Year 5: Equivalent fractions
Part of the Year 5 equivalent fractions and mixed numbers chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Equivalent fractions
Equivalent fractions are different fractions that are worth the same amount. Half a pizza is the same amount of pizza as two quarters or four eighths. Look at the bars. They are all the same length. In each bar the shaded part ends at the same place, so
Why does it work? When you cut every part of a bar into 2 smaller equal parts, there are twice as many parts (the bottom number doubles) and you shade twice as many parts (the top number doubles). The amount shaded has not changed. So the rule is: multiply the top and the bottom by the same number. You can also divide the top and the bottom by the same number, as long as both numbers divide exactly.
Tenths and hundredths. A hundred square is cut into 100 small squares. Each row is one tenth, and each row has 10 small squares. So 1 tenth is the same as 10 hundredths. This means
Key ideas
- Equivalent fractions show the same amount.
- To make an equivalent fraction, multiply the top and the bottom by the same number:
2 3 2 × 4 3 × 4 8 12 - You can also divide the top and the bottom by the same number:
6 9 2 3 - 1 tenth = 10 hundredths, so
7 10 70 100 - Equivalent fractions are at the same point on a number line.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 3 by to get 12? This tells us how the fraction has been changed. We must do the same to the other number.3 × 4 = 12, so the multiplier is 4.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 4.2 × 4 = 8
- Write the equivalent fractions. Now both numbers are filled in.
2 3 8 12
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 3 by to get 9? This tells us how the fraction has been changed. We must do the same to the other number.3 × 3 = 9, so the multiplier is 3.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 3.4 × 3 = 12
- Write the equivalent fractions. Now both numbers are filled in.
3 4 9 12
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 16 by to get 4? This tells us how the fraction has been changed. We must do the same to the other number.16 ÷ 4 = 4, so the divider is 4.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 4.12 ÷ 4 = 3
- Write the equivalent fractions. Now both numbers are filled in.
12 16 3 4
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 10 by to get 100? This tells us how the fraction has been changed. We must do the same to the other number.10 × 10 = 100, so the multiplier is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 10.3 × 10 = 30
- Write the equivalent fractions. Now both numbers are filled in.
3 10 30 100
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 100 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.100 ÷ 10 = 10, so the divider is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 10.40 ÷ 10 = 4
- Write the equivalent fractions. Now both numbers are filled in.
40 100 4 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 5 by to get 35? This tells us how the fraction has been changed. We must do the same to the other number.5 × 7 = 35, so the multiplier is 7.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 7.6 × 7 = 42
- Write the equivalent fractions. Now both numbers are filled in.
5 6 35 42
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Multiply the top and the bottom of the fraction by the same number each time. Every answer is an equivalent fraction.
- Multiply the top and the bottom by 2. Multiplying both numbers by 2 cuts every part into 2 smaller equal parts, so the amount stays the same.
2 5 2 × 2 5 × 2 4 10 - Multiply the top and the bottom by 3. Multiplying both numbers by 3 cuts every part into 3 smaller equal parts, so the amount stays the same.
2 5 2 × 3 5 × 3 6 15 - Multiply the top and the bottom by 4. Multiplying both numbers by 4 cuts every part into 4 smaller equal parts, so the amount stays the same.
2 5 2 × 4 5 × 4 8 20 - Write your list. These fractions are all equivalent to the first one.
4 10 6 15 8 20
Check. Each one simplifies back to
Watch out. Multiply the top and the bottom. Adding the same number to both changes the value.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Write both fractions in their simplest form. If the simplest forms are the same, the fractions are equivalent.
- Write
6 9 6 9 6 ÷ 3 9 ÷ 3 2 3 - Write
4 6 4 6 4 ÷ 2 6 ÷ 2 2 3 - Compare the simplest forms. Equivalent fractions have the same simplest form.
2 3 2 3
Check. As a picture: both bars shade the same amount. ✓
Watch out. Do not just look at the numbers. 4/6 and 6/9 look different but are equivalent.
