is a bar cut into tenths. 10 tenths make 1 whole, so 10/10 = 1.
Counting in tenths. 1/10, 2/10, 3/10 ... 9/10, then 10/10 which is 1 whole, then 1 1/10, 1 2/10 ... and 2. We can count backwards too.
Hundredths. Now cut each tenth into 10 equal parts. The whole is now cut into 10 × 10 = 100 equal parts. Each part is one hundredth, written 1/100. A hundred square shows this. Each row is one tenth. Each small square is one hundredth.
Tenths and hundredths are linked. 1 tenth is 10 hundredths: 1/10 = 10/100. So 3/10 = 30/100. To change tenths into hundredths, multiply the top and bottom by 10 (see Section 5.3). We count in hundredths in the same way: 1/100, 2/100 ... 99/100, then 100/100 = 1 whole. Later (Chapter 6) you will see that these fractions can also be written as decimals.
Key words. A tenth is one of 10 equal parts of a whole. A hundredth is one of 100 equal parts of a whole.
Key ideas
- A tenth is 1 of 10 equal parts: 1/10. 10 tenths = 1 whole.
- A hundredth is 1 of 100 equal parts: 1/100. 100 hundredths = 1 whole.
- 1/10 ÷ 10 = 1/100. Cutting each tenth into 10 parts makes hundredths.
- 1/10 = 10/100, so tenths × 10 = hundredths.
- Counting in tenths: after 9/10 comes 1 whole, then 1 1/10, 1 2/10.
- In a hundred square, each row is one tenth and each small square is one hundredth.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. Tenths are made by cutting a whole into 10 equal parts. Count the shaded parts for the top number.
- Count the equal parts. The whole is cut into 10 equal parts. Each part is one tenth.There are 10 parts, so the bottom number is 10.
- Count the shaded parts. This is the top number.7 parts are shaded, so the top number is 7.
- Write the fraction.
7 10
Check. 7 shaded and 3 white make 10 parts. ✓
Watch out. The bottom number is the number of parts in the whole (10), not the number shaded.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. A hundred square has 100 small squares. Each one is a hundredth. Count the shaded squares for the top number.
- Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.10 × 10 = 100 small squares, so the bottom number is 100.
- Count the shaded squares. Count whole rows first (10 squares each), then the extra squares.3 full rows = 3 × 10 = 30 squares
30 + 7 = 37 - Write the fraction.
37 100
Check. 37 shaded and 63 white make 100. ✓
Watch out. Count in tens for the full rows to save time.
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count on in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.
6 10 7 10 1 10 - Count on in tenths. Remember that 10 tenths make 1 whole, so
10 10 6 10 7 10 8 10 9 10 - Write the missing numbers.
8 10
Check. Count on again from the first number and see that the jump is always
Watch out. When the top number reaches the bottom number you have a whole:
1310, 1210, ?, 1, ?,
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count back in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.1310 to 1210: the jump is
1 10 - Count back in tenths. Remember that 1 whole is
10 10 1310, 1210, 1110, 1,9 10 8 10 7 10 - Write the missing numbers. 1110,
9 10
Check. Count back again from the first number and see that the jump is always
Watch out. Be careful when you pass a whole number going backwards: 1 is the same as
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.3 × 10 = 30
- Write the equivalent fractions. Both fractions show the same amount.
3 10 30 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count on in hundredths. Remember that 100 hundredths make 1 whole.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.
96 100 97 100 1 100 - Count on in hundredths. Remember that 100 hundredths make 1 whole, so
100 100 96 100 97 100 98 100 99 100 - Write the missing numbers.
98 100
Check. Count on again from the first number and see that the jump is always
Watch out. When the top number reaches the bottom number you have a whole:
Method. Cut each tenth into 10 equal parts. Each new part is a hundredth.
- Start with one tenth. A whole cut into 10 equal parts gives tenths.
