Step-by-step Maths Level 4: Equivalent fractions
Part of the Step-by-step Maths Level 4 fractions of wholes and equivalent fractions chapter. Chapter overview · whole chapter on one page
Equivalent fractions
Equivalent fractions are the same amount, written with different numbers. 1/2 = 2/4 = 4/8.
To find an equal fraction, multiply the top and bottom by the same number. To simplify, divide both by the same number.
Key ideas
- Do the same to the top and the bottom.
- Equal fractions are the same amount of the whole.
- Double, or halve, the top and bottom together.
Method. Equivalent fractions: multiply the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.1 × 2 = 2
- Multiply the bottom number by 2. The fraction keeps the same value.2 × 2 = 4
- Write the missing number. This is the bottom number of the equal fraction.4
Check. Check: 2/4 and 1/2 are the same part of a whole.
Watch out. Do the same to the top and the bottom.
Method. Equivalent fractions: multiply the top and bottom by the same number.
- Multiply the top number by 2. Double the top number.2 × 2 = 4
- Multiply the bottom number by 2. Double the bottom number too.5 × 2 = 10
- Write the missing number. This is the bottom number of the equal fraction.10
Check. Check: 4/10 and 2/5 are equal.
Watch out. Double the top and the bottom together.
Method. Equivalent fractions: divide the top and bottom by the same number.
- Divide the top number by 2. Halve the top number.6 ÷ 2 = 3
- Divide the bottom number by 2. Halve the bottom number too.8 ÷ 2 = 4
- Write the missing number. This is the top number of the simpler fraction.3
Check. Check: 3/4 and 6/8 are equal.
Watch out. Halve the top and the bottom together.
Watch out
Watch out. Doubling only the top gives 4/5, which is not 2/5. Double both the top and the bottom.
Exam tip
Grown-up tip. Shade 1/2 of a bar, then the same amount on a bar split into 4. Ask: “How many parts are shaded now?”
Exercise 7D Practice: equivalent fractions
Non-calculatorMethod. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.6 ÷ 2 = 3
- Divide the bottom number by 2. The fraction keeps the same value.10 ÷ 2 = 5
- Write the missing number. This is the top number of the simpler fraction.3
Check. Check: 6/10 and 3/5 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.2 shaded of 3
- Look at the second bar. It has twice as many parts, and twice as many shaded.4 shaded of 6
- Write the missing number. The bottom number is the total parts in the second bar.6
Check. Check: 4/6 is the same as 2/3.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 3. Do the same to the top and the bottom.1 × 3 = 3
- Multiply the bottom number by 3. The fraction keeps the same value.2 × 3 = 6
- Write the missing number. This is the bottom number of the equal fraction.6
Check. Check: 1/2 and 3/6 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.6 ÷ 2 = 3
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/6 and 1/3 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.1 × 2 = 2
- Multiply the bottom number by 2. The fraction keeps the same value.2 × 2 = 4
- Write the missing number. This is the bottom number of the equal fraction.4
Check. Check: 1/2 and 2/4 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 3. Divide the top and the bottom by the same number.3 ÷ 3 = 1
- Divide the bottom number by 3. The fraction keeps the same value.6 ÷ 3 = 2
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 3/6 and 1/2 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.10 ÷ 2 = 5
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/10 and 1/5 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.3 shaded of 4
- Look at the second bar. It has twice as many parts, and twice as many shaded.6 shaded of 8
- Write the missing number. The bottom number is the total parts in the second bar.8
Check. Check: 6/8 is the same as 3/4.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 3. Do the same to the top and the bottom.1 × 3 = 3
- Multiply the bottom number by 3. The fraction keeps the same value.4 × 3 = 12
- Write the missing number. This is the bottom number of the equal fraction.12
Check. Check: 1/4 and 3/12 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.4 ÷ 2 = 2
- Divide the bottom number by 2. The fraction keeps the same value.6 ÷ 2 = 3
- Write the missing number. This is the top number of the simpler fraction.2
Check. Check: 4/6 and 2/3 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.1 shaded of 2
- Look at the second bar. It has twice as many parts, and twice as many shaded.2 shaded of 4
- Write the missing number. The bottom number is the total parts in the second bar.4
Check. Check: 2/4 is the same as 1/2.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.4 ÷ 2 = 2
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/4 and 1/2 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.2 × 2 = 4
- Multiply the bottom number by 2. The fraction keeps the same value.3 × 2 = 6
- Write the missing number. This is the bottom number of the equal fraction.6
Check. Check: 2/3 and 4/6 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 3. Divide the top and the bottom by the same number.6 ÷ 3 = 2
- Divide the bottom number by 3. The fraction keeps the same value.9 ÷ 3 = 3
- Write the missing number. This is the top number of the simpler fraction.2
Check. Check: 6/9 and 2/3 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.2 × 2 = 4
- Multiply the bottom number by 2. The fraction keeps the same value.5 × 2 = 10
- Write the missing number. This is the bottom number of the equal fraction.10
Check. Check: 2/5 and 4/10 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Multiply the top number by 2. Do the same to the top and the bottom.4 × 2 = 8
- Multiply the bottom number by 2. The fraction keeps the same value.5 × 2 = 10
- Write the missing number. This is the bottom number of the equal fraction.10
Check. Check: 4/5 and 8/10 are equal, both are the same part of a whole.
Watch out. Do the same to the top and the bottom. Never change one and not the other.