Watch out
Never add the same number to the top and the bottom.Exercise 6A Equivalent fractions
Non-calculatorKey words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 3 by to get 6? This tells us how the fraction has been changed. We must do the same to the other number.3 × 2 = 6, so the multiplier is 2.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 2.1 × 2 = 2
- Write the equivalent fractions. Now both numbers are filled in.
1 3 2 6
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 4 by to get 12? This tells us how the fraction has been changed. We must do the same to the other number.4 × 3 = 12, so the multiplier is 3.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 3.3 × 3 = 9
- Write the equivalent fractions. Now both numbers are filled in.
3 4 9 12
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the top numbers. What do we divide 4 by to get 2? This tells us how the fraction has been changed. We must do the same to the other number.4 ÷ 2 = 2, so the divider is 2.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be divided by 2.10 ÷ 2 = 5
- Write the equivalent fractions. Now both numbers are filled in.
4 10 2 5
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 3 by to get 6? This tells us how the fraction has been changed. We must do the same to the other number.3 × 2 = 6, so the multiplier is 2.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 2.1 × 2 = 2
- Write the equivalent fractions. Now both numbers are filled in.
1 3 2 6
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 5 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.5 × 2 = 10, so the multiplier is 2.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 2.2 × 2 = 4
- Write the equivalent fractions. Now both numbers are filled in.
2 5 4 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 4 by to get 12? This tells us how the fraction has been changed. We must do the same to the other number.4 × 3 = 12, so the multiplier is 3.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 3.3 × 3 = 9
- Write the equivalent fractions. Now both numbers are filled in.
3 4 9 12
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 6 by to get 18? This tells us how the fraction has been changed. We must do the same to the other number.6 × 3 = 18, so the multiplier is 3.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 3.5 × 3 = 15
- Write the equivalent fractions. Now both numbers are filled in.
5 6 15 18
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 10 by to get 100? This tells us how the fraction has been changed. We must do the same to the other number.10 × 10 = 100, so the multiplier is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 10.7 × 10 = 70
- Write the equivalent fractions. Now both numbers are filled in.
7 10 70 100
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 9 by to get 27? This tells us how the fraction has been changed. We must do the same to the other number.9 × 3 = 27, so the multiplier is 3.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 3.4 × 3 = 12
- Write the equivalent fractions. Now both numbers are filled in.
4 9 12 27
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 2 by to get 8? This tells us how the fraction has been changed. We must do the same to the other number.2 × 4 = 8, so the multiplier is 4.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 4.3 × 4 = 12
- Write the equivalent fractions. Now both numbers are filled in.
2 3 8 12
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 3 by to get 12? This tells us how the fraction has been changed. We must do the same to the other number.3 × 4 = 12, so the multiplier is 4.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 4.5 × 4 = 20
- Write the equivalent fractions. Now both numbers are filled in.
3 5 12 20
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 5 by to get 15? This tells us how the fraction has been changed. We must do the same to the other number.5 × 3 = 15, so the multiplier is 3.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 3.8 × 3 = 24
- Write the equivalent fractions. Now both numbers are filled in.
5 8 15 24
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 7 by to get 70? This tells us how the fraction has been changed. We must do the same to the other number.7 × 10 = 70, so the multiplier is 10.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 10.10 × 10 = 100
- Write the equivalent fractions. Now both numbers are filled in.
7 10 70 100
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 1 by to get 5? This tells us how the fraction has been changed. We must do the same to the other number.1 × 5 = 5, so the multiplier is 5.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 5.4 × 5 = 20
- Write the equivalent fractions. Now both numbers are filled in.
1 4 5 20
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the top numbers. What do we multiply 3 by to get 21? This tells us how the fraction has been changed. We must do the same to the other number.3 × 7 = 21, so the multiplier is 7.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be multiplied by 7.7 × 7 = 49
- Write the equivalent fractions. Now both numbers are filled in.
