Year 6 Maths reasoning (SATs) Fractions and decimals reasoning: Equivalent fractions and simplifying
Part of the Year 6 Maths reasoning (SATs) fractions and decimals reasoning chapter. Chapter overview · whole chapter on one page
Equivalent fractions and simplifying
Rule
An equivalent fraction has the same value. Multiply (or divide) the top and bottom by the same number.
To simplify, divide the top and bottom by their highest common factor (HCF). 18/24 = 3/4, because the HCF of 18 and 24 is 6.
Key ideas
- Multiply or divide the top and bottom by the same number.
- A fraction is in its simplest form when the top and bottom have no common factor except 1.
- Equal fractions can be checked by cross-multiplying, for example 2/3 = 4/6 because 2 x 6 = 3 x 4.
Method. Multiply the top and the bottom by the same number.
- Find what the bottom was multiplied by. 5 x 4 = 20.x 4
- Do the same to the top. Multiply the top by 4 as well.3 x 4 = 12
- Write the fraction. Both parts are multiplied by the same number, so the value does not change.12/20
- Write the answer. 12/20
Check. 3/5 = 12/20, because both are multiplied by 4. ✓
Method. Divide the top and bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides 18 and 24 is 6.HCF = 6
- Divide the top and bottom by it. 18 / 6 = 3 and 24 / 6 = 4.3/4
- Write the answer. 3/4
Check. 3 and 4 have no common factor. ✓
Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.
Method. Equivalent fractions have the same value.
- Check 4/6. Multiply 2/3 by 2 on the top and the bottom: 4/6.2/3 = 4/6
- Check the others. 3/4 and 5/6 do not have the same value as 2/3.3/4 and 5/6 are not equal to 2/3
- Write the answer. Only 4/6 is equivalent.4/6
- Write the answer. 4/6
Check. 4 x 3 = 6 x 2, so 4/6 = 2/3. ✓
Watch out
Watch out. When you simplify, divide the top and the bottom by the same number. Dividing only one of them changes the value.
Exam tip
Practice guide. Find the highest common factor first. It is quicker than dividing by 2 many times.
Exercise 2B Practice: equivalent fractions and simplifying
Non-calculatorMethod. Multiply the top and the bottom by the same number.
- Find what the bottom was multiplied by. 7 x 5 = 35.x 5
- Do the same to the top. Multiply the top by 5 as well.2 x 5 = 10
- Write the fraction. Both parts are multiplied by the same number, so the value does not change.10/35
- Write the answer. 10/35
Check. 2/7 = 10/35, because both are multiplied by 5. ✓
Method. Multiply the top and the bottom by the same number.
- Find what the bottom was multiplied by. 8 x 3 = 24.x 3
- Do the same to the top. Multiply the top by 3 as well.5 x 3 = 15
- Write the fraction. Both parts are multiplied by the same number, so the value does not change.15/24
- Write the answer. 15/24
Check. 5/8 = 15/24, because both are multiplied by 3. ✓
Method. Divide the top and bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides 45 and 60 is 15.HCF = 15
- Divide the top and bottom by it. 45 / 15 = 3 and 60 / 15 = 4.3/4
- Write the answer. 3/4
Check. 3 and 4 have no common factor. ✓
Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.
Method. Divide the top and bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides 36 and 48 is 12.HCF = 12
- Divide the top and bottom by it. 36 / 12 = 3 and 48 / 12 = 4.3/4
- Write the answer. 3/4
Check. 3 and 4 have no common factor. ✓
Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.
Method. Divide the top and bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides 28 and 42 is 14.HCF = 14
- Divide the top and bottom by it. 28 / 14 = 2 and 42 / 14 = 3.2/3
- 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. Divide the top and bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides 56 and 64 is 8.HCF = 8
- Divide the top and bottom by it. 56 / 8 = 7 and 64 / 8 = 8.7/8
- Write the answer. 7/8
Check. 7 and 8 have no common factor. ✓
Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.
Method. Find what the bottom was multiplied by, then do the same to the top.
- Find the multiplier. 4 x 5 = 20, so multiply by 5.x 5
- Multiply the top. 3 x 5 = 15.15/20
- Write the answer. 15
Check. 3/4 = 15/20, both are 0.75. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. Each ticked fraction is one half when simplified.2/4, 5/10, 6/12
- Leave the others unticked. These do not match.3/5, 4/9 are not ticked
- Write the answer. 2/4, 5/10, 6/12
Check. Each ticked option is true. ✓
Watch out. 3/5 is more than one half, and 4/9 is less than one half.
Method. Find the HCF of 9 and 12.
- HCF of 9 and 12. The highest common factor is 3.3
- Divide the top and bottom by 3. 9 / 3 = 3 and 12 / 3 = 4.3/4
- Write the answer. 3/4
Check. 3 and 4 have no common factor except 1. ✓
Method. Simplify 6/8.
- Find the HCF of 6 and 8. The HCF is 2.2
- Divide the top and bottom by 2. 6 / 2 = 3 and 8 / 2 = 4.3/4
- Write the answer. Yes, because 6/8 divided by 2 on the top and bottom is 3/4.
Check. 6/8 = 3/4. ✓
Method. Add the fractions with a common denominator, then simplify.
- Common denominator. 1/2 = 5/10 and 3/10 is already in tenths.5/10 + 3/10
- Add the tops. 5 + 3 = 8, so the total is 8/10.8/10
- Simplify. The HCF of 8 and 10 is 2, so 8/10 = 4/5.4/5
- Write the answer. 4/5
Check. 4/5 of the paint is used. ✓
Method. Divide the top and bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides 84 and 108 is 12.HCF = 12
- Divide the top and bottom by it. 84 / 12 = 7 and 108 / 12 = 9.7/9
- Write the answer. 7/9
Check. 7 and 9 have no common factor. ✓
Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.
Method. Multiply the top and bottom by 2, then by 3.
- Multiply by 2. 5 x 2 = 10 and 6 x 2 = 12.10/12
- Multiply by 3. 5 x 3 = 15 and 6 x 3 = 18.15/18
- Write the answer. 10/12 and 15/18.
Check. 10/12 and 15/18 both simplify to 5/6. ✓
Method. Check whether 4 and 10 have the same ratio as 2 and 5.
- Divide the top and bottom of 4/10 by 2. 4 / 2 = 2 and 10 / 2 = 5.2/5
- Compare. So 4/10 = 2/5.yes
- Write the answer. yes
Check. 4/10 = 2/5. ✓
Watch out. Ben is right here, but he must check by dividing both numbers, not because of the 2.
Method. Write 0.6 as tenths, then simplify.
- Write as tenths. 0.6 = 6/10.6/10
- Simplify. The HCF of 6 and 10 is 2, so 6/10 = 3/5.3/5
- Write the answer. 3/5
Check. 3/5 = 0.6. ✓