Year 6 Maths reasoning (SATs): Multiplying and dividing fractions
Part of the Year 6 Maths reasoning (SATs) fractions and decimals reasoning chapter. Chapter overview · whole chapter on one page
Multiplying and dividing fractions
Rule
To multiply a fraction by a whole number, multiply the top. 2/5 x 6 = 12/5 = 2 2/5.
To multiply two fractions, multiply the tops and multiply the bottoms. To divide by a whole number, multiply the bottom by it: 3/4 / 3 = 3/12 = 1/4.
Key ideas
- Fraction x whole number: multiply the top only.
- Fraction x fraction: multiply tops and bottoms, then simplify.
- Fraction / whole number: multiply the bottom by the whole number.
Method. Multiply the whole number by the top of the fraction.
- Write the whole number as a fraction. 6 = 6/1.6/1
- Multiply the tops and the bottoms. 6 x 2 = 12, and 1 x 5 = 5.12/5
- Simplify and write as a mixed number. 12 divided by 5 gives the whole part.2 2/5
- Write the answer. 2 2/5
Check. 6 lots of 2/5 is 2 2/5. ✓
Method. Multiply the tops, multiply the bottoms, then simplify.
- Multiply the tops. 3 x 2 = 6.6
- Multiply the bottoms. 4 x 5 = 20.20
- Simplify. Divide the top and bottom by any common factor.3/10
- Write the answer. 3/10
Check. 6/20 simplifies to 3/10. ✓
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.
- Multiply by the reciprocal of the whole number. Dividing by 3 is the same as multiplying by 1/3.3/4 x 1/3
- Multiply the bottoms. 4 x 3 = 12.3/12
- Simplify. Divide the top and bottom by their highest common factor.1/4
- Write the answer. 1/4
Check. 1/4 x 3 = 3/4. ✓
Watch out. Dividing by 2 makes a fraction smaller, not bigger.
Watch out
Watch out. Dividing a fraction by 3 makes it smaller. It does not make it bigger.
Exam tip
Practice guide. Simplify before you multiply when a top and a bottom share a factor.
Exercise 2D Practice: multiplying and dividing fractions
Non-calculatorMethod. Multiply the whole number by the top of the fraction.
- Write the whole number as a fraction. 5 = 5/1.5/1
- Multiply the tops and the bottoms. 5 x 3 = 15, and 1 x 4 = 4.15/4
- Simplify and write as a mixed number. 15 divided by 4 gives the whole part.3 3/4
- Write the answer. 3 3/4
Check. 5 lots of 3/4 is 3 3/4. ✓
Method. Multiply the whole number by the top of the fraction.
- Write the whole number as a fraction. 8 = 8/1.8/1
- Multiply the tops and the bottoms. 8 x 5 = 40, and 1 x 6 = 6.40/6
- Simplify and write as a mixed number. 40 divided by 6 gives the whole part.6 2/3
- Write the answer. 6 2/3
Check. 8 lots of 5/6 is 6 2/3. ✓
Method. Multiply the tops, multiply the bottoms, then simplify.
- Multiply the tops. 2 x 3 = 6.6
- Multiply the bottoms. 3 x 4 = 12.12
- Simplify. Divide the top and bottom by any common factor.1/2
- Write the answer. 1/2
Check. 6/12 simplifies to 1/2. ✓
Watch out. Simplify first when you can: cancel a factor from a top and a factor from a bottom.
Method. Multiply the tops, multiply the bottoms, then simplify.
- Multiply the tops. 5 x 3 = 15.15
- Multiply the bottoms. 6 x 10 = 60.60
- Simplify. Divide the top and bottom by any common factor.1/4
- Write the answer. 1/4
Check. 15/60 simplifies to 1/4. ✓
Watch out. Simplify first when you can: cancel a factor from a top and a factor from a bottom.
Method. Multiply the tops, multiply the bottoms, then simplify.
- Multiply the tops. 4 x 3 = 12.12
- Multiply the bottoms. 9 x 8 = 72.72
- Simplify. Divide the top and bottom by any common factor.1/6
- Write the answer. 1/6
Check. 12/72 simplifies to 1/6. ✓
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.