- Cut that tenth into 10 equal parts. This is the same as dividing the tenth by 10.
1 10 1 100 - Count the parts in the whole. There are 10 tenths, and each tenth is 10 hundredths.10 × 10 = 100 parts, so each part is
1 100
Check. 10 hundredths make 1 tenth:
Watch out. Dividing a tenth by 10 makes a hundredth, which is a much smaller piece.
Watch out
Hundredths are much smaller than tenths. 1/100 is smaller than 1/10, because the whole is cut into more parts. And do not forget the whole number when you count: after 9/10 comes 1 (10/10), then 1 1/10. After 99/100 comes 1.Exercise 5G Tenths and hundredths
Non-calculatorKey words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. Tenths are made by cutting a whole into 10 equal parts. Count the shaded parts for the top number.
- Count the equal parts. The whole is cut into 10 equal parts. Each part is one tenth.There are 10 parts, so the bottom number is 10.
- Count the shaded parts. This is the top number.3 parts are shaded, so the top number is 3.
- Write the fraction.
3 10
Check. 3 shaded and 7 white make 10 parts. ✓
Watch out. The bottom number is the number of parts in the whole (10), not the number shaded.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. Tenths are made by cutting a whole into 10 equal parts. Count the shaded parts for the top number.
- Count the equal parts. The whole is cut into 10 equal parts. Each part is one tenth.There are 10 parts, so the bottom number is 10.
- Count the shaded parts. This is the top number.7 parts are shaded, so the top number is 7.
- Write the fraction.
7 10
Check. 7 shaded and 3 white make 10 parts. ✓
Watch out. The bottom number is the number of parts in the whole (10), not the number shaded.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. Tenths are made by cutting a whole into 10 equal parts. Count the shaded parts for the top number.
- Count the equal parts. The whole is cut into 10 equal parts. Each part is one tenth.There are 10 parts, so the bottom number is 10.
- Count the shaded parts. This is the top number.9 parts are shaded, so the top number is 9.
- Write the fraction.
9 10
Check. 9 shaded and 1 white make 10 parts. ✓
Watch out. The bottom number is the number of parts in the whole (10), not the number shaded.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. A hundred square has 100 small squares. Each one is a hundredth. Count the shaded squares for the top number.
- Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.10 × 10 = 100 small squares, so the bottom number is 100.
- Count the shaded squares. Count whole rows first (10 squares each), then the extra squares.2 full rows = 2 × 10 = 20 squares
20 + 3 = 23 - Write the fraction.
23 100
Check. 23 shaded and 77 white make 100. ✓
Watch out. Count in tens for the full rows to save time.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. A hundred square has 100 small squares. Each one is a hundredth. Count the shaded squares for the top number.
- Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.10 × 10 = 100 small squares, so the bottom number is 100.
- Count the shaded squares. Count whole rows first (10 squares each), then the extra squares.5 full rows = 5 × 10 = 50 squares
50 + 8 = 58 - Write the fraction.
58 100
Check. 58 shaded and 42 white make 100. ✓
Watch out. Count in tens for the full rows to save time.
Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.
Method. A hundred square has 100 small squares. Each one is a hundredth. Count the shaded squares for the top number.
- Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.10 × 10 = 100 small squares, so the bottom number is 100.
- Count the shaded squares. Count whole rows first (10 squares each), then the extra squares.9 full rows = 9 × 10 = 90 squares
90 + 1 = 91 - Write the fraction.
91 100
Check. 91 shaded and 9 white make 100. ✓
Watch out. Count in tens for the full rows to save time.
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count on in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.
3 10 4 10 1 10 - Count on in tenths. Remember that 10 tenths make 1 whole, so
10 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 - Write the missing numbers.
5 10 7 10
Check. Count on again from the first number and see that the jump is always
Watch out. When the top number reaches the bottom number you have a whole:
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count on in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.
