GCSE Maths Fractions (Foundation): check-up and exam-style questions

Method. Simplify by dividing the top and the bottom by the same number: the highest common factor (HCF).

1. Say what we are trying to do. To simplify means to write the fraction with smaller numbers without changing its value. We do this by dividing the top and the bottom by a number that goes into both.
   1218
2. List the factors of the top and of the bottom. A factor of a number divides into it exactly. We want factors that the two numbers share.
   Factors of 12: 1, 2, 3, 4, 6, 12
   Factors of 18: 1, 2, 3, 6, 9, 18
3. Pick the highest common factor (HCF). The HCF is the biggest number in both lists. Dividing by it simplifies completely in one go.
   Common factors: 1, 2, 3, 6
   HCF = 6
4. Divide the top by 6. Whatever we do to the top we must also do to the bottom.
   12 ÷ 6 = 2
5. Divide the bottom by 6. Dividing top and bottom by the same number keeps the fraction the same size but with smaller numbers.
   18 ÷ 6 = 3
6. Write the simplified fraction. Check that nothing more can be divided out: the HCF was used, so the top and bottom now share only the factor 1.
   1218 = 23

Check. A different route: divide in small steps (÷ 2, then ÷ 3). 1218 → 69 → 23. We reach the same fraction. As decimals, 1218 = 0.6667 and 23 = 0.6667. ✓

Watch out. Divide the top and the bottom. If you divide only one of them you change the value of the fraction.

Method. To add fractions, give them the same denominator, then add the numerators and keep the denominator.

1. Read the question and decide the plan. We can only add pieces that are the same size. So first look at the type of numbers and at the denominators (the bottom numbers).
   34 + 23
2. Find a common denominator: the LCM of 4 and 3. We can only add or subtract pieces of the same size, so the denominators must match. The lowest common multiple (LCM) is the smallest number that both denominators divide into.
   Multiples of 4: 4, 8, 12
   Multiples of 3: 3, 6, 9, 12
   LCM = 12
3. Rewrite both fractions with denominator 12. Multiply the top and the bottom by the same number so the value does not change.
   34 = 912 (× 3)
   23 = 812 (× 4)
4. Add the numerators and keep the denominator. The denominator only tells us the size of each piece, so it stays the same.
   912 + 812 = 1712
5. Write the improper fraction as a mixed number. The top is bigger than the bottom, so the answer is more than 1. Divide to find the whole number and the remainder.
   17 ÷ 12 = 1 remainder 5
   1712 = 1512

Check. A different route, as decimals: 0.75 + 0.6667 = 1.4167, and our answer 1512 = 1.4167. ✓

Watch out. Never add the denominators. The denominator stays the same once the pieces are the same size.

Method. To subtract fractions, give them the same denominator, then subtract the numerators and keep the denominator.

1. Read the question and decide the plan. We can only subtract pieces that are the same size. So first look at the type of numbers and at the denominators (the bottom numbers).
   78 − 14
2. Find a common denominator: the LCM of 8 and 4. We can only add or subtract pieces of the same size, so the denominators must match. The lowest common multiple (LCM) is the smallest number that both denominators divide into.
   Multiples of 8: 8
   Multiples of 4: 4, 8
   LCM = 8
3. Rewrite both fractions with denominator 8. Multiply the top and the bottom by the same number so the value does not change.
   78 = 78 (× 1)
   14 = 28 (× 2)
4. Subtract the numerators and keep the denominator. The denominator only tells us the size of each piece, so it stays the same.
   78 − 28 = 58
5. Check the answer is in its simplest form. See whether any number except 1 divides into both the top and the bottom. If not, we are finished.
   5 and 8 have no common factor except 1, so 58 is the answer.

Check. A different route, as decimals: 0.875 − 0.25 = 0.625, and our answer 58 = 0.625. ✓

Watch out. Subtract in the right order: the first fraction minus the second.

Method. To multiply fractions, multiply the numerators together and the denominators together (cancel first to keep the numbers small).

1. Read the question and decide the plan. Multiplying fractions does not need a common denominator. First look at the type of numbers we have.
   25 × 34
2. Cancel common factors first. A number on the top of one fraction and a number on the bottom of the other can be divided by a common factor. This keeps the numbers small and gives an answer already in its simplest form.
   25 × 34 = 15 × 32
3. Multiply the numerators, then the denominators. Multiplying fractions is just multiplying across: top × top and bottom × bottom.
   1 × 3 = 3
   5 × 2 = 10
   310
4. Check the answer is in its simplest form. See whether any number except 1 divides into both the top and the bottom. If not, we are finished.
   3 and 10 have no common factor except 1, so 310 is the answer.

