Year 4 Fractions: check-up and SATs-style questions

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 6 equal parts. The denominator is 6.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   5 parts are shaded. The numerator is 5.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   56   (say “five sixths”)

Check. The parts that are shaded and the other parts together make all 6 parts: 5 + 1 = 6. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

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.

1. Draw a bar and cut it into equal parts. The bottom number of 15 is 5, so we cut the whole amount into 5 equal parts.
   The whole amount is 40.
2. Divide 40 by 5 to find the size of ONE part. 40 is shared into 5 equal parts. One part is 15 of the amount.
   40 ÷ 5 = 8
3. Write the answer. The top number is 1, so we only need one part.
   15 of 40 = 8

Check. Multiply back: 8 × 5 = 40. ✓

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.

1. Draw a bar and cut it into equal parts. The bottom number of 38 is 8, so we cut the whole amount into 8 equal parts.
   The whole amount is 24.
2. Divide 24 by 8 to find the size of ONE part. 24 is shared into 8 equal parts. One part is 18 of the amount.
   24 ÷ 8 = 3
3. Multiply by 3 to get 3 parts. The top number is 3, so we need 3 of the parts.
   3 × 3 = 9

Check. The other 5 parts make 15. 9 + 15 = 24. ✓

Watch out. Divide by the bottom number first. Then multiply by the top number.

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.

1. Look at the bottom numbers. We need to go from 3 to 9. What do we multiply by?
   3 × 3 = 9
2. Do the same to the top number. Every piece is cut into 3 smaller pieces, so the top number is multiplied too. The fraction stays the same size.
   2 × 3 = 6
3. Write the equivalent fractions. Both fractions show the same amount.
   23 = 69

Check. 23 and 69 are the same size. ✓

Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.

Key words. The numerator is the top number. The denominator is the bottom number.

Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.

1. Check the bottom numbers. They are all 9. That means every piece is the same size (ninths), so we can add them.
   39 + 49
2. Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.
   3 + 4 = 7
3. Keep the bottom number the same. The pieces are still ninths. Adding does not change the size of the pieces.
   39 + 49 = 79

Check. Take away one of the fractions from the answer: 7 − 4 = 3. That is the top of the other fraction. ✓

Watch out. Do not add the bottom numbers. The pieces stay ninths, so the bottom number stays 9.

Key words. The numerator is the top number. The denominator is the bottom number.

Method. Write 1 whole as 7/7. Then subtract.

1. Write 1 whole as a fraction. 1 whole is 7 pieces of size 17, because the pieces are sevenths.
   1 = 77
2. Subtract the top numbers. We take away 2 pieces from 7 pieces.
   7 − 2 = 5
3. Keep the bottom number the same. The pieces are still sevenths.
   1 − 27  →  77 − 27 = 57

Check. Add: 27 + 57 = 77 = 1. ✓

Watch out. 1 whole is 7 sevenths. It is not 1 seventh.

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.

1. Look at the bottom numbers. They are different. But 10 is in the 5 times table, so we can change 35 into tenths.
   5 × 2 = 10
2. Rewrite 35 as tenths. Multiply the top and the bottom by the same number.
   35 = 610
3. Compare the top numbers. Now the bottom numbers are the same (10).
   6 and 7: 6 < 7
4. Write the answer.
   35 < 710

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. 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. An improper fraction is more than 1 whole. Find how many wholes it contains. The parts left over make the fraction part.

1. Ask: how many wholes are in it? 5 fifths make 1 whole. So we ask how many 5s fit into 14.
   5 × 2 = 10, which is not more than 14.
   5 × 3 = 15, which is more than 14.
   So there are 2 whole ones.
2. Find how many parts are left over. Take the parts in the whole ones away from all the parts.
   14 − 10 = 4
3. Write the mixed number. The whole number is 2. The left over parts make the fraction, still fifths.
   145 = 245

Check. Go back: 2 × 5 + 4 = 14 = 14. ✓

Watch out. The bottom number stays the same. Only the top number and the whole number change.

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.

1. Find the jump between two numbers you know. The numbers go up by the same amount each time.
   810 to 910: the jump is 110
2. Count on in tenths. Remember that 10 tenths make 1 whole, so 1010 is written as 1.
   810,  910,  1,  1110,  1210,  1310
3. Write the missing numbers.
   1,  1110

Check. Count on again from the first number and see that the jump is always 110. ✓

Watch out. When the top number reaches the bottom number you have a whole: 1010 is written as 1. After the whole, the fractions carry on: 1 110.

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. Find the fraction of the amount that is used. If you want what is left, take it away from the whole amount.

1. Find one part: divide £35 by 5. 35 means 3 out of 5 equal parts, so we first find one part.
   £35 ÷ 5 = £7
2. Find the amount for 3 parts: multiply by 3. The top number of 35 is 3, so we need 3 of the parts.
   £7 × 3 = £21
3. Take it away from £35 to find what is left. What is left is the amount we started with, take away the amount used.
   £35 − £21 = £14

Check. The parts left are 2 out of 5. 2 × £7 = £14. ✓

Watch out. Read the question again: do you want the amount used, or the amount left?

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 10 equal parts. The denominator is 10.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   3 parts are shaded. The numerator is 3.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   310   (say “three tenths”)

Check. The parts that are shaded and the other parts together make all 10 parts: 3 + 7 = 10. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

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.

