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Home / Practice / Maths
Fractions that look different and are worth the same, and how to simplify them.
Question 1 of 12
1/4 = ?/28. What number goes in place of the question mark?
Look at the bottoms first: 4 has become 28, so it has been multiplied by 7 (28 ÷ 4 = 7). Whatever is done to the bottom must be done to the top, so the top becomes 1 × 7 = 7. The fraction 7/28 is the same amount as 1/4. Work out what happened to the denominator before touching the numerator. The bottom tells you the rule.
The answer is D. Look at the bottoms first: 4 has become 28, so it has been multiplied by 7 (28 ÷ 4 = 7). Whatever is done to the bottom must be done to the top, so the top becomes 1 × 7 = 7. The fraction 7/28 is the same amount as 1/4. Work out what happened to the denominator before touching the numerator. The bottom tells you the rule.
3/7 = ?/21. What number goes in place of the question mark?
Look at the bottoms first: 7 has become 21, so it has been multiplied by 3 (21 ÷ 7 = 3). Whatever is done to the bottom must be done to the top, so the top becomes 3 × 3 = 9. The fraction 9/21 is the same amount as 3/7. Divide the new bottom by the old bottom. That single division is the whole question.
The answer is C. Look at the bottoms first: 7 has become 21, so it has been multiplied by 3 (21 ÷ 7 = 3). Whatever is done to the bottom must be done to the top, so the top becomes 3 × 3 = 9. The fraction 9/21 is the same amount as 3/7. Divide the new bottom by the old bottom. That single division is the whole question.
Write 16/28 in its simplest form.
Simplest form means dividing the top and the bottom by the largest number that goes into both. 4 divides into both: 16 ÷ 4 = 4 and 28 ÷ 4 = 7. That gives 4/7, and nothing divides into 4 and 7 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. A fraction is fully simplified when the only number dividing into both parts is 1.
The answer is C. Simplest form means dividing the top and the bottom by the largest number that goes into both. 4 divides into both: 16 ÷ 4 = 4 and 28 ÷ 4 = 7. That gives 4/7, and nothing divides into 4 and 7 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. A fraction is fully simplified when the only number dividing into both parts is 1.
1/5 = ?/30. What number goes in place of the question mark?
Look at the bottoms first: 5 has become 30, so it has been multiplied by 6 (30 ÷ 5 = 6). Whatever is done to the bottom must be done to the top, so the top becomes 1 × 6 = 6. The fraction 6/30 is the same amount as 1/5. Adding the same number to both parts is the wrong move here, however natural it feels.
The answer is B. Look at the bottoms first: 5 has become 30, so it has been multiplied by 6 (30 ÷ 5 = 6). Whatever is done to the bottom must be done to the top, so the top becomes 1 × 6 = 6. The fraction 6/30 is the same amount as 1/5. Adding the same number to both parts is the wrong move here, however natural it feels.
Which of these is equivalent to 2/3?
Two fractions are equivalent when one can be reached from the other by multiplying the top and the bottom by the same number. Multiplying both parts of 2/3 by 6 gives 2 × 6 = 12 on the top and 3 × 6 = 18 on the bottom, so 12/18. Adding 6 to both parts instead would give 8/9, which is a different amount — that is the trap here, and it catches a lot of children. Whatever you do to the top you must do to the bottom, and it must be multiplying or dividing, never adding.
The answer is A. Two fractions are equivalent when one can be reached from the other by multiplying the top and the bottom by the same number. Multiplying both parts of 2/3 by 6 gives 2 × 6 = 12 on the top and 3 × 6 = 18 on the bottom, so 12/18. Adding 6 to both parts instead would give 8/9, which is a different amount — that is the trap here, and it catches a lot of children. Whatever you do to the top you must do to the bottom, and it must be multiplying or dividing, never adding.
Which of these is equivalent to 1/2?
Two fractions are equivalent when one can be reached from the other by multiplying the top and the bottom by the same number. Multiplying both parts of 1/2 by 5 gives 1 × 5 = 5 on the top and 2 × 5 = 10 on the bottom, so 5/10. Adding 5 to both parts instead would give 6/7, which is a different amount — that is the trap here, and it catches a lot of children. Check by simplifying the answer back down. If it returns to the fraction you started with, it is equivalent.