Check. A different route, as decimals: 0.4 × 0.75 = 0.3, and our answer 310 = 0.3. ✓

Watch out. Do not find a common denominator when multiplying. That is only for adding and subtracting.

Method. To divide by a fraction, turn the second fraction upside down and multiply: keep, change, flip.

1. Read the question and decide the plan. Dividing by a fraction is done by multiplying by its reciprocal. First look at the type of numbers we have.
   56 ÷ 512
2. Keep, change, flip. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down). For example, dividing by 1/2 asks "how many halves fit?", which is the same as multiplying by 2.
   56 ÷ 512 = 56 × 125
3. Cancel common factors. Divide a top and a bottom by a number they share, to keep the numbers small.
   56 × 125 = 11 × 21
4. Multiply the numerators, then the denominators. Now it is an ordinary multiplication: top × top and bottom × bottom.
   1 × 2 = 2
   1 × 1 = 1
   21
5. Write the answer. The bottom number is 1, so the answer is a whole number.
   21 = 2

Check. Multiply back: 2 × 512 should give 56. 2 × 0.4167 = 0.8333 and 56 = 0.8333. ✓

Watch out. Only flip the second fraction (the one you are dividing by), never the first.

Method. Divide the top by the bottom: the answer is the whole number, the remainder goes over the same bottom number.

1. Say what the fraction means. 236 means 23 pieces, each one 16 of a whole. It is called improper because the top is bigger than the bottom, so it is more than one whole.
   23 pieces of size 16
2. Work out how many pieces make one whole. The bottom number tells us this: 6 pieces make 1 whole. So we want to know how many groups of 6 we can make from 23 pieces.
   6 pieces = 1 whole
3. Divide 23 by 6 to find the whole number. Count how many whole groups of 6 fit into 23. 6 × 3 = 18, but 6 × 4 = 24 is too big.
   23 ÷ 6 = 3 remainder 5
4. Find the pieces left over. After 3 whole ones we have used 18 pieces. The rest are the remainder.
   23 − 18 = 5
5. Write the mixed number. The whole number is 3. The 5 leftover pieces of size 16 make the fraction 56. The bottom number stays 6 because the pieces are the same size.
   236 = 356

Check. Convert back: 3 × 6 + 5 = 18 + 5 = 23. As decimals, 23 ÷ 6 = 3.8333 and 356 = 3.8333. ✓

Watch out. Keep the original denominator. Do not use the remainder as the denominator.

Method. To find a fraction of an amount: divide by the denominator to find one part, then multiply by the numerator.

1. Say what 59 of 72 means. The denominator 9 says the amount is split into 9 equal parts. The numerator 5 says we take 5 of those parts. The word "of" tells us we are finding a share of an amount.
   Split 72 into 9 equal parts. Take 5 parts.
2. Divide 72 by the denominator 9. Sharing into 9 equal parts finds the size of one part (this is 19 of the amount).
   72 ÷ 9 = 8
3. Multiply by the numerator 5. The numerator 5 tells us how many parts we take. Here 8 × 5 gives the size of 5 parts.
   8 × 5 = 40
4. Write the answer. Give the answer with its units.
   59 of 72 = 40

Check. A different route: multiply first, then divide. 72 × 5 = 360, and 360 ÷ 9 = 40. The answers match. ✓ Also the other 4 parts make 32, and 40 + 32 = 72.

Watch out. Divide by the denominator first, then multiply by the numerator. Do not multiply by the denominator.

Method. To compare fractions with different denominators, rewrite them with the same denominator (the lowest common multiple of the denominators). Then compare the numerators.

1. Find the lowest common multiple (LCM) of 8 and 12. The LCM is the smallest number that both denominators divide into. It will be our common denominator.
   Multiples of 8: 8, 16, 24
   Multiples of 12: 12, 24
   LCM = 24
2. Rewrite the first fraction with denominator 24. Multiply the top and the bottom by the same number: 24 ÷ 8 = 3.
   58 = 1524 (× 3)
3. Rewrite the second fraction with denominator 24. 24 ÷ 12 = 2, so multiply the top and the bottom by 2.
   712 = 1424 (× 2)
4. Compare the numerators. The denominators now match, so the pieces are the same size and the bigger numerator is the bigger fraction.
   15 > 14
5. Write the answer using the original fractions. The first fraction is bigger.
   58 > 712

Check. A different route, as decimals: 58 = 0.625 and 712 = 0.5833, so 0.625 > 0.5833. ✓

Watch out. Do not compare the denominators alone: for fractions with the same top, a bigger denominator means a smaller fraction.