3 7 21 49
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 8 by to get 4? This tells us how the fraction has been changed. We must do the same to the other number.8 ÷ 2 = 4, so the divider is 2.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 2.6 ÷ 2 = 3
- Write the equivalent fractions. Now both numbers are filled in.
6 8 3 4
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 15 by to get 3? This tells us how the fraction has been changed. We must do the same to the other number.15 ÷ 5 = 3, so the divider is 5.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 5.10 ÷ 5 = 2
- Write the equivalent fractions. Now both numbers are filled in.
10 15 2 3
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 16 by to get 4? This tells us how the fraction has been changed. We must do the same to the other number.16 ÷ 4 = 4, so the divider is 4.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 4.12 ÷ 4 = 3
- Write the equivalent fractions. Now both numbers are filled in.
12 16 3 4
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 100 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.100 ÷ 10 = 10, so the divider is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 10.40 ÷ 10 = 4
- Write the equivalent fractions. Now both numbers are filled in.
40 100 4 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the top numbers. What do we divide 9 by to get 3? This tells us how the fraction has been changed. We must do the same to the other number.9 ÷ 3 = 3, so the divider is 3.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be divided by 3.12 ÷ 3 = 4
- Write the equivalent fractions. Now both numbers are filled in.
9 12 3 4
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the top numbers. What do we divide 20 by to get 2? This tells us how the fraction has been changed. We must do the same to the other number.20 ÷ 10 = 2, so the divider is 10.
- Do the same to the bottom number. To keep the fraction the same size, the top and the bottom must both be divided by 10.50 ÷ 10 = 5
- Write the equivalent fractions. Now both numbers are filled in.
20 50 2 5
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. The denominator (bottom number) tells us how many equal parts the whole is cut into. The numerator (top number) tells us how many parts we have.
Method. Each row of the hundred square is one tenth. 1 tenth is 10 hundredths.
- Count the shaded small squares. There are 100 small squares in the whole, so the denominator is 100.30 shaded squares, so 30 out of 100.
- Write the fraction.
30 100
Check. 3 full rows of 10 = 30 squares. ✓
Watch out. The whole square is 100 small squares, not 10.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 100 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.100 ÷ 10 = 10, so the divider is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 10.30 ÷ 10 = 3
- Write the equivalent fractions. Now both numbers are filled in.
30 100 3 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 10 by to get 100? This tells us how the fraction has been changed. We must do the same to the other number.10 × 10 = 100, so the multiplier is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 10.7 × 10 = 70
- Write the equivalent fractions. Now both numbers are filled in.
7 10 70 100
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by divideing the top and the bottom by the same number.
- Look at the bottom numbers. What do we divide 100 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.100 ÷ 10 = 10, so the divider is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be divided by 10.60 ÷ 10 = 6
- Write the equivalent fractions. Now both numbers are filled in.
60 100 6 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 2 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.2 × 5 = 10, so the multiplier is 5.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 5.1 × 5 = 5
- Write the equivalent fractions. Now both numbers are filled in.
1 2 5 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 5 by to get 10? This tells us how the fraction has been changed. We must do the same to the other number.5 × 2 = 10, so the multiplier is 2.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 2.3 × 2 = 6
- Write the equivalent fractions. Now both numbers are filled in.
3 5 6 10
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 10 by to get 100? This tells us how the fraction has been changed. We must do the same to the other number.10 × 10 = 100, so the multiplier is 10.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 10.9 × 10 = 90
- Write the equivalent fractions. Now both numbers are filled in.
9 10 90 100
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 4 by to get 100? This tells us how the fraction has been changed. We must do the same to the other number.4 × 25 = 100, so the multiplier is 25.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 25.1 × 25 = 25
- Write the equivalent fractions. Now both numbers are filled in.
1 4 25 100
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Multiply the top and the bottom of the fraction by the same number each time. Every answer is an equivalent fraction.
- Multiply the top and the bottom by 2. Multiplying both numbers by 2 cuts every part into 2 smaller equal parts, so the amount stays the same.
