Year 6 Maths reasoning (SATs) Fractions and decimals reasoning: check-up and practice test questions

Method. Make the denominators the same, then compare the tops.

1. Find a common denominator. The denominators are 9 and 7. Both divide into 63.
   common denominator 63
2. Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 63 on the bottom.
   5/9 = 35/63 and 4/7 = 36/63
3. Compare the tops. With the same bottom number, the bigger top number is the larger fraction.
   35 and 36
4. Write the answer.
   4/7

Check. 35/63 and 36/63: the one with the bigger top is larger. ✓

Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.

Method. Multiply the top and the bottom by the same number.

1. Find what the bottom was multiplied by. 7 x 4 = 28.
   x 4
2. Do the same to the top. Multiply the top by 4 as well.
   3 x 4 = 12
3. Write the fraction. Both parts are multiplied by the same number, so the value does not change.
   12/28
4. Write the answer.
   12/28

Check. 3/7 = 12/28, because both are multiplied by 4. ✓

Method. Divide the top and bottom by the highest common factor.

1. Find the highest common factor of the top and bottom. The biggest number that divides 48 and 72 is 24.
   HCF = 24
2. Divide the top and bottom by it. 48 / 24 = 2 and 72 / 24 = 3.
   2/3
3. Write the answer.
   2/3

Check. 2 and 3 have no common factor. ✓

Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.

Method. Use a common denominator, add or subtract the tops, then simplify.

1. Write both with the same bottom number. The bottoms are 3 and 8, so use 24.
   2/3 = 16/24 and 3/8 = 9/24
2. Work out the tops. 16 + 9 = 25.
   25/24
3. Simplify, or write as a mixed number. Divide the top and bottom by any common factor, or by the bottom if the top is bigger.
   1 1/24
4. Write the answer.
   1 1/24

Check. 1 1/24 is the same as 25/24. ✓

Watch out. Add or subtract the tops only. The bottom number stays the same.

Method. Add the whole parts and the fraction parts, then simplify.

1. Add the whole numbers. 2 + 1 = 3.
   3
2. Add the fractions with a common denominator. Use 12 as the common bottom number.
   3/4 + 1/6 = 11/12
3. Put the parts together. Add the whole number part to the whole part of the fraction total.
   3 11/12
4. Write the answer.
   3 11/12

Check. 3 11/12 is the total. ✓

Watch out. When the fraction parts add to more than 1, carry the whole number into the front.

Method. Multiply the tops, multiply the bottoms, then simplify.

1. Multiply the tops. 3 x 10 = 30.
   30
2. Multiply the bottoms. 5 x 9 = 45.
   45
3. Simplify. Divide the top and bottom by any common factor.
   2/3
4. Write the answer.
   2/3

Check. 30/45 simplifies to 2/3. ✓

Watch out. Simplify first when you can: cancel a factor from a top and a factor from a bottom.

Method. Dividing by a whole number makes the piece smaller.

1. Multiply by the reciprocal of the whole number. Dividing by 2 is the same as multiplying by 1/2.
   7/8 x 1/2
2. Multiply the bottoms. 8 x 2 = 16.
   7/16
3. Simplify. Divide the top and bottom by their highest common factor.
   7/16
4. Write the answer.
   7/16

Check. 7/16 x 2 = 7/8. ✓

Watch out. Dividing by 2 makes a fraction smaller, not bigger.

Method. Multiply by 100 moves the digits 2 places.

1. Decide which way the digits move. Multiplying by 100 moves each digit 2 places to the left; dividing moves them to the right.
   multiply by 100
2. Move the digits. Move each digit 2 places left, and fill the gaps with zeros.
   0.46 becomes 46
3. Write the answer. The decimal point ends in the new place.
   46
4. Write the answer.
   46

Check. 46 / 100 = 0.46. ✓

Watch out. Dividing by 100 moves the digits two places to the right, not to the left.

Method. Look at the digit after the rounding place.

1. Look at the digit after the hundredth place. This digit decides whether to round up or down.
   digit = 7
2. Decide. 5 or more rounds up; 4 or less rounds down.
   7 is 5 or more, so round up
3. Write the rounded number. Keep the digits up to the hundredth place.
   5.65
4. Write the answer.
   5.65

Check. 5.65 is the closest value to 5.6478 at this accuracy. ✓

Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.

Method. Find 1% first, then multiply.