Method. To add fractions, give them the same denominator, then add the numerators and keep the denominator.

1. Read the question and decide the plan. We can only add pieces that are the same size. So first look at the type of numbers and at the denominators (the bottom numbers).
   212 + 123
2. Change the mixed numbers to improper fractions. A mixed number is a whole number plus a fraction. Multiply the whole number by the denominator, add the numerator, and keep the denominator. This lets us calculate with a single fraction.
   212 = (2 × 2 + 1) over 2 = 52
   123 = (1 × 3 + 2) over 3 = 53
3. Find a common denominator: the LCM of 2 and 3. We can only add or subtract pieces of the same size, so the denominators must match. The lowest common multiple (LCM) is the smallest number that both denominators divide into.
   Multiples of 2: 2, 4, 6
   Multiples of 3: 3, 6
   LCM = 6
4. Rewrite both fractions with denominator 6. Multiply the top and the bottom by the same number so the value does not change.
   52 = 156 (× 3)
   53 = 106 (× 2)
5. Add the numerators and keep the denominator. The denominator only tells us the size of each piece, so it stays the same.
   156 + 106 = 256
6. Write the improper fraction as a mixed number. The top is bigger than the bottom, so the answer is more than 1. Divide to find the whole number and the remainder.
   25 ÷ 6 = 4 remainder 1
   256 = 416

Check. A different route, as decimals: 2.5 + 1.6667 = 4.1667, and our answer 416 = 4.1667. ✓

Watch out. Never add the denominators. The denominator stays the same once the pieces are the same size.

Method. Use place value to write the decimal as a fraction over 10, 100 or 1000, then simplify.

1. Count the digits after the decimal point. Each digit is a place value: the first is tenths, the second is hundredths, the third is thousandths. This tells us the denominator.
   0.45 has 2 decimal places, so it is in hundredths.
2. Write the digits as a fraction over 10, 100 or 1000. 2 decimal places means the denominator is 1 followed by 2 zeros.
   0.45 = 45100
3. Find the highest common factor (HCF) of the top and the bottom. We want to simplify the fraction fully.
   Factors of 45: 1, 3, 5, 9, 15, 45
   HCF of 45 and 100 = 5
4. Divide the top and the bottom by 5. Dividing both by the same number keeps the value and gives smaller numbers.
   45 ÷ 5 = 9 and 100 ÷ 5 = 20
   45100 = 920

Check. Divide the top by the bottom: 920 gives 45 ÷ 100 = 0.45. ✓

Watch out. Count the decimal places carefully: 0.08 is hundredths (8 over 100), not tenths.

Method. The shape has 10 equal parts, but the fraction has denominator 5. Make an equivalent fraction with denominator 10.

1. Compare the denominators. The shape is split into 10 equal parts, but the fraction is in fifths. We need the fraction in tenths.
   35 = ?10
2. Find the multiplier. 10 ÷ 5 = 2, so the bottom was multiplied by 2.
   10 ÷ 5 = 2
3. Multiply the top by the same number. To keep the same value, the top must be multiplied by 2 too.
   3 × 2 = 6, so 35 = 610
4. Shade the parts. The top number 6 tells us how many of the 10 parts to shade.
   Shade 6 of the 10 parts.

Check. 6 shaded out of 10 is 610. Divide the top and the bottom by 2: 610 = 35. ✓

Watch out. Do not shade 3 parts. The fraction must be written in tenths first.

Method. Simplify by dividing the top and the bottom by the same number: the highest common factor (HCF).

1. Say what we are trying to do. To simplify means to write the fraction with smaller numbers without changing its value. We do this by dividing the top and the bottom by a number that goes into both.
   1824
2. List the factors of the top and of the bottom. A factor of a number divides into it exactly. We want factors that the two numbers share.
   Factors of 18: 1, 2, 3, 6, 9, 18
   Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
3. Pick the highest common factor (HCF). The HCF is the biggest number in both lists. Dividing by it simplifies completely in one go.
   Common factors: 1, 2, 3, 6
   HCF = 6
4. Divide the top by 6. Whatever we do to the top we must also do to the bottom.
   18 ÷ 6 = 3
5. Divide the bottom by 6. Dividing top and bottom by the same number keeps the fraction the same size but with smaller numbers.
   24 ÷ 6 = 4
6. Write the simplified fraction. Check that nothing more can be divided out: the HCF was used, so the top and bottom now share only the factor 1.
   1824 = 34

Check. A different route: divide in small steps (÷ 2, then ÷ 3). 1824 → 912 → 34. We reach the same fraction. As decimals, 1824 = 0.75 and 34 = 0.75. ✓

Watch out. Divide the top and the bottom. If you divide only one of them you change the value of the fraction.