- Multiply by the reciprocal of the whole number. Dividing by 2 is the same as multiplying by 1/2.5/6 x 1/2
- Multiply the bottoms. 6 x 2 = 12.5/12
- Simplify. Divide the top and bottom by their highest common factor.5/12
- Write the answer. 5/12
Check. 5/12 x 2 = 5/6. ✓
Watch out. Dividing by 2 makes a fraction smaller, not bigger.
Method. Dividing by a whole number makes the piece smaller.
- Multiply by the reciprocal of the whole number. Dividing by 3 is the same as multiplying by 1/3.4/5 x 1/3
- Multiply the bottoms. 5 x 3 = 15.4/15
- Simplify. Divide the top and bottom by their highest common factor.4/15
- Write the answer. 4/15
Check. 4/15 x 3 = 4/5. ✓
Watch out. Dividing by 2 makes a fraction smaller, not bigger.
Method. Multiply the number of portions by the cup for each portion.
- Choose the operation. Total = 6 x 3/4.6 x 3/4
- Multiply. 6 x 3 = 18, so 18/4 = 4 1/2.18/4 = 4 1/2
- Write the answer. 4 1/2
Check. 4 1/2 x 2 = 9 and 3/4 x 6 = 4 1/2. ✓
Method. Divide the length by 3.
- Choose the operation. One piece = 3/4 / 3.3/4 / 3
- Work it out. Multiply the bottom by 3: 3/12, which simplifies to 1/4.3/12 = 1/4
- Write the answer. 1/4
Check. 3 pieces of 1/4 make 3/4. ✓
Method. Work out what is left after the first sale, then take half of it.
- Left after the first sale. 1 - 2/3 = 1/3 of the cake is left.1/3
- Take half of what is left. Half of 1/3 is 1/3 x 1/2 = 1/6, so 1/6 is sold in the second sale.1/6 sold
- What is left. 1/3 - 1/6 = 1/6 is left.1/6
- Write the answer. 1/6
Check. 2/3 + 1/6 + 1/6 = 1. ✓
Method. Multiply the top by 15, then divide by 5.
- Multiply the top. 2 x 15 = 30, so 30/5.30/5
- Simplify. 30 / 5 = 6.6
- Write the answer. 6
Check. 6 / 15 = 2/5. ✓
Method. Check with an example.
- Multiply. 1/4 x 3 = 3/4.3/4
- Compare. 3/4 is bigger than 1/4.3/4 > 1/4
- Write the answer. Yes, because 1/4 x 3 = 3/4, which is bigger than 1/4.
Check. 3/4 > 1/4. ✓
Method. Divide, then compare.
- Divide. 3/4 / 3 = 3/12 = 1/4.1/4
- Compare. 1/4 is smaller than 3/4.1/4 < 3/4
- Write the answer. Yes, because 3/4 / 3 = 1/4, which is smaller than 3/4.
Check. 1/4 < 3/4. ✓
Method. Multiply the tops, multiply the bottoms, then simplify.
- Multiply the tops. 7 x 4 = 28.28
- Multiply the bottoms. 8 x 7 = 56.56
- Simplify. Divide the top and bottom by any common factor.1/2
- Write the answer. 1/2
Check. 28/56 simplifies to 1/2. ✓
Watch out. Simplify first when you can: cancel a factor from a top and a factor from a bottom.
Method. Multiply, then compare with 1/2.
- Multiply. 3/4 x 1/2 = 3/8.3/8
- Compare. 3/8 is less than 4/8 = 1/2.3/8 < 1/2
- Write the answer. yes
Check. 3/8 < 4/8. ✓
Method. Multiply the three numbers, then simplify.
- Multiply the tops. 3 x 2 x 3 = 18.18
- Multiply the bottoms. 1 x 9 x 4 = 36.36
- Simplify. 18/36 = 1/2.1/2
- Write the answer. 1/2
Check. 18 / 36 = 1/2. ✓