1. Find one per cent. Divide 60 by 100.
   60 / 100 = 0.6
2. Multiply by the number of per cent. Multiply the answer by 15.
   0.6 x 15 = 9
3. Write the answer. 15% of 60 is 9.
   9
4. Write the answer.
   9

Check. 1% of 60 is 0.6, so 15% is 9. ✓

Method. Use a common denominator, add or subtract the tops, then simplify.

1. Write both with the same bottom number. The bottoms are 4 and 8, so use 8.
   3/4 = 6/8 and 1/8 = 1/8
2. Work out the tops. 6 - 1 = 5.
   5/8
3. Simplify, or write as a mixed number. Divide the top and bottom by any common factor, or by the bottom if the top is bigger.
   5/8
4. Write the answer.
   5/8

Check. 5/8 is the same as 5/8. ✓

Watch out. Add or subtract the tops only. The bottom number stays the same.

Method. Make the denominators the same, then compare the tops.

1. Find a common denominator. The denominators are 5 and 9. Both divide into 45.
   common denominator 45
2. Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 45 on the bottom.
   4/5 = 36/45 and 7/9 = 35/45
3. Compare the tops. With the same bottom number, the bigger top number is the larger fraction.
   36 and 35
4. Write the answer.
   4/5

Check. 36/45 and 35/45: the one with the bigger top is larger. ✓

Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.

Method. Look at the digit after the rounding place.

1. Look at the digit after the tenth place. This digit decides whether to round up or down.
   digit = 9
2. Decide. 5 or more rounds up; 4 or less rounds down.
   9 is 5 or more, so round up
3. Write the rounded number. Keep the digits up to the tenth place.
   3.5
4. Write the answer.
   3.5

Check. 3.5 is the closest value to 3.4961 at this accuracy. ✓

Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.

Method. Write 0.125 as thousandths, then simplify.

1. Write as thousandths. 0.125 = 125/1000.
   125/1000
2. Simplify. The HCF of 125 and 1000 is 125, so 125/1000 = 1/8.
   1/8
3. Write the answer.
   1/8

Check. 1/8 = 0.125. ✓

Method. Multiply the whole number by the top of the fraction.

1. Write the whole number as a fraction. 4 = 4/1.
   4/1
2. Multiply the tops and the bottoms. 4 x 5 = 20, and 1 x 6 = 6.
   20/6
3. Simplify and write as a mixed number. 20 divided by 6 gives the whole part.
   3 1/3
4. Write the answer.
   3 1/3

Check. 4 lots of 5/6 is 3 1/3. ✓

Method. Divide 2.5 by 0.05, or count how many 0.05s fit into 2.5.

1. Think in hundredths. 2.5 = 250 hundredths and 0.05 = 5 hundredths.
   250 / 5
2. Divide. 250 / 5 = 50 cups.
   50
3. Write the answer.
   50

Check. 50 x 5 = 250. ✓

Method. Subtract with a common denominator.

1. Common denominator. 2 1/2 = 2 2/4 and 1 3/4 stays the same.
   2 2/4 - 1 3/4
2. Subtract. 2 2/4 - 1 3/4 = 3/4.
   3/4
3. Write the answer.
   3/4

Check. 1 3/4 + 3/4 = 2 1/2. ✓

Method. Write both with the same bottom number.

1. Common denominator. 1/2 = 4/8.
   4/8
2. Compare. 5 eighths is more than 4 eighths.
   5/8 > 4/8
3. Write the answer.
   1/2 = 4/8, and 5/8 is bigger than 4/8.

Check. 5/8 > 4/8. ✓

Method. Find 1% first.

1. Find 1%. 200 / 100 = 2.
   2
2. Multiply by 35. 2 x 35 = 70.
   70
3. Write the answer.
   70

Check. 70 / 200 = 35%. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. Each ticked fraction is less than 2/3, for example 5/9 is less than 6/9.
   1/2, 5/9, 7/12
3. Leave the others unticked. These do not match.
   3/4, 4/6 are not ticked
4. Write the answer.
   1/2, 5/9, 7/12

Check. Each ticked option is true. ✓

Method. Multiply the top by 4.

1. Multiply. 4 x 3/5 = 12/5.
   12/5
2. Write as a mixed number. 12 / 5 = 2 remainder 2, so 2 2/5.
   2 2/5
3. Write the answer.
   Yes, because 4 x 3 = 12, so 12/5 = 2 2/5.

Check. 12/5 = 2 2/5. ✓