7 10 8 10 1 10 - Count on in tenths. Remember that 10 tenths make 1 whole, so
10 10 7 10 8 10 9 10 - Write the missing numbers. 1, 1210
Check. Count on again from the first number and see that the jump is always
Watch out. When the top number reaches the bottom number you have a whole:
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count on in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.
4 10 6 10 2 10 - Count on in tenths. Remember that 10 tenths make 1 whole, so
10 10 4 10 6 10 8 10 - Write the missing numbers. 1, 1410
Check. Count on again from the first number and see that the jump is always
Watch out. When the top number reaches the bottom number you have a whole:
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count back in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.
9 10 8 10 1 10 - Count back in tenths. Remember that 1 whole is
10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 - Write the missing numbers.
7 10 4 10
Check. Count back again from the first number and see that the jump is always
Watch out. Be careful when you pass a whole number going backwards: 1 is the same as
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count back in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.1210 to 1110: the jump is
1 10 - Count back in tenths. Remember that 1 whole is
10 10 1410, 1310, 1210, 1110, 1,9 10 8 10 - Write the missing numbers. 1310, 1
Check. Count back again from the first number and see that the jump is always
Watch out. Be careful when you pass a whole number going backwards: 1 is the same as
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count back in tenths. Remember that 10 tenths make 1 whole.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.1610 to 1410: the jump is
2 10 - Count back in tenths. Remember that 1 whole is
10 10 1610, 1410, 1210, 1,8 10 6 10 - Write the missing numbers. 1,
6 10
Check. Count back again from the first number and see that the jump is always
Watch out. Be careful when you pass a whole number going backwards: 1 is the same as
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count on in hundredths. Remember that 100 hundredths make 1 whole.
- Find the jump between two numbers you know. The numbers go up by the same amount each time.
97 100 98 100 1 100 - Count on in hundredths. Remember that 100 hundredths make 1 whole, so
100 100 97 100 98 100 99 100 - Write the missing numbers.
99 100
Check. Count on again from the first number and see that the jump is always
Watch out. When the top number reaches the bottom number you have a whole:
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Find the jump. Then count back in hundredths. Remember that 100 hundredths make 1 whole.
- Find the jump between two numbers you know. The numbers go down by the same amount each time.
2 100 1 100 1 100 - Count back in hundredths. Remember that 1 whole is
100 100 6 100 5 100 4 100 3 100 2 100 1 100 - Write the missing numbers.
5 100 3 100
Check. Count back again from the first number and see that the jump is always
Watch out. Be careful when you pass a whole number going backwards: 1 is the same as
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Count the steps between 0 and 1 for the bottom number. Count the steps from 0 to the point for the top number.
- Count the equal steps between 0 and 1. This is the bottom number. All the steps are the same size.There are 10 steps from 0 to 1. Each step is
1 10 - Count the steps from 0 to the point. This is the top number.The point is 13 steps from 0, so it is
13 10 - Write the answer. 10 steps make 1 whole.
13 10
Check. 13 steps of
Watch out. Count the spaces (steps), not the tick marks.
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Count the steps between 0 and 1 for the bottom number. Count the steps from 0 to the point for the top number.
- Count the equal steps between 0 and 1. This is the bottom number. All the steps are the same size.There are 10 steps from 0 to 1. Each step is
1 10 - Count the steps from 0 to the point. This is the top number.The point is 7 steps from 0, so it is
7 10 - Write the answer. 10 steps make 1 whole.
7 10
Check. 7 steps of
Watch out. Count the spaces (steps), not the tick marks.
Key words. An improper fraction has a top number at least as big as the bottom, like 7/4. A mixed number is a whole number and a fraction, like 1 3/4.
Method. Count the steps between 0 and 1 for the bottom number. Count the steps from 0 to the point for the top number.