1 4 1 × 2 4 × 2 2 8 - Multiply the top and the bottom by 3. Multiplying both numbers by 3 cuts every part into 3 smaller equal parts, so the amount stays the same.
1 4 1 × 3 4 × 3 3 12 - Multiply the top and the bottom by 4. Multiplying both numbers by 4 cuts every part into 4 smaller equal parts, so the amount stays the same.
1 4 1 × 4 4 × 4 4 16 - Write your list. These fractions are all equivalent to the first one.
2 8 3 12 4 16
Check. Each one simplifies back to
Watch out. Multiply the top and the bottom. Adding the same number to both changes the value.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Multiply the top and the bottom of the fraction by the same number each time. Every answer is an equivalent fraction.
- Multiply the top and the bottom by 2. Multiplying both numbers by 2 cuts every part into 2 smaller equal parts, so the amount stays the same.
2 3 2 × 2 3 × 2 4 6 - Multiply the top and the bottom by 3. Multiplying both numbers by 3 cuts every part into 3 smaller equal parts, so the amount stays the same.
2 3 2 × 3 3 × 3 6 9 - Multiply the top and the bottom by 4. Multiplying both numbers by 4 cuts every part into 4 smaller equal parts, so the amount stays the same.
2 3 2 × 4 3 × 4 8 12 - Write your list. These fractions are all equivalent to the first one.
4 6 6 9 8 12
Check. Each one simplifies back to
Watch out. Multiply the top and the bottom. Adding the same number to both changes the value.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Multiply the top and the bottom of the fraction by the same number each time. Every answer is an equivalent fraction.
- Multiply the top and the bottom by 2. Multiplying both numbers by 2 cuts every part into 2 smaller equal parts, so the amount stays the same.
3 5 3 × 2 5 × 2 6 10 - Multiply the top and the bottom by 3. Multiplying both numbers by 3 cuts every part into 3 smaller equal parts, so the amount stays the same.
3 5 3 × 3 5 × 3 9 15 - Multiply the top and the bottom by 4. Multiplying both numbers by 4 cuts every part into 4 smaller equal parts, so the amount stays the same.
3 5 3 × 4 5 × 4 12 20 - Write your list. These fractions are all equivalent to the first one.
6 10 9 15 12 20
Check. Each one simplifies back to
Watch out. Multiply the top and the bottom. Adding the same number to both changes the value.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 3 by to get 6? This tells us how the fraction has been changed. We must do the same to the other number.3 × 2 = 6, so the multiplier is 2.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 2.2 × 2 = 4
- Write the equivalent fractions. Now both numbers are filled in.
2 3 4 6
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions are made by multiplying the top and the bottom by the same number.
- Look at the bottom numbers. What do we multiply 3 by to get 12? This tells us how the fraction has been changed. We must do the same to the other number.3 × 4 = 12, so the multiplier is 4.
- Do the same to the top number. To keep the fraction the same size, the top and the bottom must both be multiplied by 4.2 × 4 = 8
- Write the equivalent fractions. Now both numbers are filled in.
2 3 8 12
Check.
Watch out. Whatever you do to the top, do to the bottom. Never add or subtract the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Write both fractions in their simplest form. If the simplest forms are the same, the fractions are equivalent.
- Write
3 4 3 4 - Write
9 12 9 12 9 ÷ 3 12 ÷ 3 3 4 - Compare the simplest forms. Equivalent fractions have the same simplest form.
3 4 3 4
Check. As a picture: both bars shade the same amount. ✓
Watch out. Do not just look at the numbers. 4/6 and 6/9 look different but are equivalent.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Write both fractions in their simplest form. If the simplest forms are the same, the fractions are equivalent.
- Write
2 5 2 5 - Write
4 15 4 15 - Compare the simplest forms. Equivalent fractions have the same simplest form.
2 5 4 15
Check.
Watch out. Do not just look at the numbers. 4/6 and 6/9 look different but are equivalent.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Write both fractions in their simplest form. If the simplest forms are the same, the fractions are equivalent.