The answer is B. Two fractions are equivalent when one can be reached from the other by multiplying the top and the bottom by the same number. Multiplying both parts of 1/2 by 5 gives 1 × 5 = 5 on the top and 2 × 5 = 10 on the bottom, so 5/10. Adding 5 to both parts instead would give 6/7, which is a different amount — that is the trap here, and it catches a lot of children. Check by simplifying the answer back down. If it returns to the fraction you started with, it is equivalent.
1/8 = ?/40. What number goes in place of the question mark?
Look at the bottoms first: 8 has become 40, so it has been multiplied by 5 (40 ÷ 8 = 5). Whatever is done to the bottom must be done to the top, so the top becomes 1 × 5 = 5. The fraction 5/40 is the same amount as 1/8. Work out what happened to the denominator before touching the numerator. The bottom tells you the rule.
The answer is A. Look at the bottoms first: 8 has become 40, so it has been multiplied by 5 (40 ÷ 8 = 5). Whatever is done to the bottom must be done to the top, so the top becomes 1 × 5 = 5. The fraction 5/40 is the same amount as 1/8. Work out what happened to the denominator before touching the numerator. The bottom tells you the rule.
Write 6/9 in its simplest form.
Simplest form means dividing the top and the bottom by the largest number that goes into both. 3 divides into both: 6 ÷ 3 = 2 and 9 ÷ 3 = 3. That gives 2/3, and nothing divides into 2 and 3 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. Look for the highest common factor in one go. Halving over and over works but takes longer and invites slips.
The answer is A. Simplest form means dividing the top and the bottom by the largest number that goes into both. 3 divides into both: 6 ÷ 3 = 2 and 9 ÷ 3 = 3. That gives 2/3, and nothing divides into 2 and 3 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. Look for the highest common factor in one go. Halving over and over works but takes longer and invites slips.
Write 45/55 in its simplest form.
Simplest form means dividing the top and the bottom by the largest number that goes into both. 5 divides into both: 45 ÷ 5 = 9 and 55 ÷ 5 = 11. That gives 9/11, and nothing divides into 9 and 11 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. If the top and bottom are both even, you can always halve. That is the easiest first move.
The answer is B. Simplest form means dividing the top and the bottom by the largest number that goes into both. 5 divides into both: 45 ÷ 5 = 9 and 55 ÷ 5 = 11. That gives 9/11, and nothing divides into 9 and 11 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. If the top and bottom are both even, you can always halve. That is the easiest first move.
Write 8/56 in its simplest form.
Simplest form means dividing the top and the bottom by the largest number that goes into both. 8 divides into both: 8 ÷ 8 = 1 and 56 ÷ 8 = 7. That gives 1/7, and nothing divides into 1 and 7 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. Look for the highest common factor in one go. Halving over and over works but takes longer and invites slips.
The answer is A. Simplest form means dividing the top and the bottom by the largest number that goes into both. 8 divides into both: 8 ÷ 8 = 1 and 56 ÷ 8 = 7. That gives 1/7, and nothing divides into 1 and 7 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. Look for the highest common factor in one go. Halving over and over works but takes longer and invites slips.
Write 72/88 in its simplest form.
Simplest form means dividing the top and the bottom by the largest number that goes into both. 8 divides into both: 72 ÷ 8 = 9 and 88 ÷ 8 = 11. That gives 9/11, and nothing divides into 9 and 11 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. Look for the highest common factor in one go. Halving over and over works but takes longer and invites slips.
The answer is A. Simplest form means dividing the top and the bottom by the largest number that goes into both. 8 divides into both: 72 ÷ 8 = 9 and 88 ÷ 8 = 11. That gives 9/11, and nothing divides into 9 and 11 except 1, so it will not go any further. Halving repeatedly gets there too, just more slowly, and only if both numbers are even. Look for the highest common factor in one go. Halving over and over works but takes longer and invites slips.
7/8 = ?/56. What number goes in place of the question mark?
Look at the bottoms first: 8 has become 56, so it has been multiplied by 7 (56 ÷ 8 = 7). Whatever is done to the bottom must be done to the top, so the top becomes 7 × 7 = 49. The fraction 49/56 is the same amount as 7/8. Work out what happened to the denominator before touching the numerator. The bottom tells you the rule.
The answer is B. Look at the bottoms first: 8 has become 56, so it has been multiplied by 7 (56 ÷ 8 = 7). Whatever is done to the bottom must be done to the top, so the top becomes 7 × 7 = 49. The fraction 49/56 is the same amount as 7/8. Work out what happened to the denominator before touching the numerator. The bottom tells you the rule.
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