- Count the equal steps between 0 and 1. This is the bottom number. All the steps are the same size.There are 10 steps from 0 to 1. Each step is
1 10 - Count the steps from 0 to the point. This is the top number.The point is 19 steps from 0, so it is
19 10 - Write the answer. 10 steps make 1 whole.
19 10
Check. 19 steps of
Watch out. Count the spaces (steps), not the tick marks.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.1 × 10 = 10
- Write the equivalent fractions. Both fractions show the same amount.
1 10 10 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.3 × 10 = 30
- Write the equivalent fractions. Both fractions show the same amount.
3 10 30 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.7 × 10 = 70
- Write the equivalent fractions. Both fractions show the same amount.
7 10 70 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.9 × 10 = 90
- Write the equivalent fractions. Both fractions show the same amount.
9 10 90 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.5 × 10 = 50
- Write the equivalent fractions. Both fractions show the same amount.
5 10 50 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 10 to 100. What do we multiply by?10 × 10 = 100
- Do the same to the top number. Every piece is cut into 10 smaller pieces, so the top number is multiplied too. The fraction stays the same size.2 × 10 = 20
- Write the equivalent fractions. Both fractions show the same amount.
2 10 20 100
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 100 to 10. What do we divide by?100 ÷ 10 = 10
- Do the same to the top number. We join 10 pieces into one bigger piece, so the top number is divided too. The fraction stays the same size.40 ÷ 10 = 4
- Write the equivalent fractions. Both fractions show the same amount.
40 100 4 10
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 100 to 10. What do we divide by?100 ÷ 10 = 10
- Do the same to the top number. We join 10 pieces into one bigger piece, so the top number is divided too. The fraction stays the same size.70 ÷ 10 = 7
- Write the equivalent fractions. Both fractions show the same amount.
70 100 7 10
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 100 to 10. What do we divide by?100 ÷ 10 = 10
- Do the same to the top number. We join 10 pieces into one bigger piece, so the top number is divided too. The fraction stays the same size.20 ÷ 10 = 2
- Write the equivalent fractions. Both fractions show the same amount.
20 100 2 10
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Equivalent fractions show the same amount. Multiply (or divide) the top and the bottom by the same number.
- Look at the bottom numbers. We need to go from 100 to 10. What do we divide by?100 ÷ 10 = 10
- Do the same to the top number. We join 10 pieces into one bigger piece, so the top number is divided too. The fraction stays the same size.90 ÷ 10 = 9
- Write the equivalent fractions. Both fractions show the same amount.
90 100 9 10
Check.
Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.
Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.
Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.
- Picture the amount cut into equal parts. The bottom number of
1 10 The whole amount is 80. - Divide 80 by 10 to find the size of ONE part. 80 is shared into 10 equal parts. One part is
1 10 80 ÷ 10 = 8 - Write the answer. The top number is 1, so we only need one part.
1 10
Check. Multiply back: 8 × 10 = 80. ✓
Watch out. Divide by the bottom number first. Then multiply by the top number.
Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.
Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.
- Picture the amount cut into equal parts. The bottom number of
3 10 The whole amount is £50. - Divide £50 by 10 to find the size of ONE part. £50 is shared into 10 equal parts. One part is
1 10 £50 ÷ 10 = £5 - Multiply by 3 to get 3 parts. The top number is 3, so we need 3 of the parts.£5 × 3 = £15
Check. The other 7 parts make £35. £15 + £35 = £50. ✓
Watch out. Divide by the bottom number first. Then multiply by the top number.
Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.
Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.
- Picture the amount cut into equal parts. The bottom number of
7 10 The whole amount is 90 g. - Divide 90 g by 10 to find the size of ONE part. 90 g is shared into 10 equal parts. One part is
1 10 90 g ÷ 10 = 9 g - Multiply by 7 to get 7 parts. The top number is 7, so we need 7 of the parts.9 g × 7 = 63 g
Check. The other 3 parts make 27 g. 63 g + 27 g = 90 g. ✓
Watch out. Divide by the bottom number first. Then multiply by the top number.
Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.
Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.
- Picture the amount cut into equal parts. The bottom number of
9 10 The whole amount is 40 m. - Divide 40 m by 10 to find the size of ONE part. 40 m is shared into 10 equal parts. One part is
1 10 40 m ÷ 10 = 4 m - Multiply by 9 to get 9 parts. The top number is 9, so we need 9 of the parts.4 m × 9 = 36 m
Check. The other 1 part makes 4 m. 36 m + 4 m = 40 m. ✓
Watch out. Divide by the bottom number first. Then multiply by the top number.
Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.
Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.
- Picture the amount cut into equal parts. The bottom number of
7 10 The whole amount is 100 litres. - Divide 100 litres by 10 to find the size of ONE part. 100 litres is shared into 10 equal parts. One part is
1 10 100 litres ÷ 10 = 10 litres - Multiply by 7 to get 7 parts. The top number is 7, so we need 7 of the parts.10 litres × 7 = 70 litres
Check. The other 3 parts make 30 litres. 70 litres + 30 litres = 100 litres. ✓
Watch out. Divide by the bottom number first. Then multiply by the top number.
Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.
Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.
- Picture the amount cut into equal parts. The bottom number of
3 10 The whole amount is 100. - Divide 100 by 10 to find the size of ONE part. 100 is shared into 10 equal parts. One part is
1 10 100 ÷ 10 = 10 - Multiply by 3 to get 3 parts. The top number is 3, so we need 3 of the parts.10 × 3 = 30
Check. The other 7 parts make 70. 30 + 70 = 100. ✓
Watch out. Divide by the bottom number first. Then multiply by the top number.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Think about how big each part is when you cut the whole into more parts. Use the picture.
- Look at the picture. One tenth is cut into 10 equal parts. Each new part is a hundredth.
- Compare the sizes. A hundredth is only a small part of a tenth. 10 hundredths are needed to make one tenth.
1 100 1 10 - Find the mistake. Aisha thinks a bigger bottom number means a bigger fraction. For unit fractions it is the other way round.No. 1/10 is bigger than 1/100.
Check. 10 ×
Watch out. More parts means each part is smaller.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 100 is in the 10 times table, so we can change
7 10 10 × 10 = 100 - Rewrite
7 10 7 10 70 100 - Compare the top numbers. Now the bottom numbers are the same (100).70 and 60: 70 > 60
- Write the answer.
7 10 60 100
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Give the fractions the same bottom number. Then put the top numbers in order, smallest first.
- Find a bottom number that all the bottom numbers go into. The biggest bottom number is 100. The other bottom numbers (10) all go into 100.Use hundredths.
- Rewrite every fraction as hundredths. Multiply the top and the bottom by the same number each time.
3 10 30 100 25 100 25 100 4 10 40 100 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.25, 30, 40
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
25 100 3 10 4 10
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.
Method. Shade 4 rows (4 tenths) of a hundred square. Then count the small squares.
- Shade 4 rows. Each row is one tenth, so 4 rows is 4/10.
- Count the small squares. Each row has 10 small squares. Each small square is a hundredth.4 × 10 = 40 small squares
- Write the answer.
4 10 40 100
Check. Multiply the top and bottom by 10: 4 × 10 = 40 and 10 × 10 = 100. ✓
Watch out. Tenths become hundredths when you multiply the top and bottom by 10.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Count the squares for each colour, add them, and take them away from 100.
- Blue squares. 3 tenths is 3 rows of 10.3 × 10 = 30 squares
- Red squares. 12 hundredths is 12 small squares.12 squares
- Squares that are shaded. Add the two colours.30 + 12 = 42
- Squares that are not shaded. The whole square has 100 small squares.100 − 42 = 58
- Write the fraction. The bottom number is 100.
58 100
Check.
Watch out. Change tenths into hundredths first so they can be added.