- Write
5 6 5 6 - Write
10 12 10 12 10 ÷ 2 12 ÷ 2 5 6 - Compare the simplest forms. Equivalent fractions have the same simplest form.
5 6 5 6
Check. As a picture: both bars shade the same amount. ✓
Watch out. Do not just look at the numbers. 4/6 and 6/9 look different but are equivalent.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Write both fractions in their simplest form. If the simplest forms are the same, the fractions are equivalent.
- Write
3 8 3 8 - Write
6 12 6 12 6 ÷ 6 12 ÷ 6 1 2 - Compare the simplest forms. Equivalent fractions have the same simplest form.
3 8 1 2
Check.
Watch out. Do not just look at the numbers. 4/6 and 6/9 look different but are equivalent.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Work out the value of each one in its simplest form. Three will be the same. The odd one out is the one that is different.
- Write each one in its simplest form. Then equal values are easy to spot.
2 4 1 2 3 6 1 2 4 10 2 5 5 10 1 2 - Find the one that is different. The other three have the same value.
4 10
Check. Check the three that match once more. ✓
Watch out. Compare values, not the look of the numbers.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Write each fraction in its simplest form.
- Write
3 4 3 4 3 4 - Simplify each option. Divide the top and the bottom by their highest common factor.
6 8 3 4 9 12 3 4 8 12 2 3 12 16 3 4 15 24 5 8 - Pick the equal ones.
6 8 9 12 12 16
Check. Multiply
Watch out. Check the top AND the bottom change by the same number.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Change both fractions so they have the same denominator, or simplify one of them. Then compare.
- Look at what Ella ate. Ella ate 4 of the 8 equal slices.
4 8 - Look at what Sam ate. Sam ate 2 of 4 equal slices of a pizza the same size.
2 4 - Write both with the same denominator. Multiply the top and the bottom of
2 4 2 4 2 × 2 4 × 2 4 8 - Compare. The fractions are equal, so they ate the same amount.
4 8 4 8
Check. Both are one half of a pizza. ✓
Watch out. Different numbers can still mean the same amount.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Work the question out yourself first. Then compare your working with the working in the question and find where it goes wrong.
- Work it out correctly. We need the right answer to compare with.
2 3 2 × 2 3 × 2 4 6 - Find the mistake. Leo added 2 to the top and 2 to the bottom (2 + 2 = 4 and 3 + 2 = 5). Adding changes the fraction. He should have multiplied both numbers by 2.Leo wrote
2 3 4 5 - Write the correct answer. The correct answer is
4 6 4 5 2 3
Check.
Watch out. Multiply or divide the top and the bottom. Never add.
Key words. Always means true every time. Never means false every time. Sometimes means true for some numbers and false for others.
Method. Test the statement with some numbers. If it is always true, never true, or true for some numbers only, that gives the answer.
- Try some examples. Testing numbers helps us see if the statement is true every time.
1 2 2 3 - Look for an example that does not work. One example that breaks the rule is a counter-example.
3 3 4 4 - Decide: always, sometimes or never? It does not work for most fractions, but it does work for a fraction that is equal to 1.Sometimes
Check. We found one example that works and one that does not. ✓
Watch out. To show a statement is “always” true you need a reason. A few examples are not enough to prove it, but one counter-example shows it is not always true.
Key words. Equivalent fractions are different fractions that are worth the same amount, like
Method. Equivalent fractions of 2/3 are 2k/3k. The top and the bottom add to 5k, so work out what k must be.
- Add the top and the bottom of the first fraction. This is the total that gets multiplied.2 + 3 = 5
- Find the multiplier. We need the total to be 35. What do we multiply 5 by to get 35?5 × 7 = 35, so the multiplier is 7.
- Multiply the top and the bottom. Multiply both by 7.
2 × 7 3 × 7 14 21 - Check the total. Add the new top and bottom.14 + 21 = 35
Check.
Watch out. The multiplier works on both numbers, so the total is multiplied too.