1. Draw a bar and cut it into equal parts. The bottom number of 34 is 4, so we cut the whole amount into 4 equal parts.
   The whole amount is 28.
2. Divide 28 by 4 to find the size of ONE part. 28 is shared into 4 equal parts. One part is 14 of the amount.
   28 ÷ 4 = 7
3. Multiply by 3 to get 3 parts. The top number is 3, so we need 3 of the parts.
   7 × 3 = 21

Check. The other 1 part makes 7. 21 + 7 = 28. ✓

Watch out. Divide by the bottom number first. Then multiply by the top number.

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.

1. Look at the bottom numbers. We need to go from 5 to 10. What do we multiply by?
   5 × 2 = 10
2. Do the same to the top number. Every piece is cut into 2 smaller pieces, so the top number is multiplied too. The fraction stays the same size.
   3 × 2 = 6
3. Write the equivalent fractions. Both fractions show the same amount.
   35 = 610

Check. 35 and 610 are the same size. ✓

Watch out. Never add or subtract the same number to the top and bottom. You must multiply or divide both.

Key words. The numerator is the top number. The denominator is the bottom number.

Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.

1. Check the bottom numbers. They are all 9. That means every piece is the same size (ninths), so we can add them.
   59 + 39
2. Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.
   5 + 3 = 8
3. Keep the bottom number the same. The pieces are still ninths. Adding does not change the size of the pieces.
   59 + 39 = 89

Check. Take away one of the fractions from the answer: 8 − 3 = 5. That is the top of the other fraction. ✓

Watch out. Do not add the bottom numbers. The pieces stay ninths, so the bottom number stays 9.

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. An improper fraction is more than 1 whole. Find how many wholes it contains. The parts left over make the fraction part.

1. Ask: how many wholes are in it? 4 quarters make 1 whole. So we ask how many 4s fit into 17.
   4 × 4 = 16, which is not more than 17.
   4 × 5 = 20, which is more than 17.
   So there are 4 whole ones.
2. Find how many parts are left over. Take the parts in the whole ones away from all the parts.
   17 − 16 = 1
3. Write the mixed number. The whole number is 4. The left over parts make the fraction, still quarters.
   174 = 414

Check. Go back: 4 × 4 + 1 = 17 = 17. ✓

Watch out. The bottom number stays the same. Only the top number and the whole number change.

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 quarters. Remember that 4 quarters make 1 whole.

1. Find the jump between two numbers you know. The numbers go up by the same amount each time.
   24 to 34: the jump is 14
2. Count on in quarters. Remember that 4 quarters make 1 whole, so 44 is written as 1.
   24,  34,  1,  114,  124,  134
3. Write the missing numbers.
   1,  124

Check. Count on again from the first number and see that the jump is always 14. ✓

Watch out. When the top number reaches the bottom number you have a whole: 44 is written as 1. After the whole, the fractions carry on: 1 14.

Key words. Equivalent fractions are different fractions that show the same amount, like 1/2 and 2/4.

Method. Rewrite 12 with each bottom number. Then see which fractions match.

1. Check A: 24.
   2 × 2 = 4 and 1 × 2 = 2. 12 = 24, the same as 24.
2. Check B: 38.
   2 × 4 = 8 and 1 × 4 = 4. 12 = 48, not the same as 38.
3. Check C: 510.
   2 × 5 = 10 and 1 × 5 = 5. 12 = 510, the same as 510.
4. Check D: 46.
   2 × 3 = 6 and 1 × 3 = 3. 12 = 36, not the same as 46.
5. Choose the matching fractions.
   A and C

Check. Each chosen fraction shows the same amount as 12. ✓

Watch out. A fraction with a bigger bottom number can still be equal if its top number is bigger too.

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.

1. Find a bottom number that all the bottom numbers go into. The biggest bottom number is 8. The other bottom numbers (2, 4) all go into 8.
   Use eighths.
2. Rewrite every fraction as eighths. Multiply the top and the bottom by the same number each time.
   34 = 68  (× 2)
   12 = 48  (× 4)
   58 = 58
3. 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.
   4, 5, 6
4. Write the ORIGINAL fractions in that order. The question uses the original fractions.
   12,  58,  34

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. The numerator is the top number. The denominator is the bottom number.

Method. Add the top numbers and keep the bottom number the same. Ben added both.

1. Look at what Ben did. Ben added the top numbers AND the bottom numbers.
   25 + 25 = 410
2. Find the mistake. The pieces are fifths. Adding does not change the size of the pieces, so the bottom number must stay 5. Adding the bottom numbers would make the pieces smaller!
3. Do the sum correctly. Add the top numbers and keep the bottom number.
   2 + 2 = 4, so 25 + 25 = 45

Check. 45 is more than 25 and more than 25, which makes sense. ✓

Watch out. When you add pieces of the same size, the size of the piece does not change.

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. Work out each step in order. The second fraction is of the money that is LEFT, not of the £48.

1. Find 1/4 of £48. Divide by 4 to find one quarter.
   £48 ÷ 4 = £12 spent on the game
2. Find how much money is left. Take the amount spent away from £48.
   £48 − £12 = £36
3. Find 1/3 of the money that is left. Divide £36 by 3.
   £36 ÷ 3 = £12 spent on the book
4. Find what is left now. Take the amount spent on the book away from £36.
   £36 − £12 = £24

Check. Add what he spent: £12 + £12 = £24. £48 − £24 = £24. ✓

Watch out. 3 marks: 1 mark for £12, 1 mark for £36 and £12, and 1 mark for the answer £24. Remember: 1/3 is of the money LEFT.