Method. To add fractions, give them the same denominator, then add the numerators and keep the denominator.

1. Read the question and decide the plan. We can only add pieces that are the same size. So first look at the type of numbers and at the denominators (the bottom numbers).
   23 + 14
2. Find a common denominator: the LCM of 3 and 4. We can only add or subtract pieces of the same size, so the denominators must match. The lowest common multiple (LCM) is the smallest number that both denominators divide into.
   Multiples of 3: 3, 6, 9, 12
   Multiples of 4: 4, 8, 12
   LCM = 12
3. Rewrite both fractions with denominator 12. Multiply the top and the bottom by the same number so the value does not change.
   23 = 812 (× 4)
   14 = 312 (× 3)
4. Add the numerators and keep the denominator. The denominator only tells us the size of each piece, so it stays the same.
   812 + 312 = 1112
5. Check the answer is in its simplest form. See whether any number except 1 divides into both the top and the bottom. If not, we are finished.
   11 and 12 have no common factor except 1, so 1112 is the answer.

Check. A different route, as decimals: 0.6667 + 0.25 = 0.9167, and our answer 1112 = 0.9167. ✓

Watch out. Never add the denominators. The denominator stays the same once the pieces are the same size.

Method. To find a fraction of an amount: divide by the denominator to find one part, then multiply by the numerator.

1. Say what 35 of 40 means. The denominator 5 says the amount is split into 5 equal parts. The numerator 3 says we take 3 of those parts. The word "of" tells us we are finding a share of an amount.
   Split 40 into 5 equal parts. Take 3 parts.
2. Divide 40 by the denominator 5. Sharing into 5 equal parts finds the size of one part (this is 15 of the amount).
   40 ÷ 5 = 8
3. Multiply by the numerator 3. The numerator 3 tells us how many parts we take. Here 8 × 3 gives the size of 3 parts.
   8 × 3 = 24
4. Write the answer. Give the answer with its units.
   35 of 40 = 24

Check. A different route: multiply first, then divide. 40 × 3 = 120, and 120 ÷ 5 = 24. The answers match. ✓ Also the other 2 parts make 16, and 24 + 16 = 40.

Watch out. Divide by the denominator first, then multiply by the numerator. Do not multiply by the denominator.

Method. To subtract fractions, give them the same denominator, then subtract the numerators and keep the denominator.

1. Read the question and decide the plan. We can only subtract pieces that are the same size. So first look at the type of numbers and at the denominators (the bottom numbers).
   56 − 34
2. Find a common denominator: the LCM of 6 and 4. We can only add or subtract pieces of the same size, so the denominators must match. The lowest common multiple (LCM) is the smallest number that both denominators divide into.
   Multiples of 6: 6, 12
   Multiples of 4: 4, 8, 12
   LCM = 12
3. Rewrite both fractions with denominator 12. Multiply the top and the bottom by the same number so the value does not change.
   56 = 1012 (× 2)
   34 = 912 (× 3)
4. Subtract the numerators and keep the denominator. The denominator only tells us the size of each piece, so it stays the same.
   1012 − 912 = 112
5. Check the answer is in its simplest form. See whether any number except 1 divides into both the top and the bottom. If not, we are finished.
   1 and 12 have no common factor except 1, so 112 is the answer.

Check. A different route, as decimals: 0.8333 − 0.75 = 0.0833, and our answer 112 = 0.0833. ✓

Watch out. Subtract in the right order: the first fraction minus the second.

Method. To put fractions in order, give them all the same denominator, then order the numerators.

1. Find the LCM of the denominators 5, 8, 12. This is the common denominator.
   LCM = 120
2. Rewrite every fraction with denominator 120. Multiply the top and bottom of each by the same number.
   35 = 72120
   58 = 75120
   712 = 70120
3. Put the numerators in order. The order is smallest first.
   70, 72, 75
4. Write the original fractions in that order. The question asks for the original fractions, not the converted ones.
   712 ,  35 ,  58

Check. As decimals: 712 = 0.5833, 35 = 0.6, 58 = 0.625.

Watch out. Always give your final answer using the original fractions, not the ones with the common denominator. And never order fractions by their denominators alone.

Method. To divide by a fraction, turn the second fraction upside down and multiply: keep, change, flip.

1. Read the question and decide the plan. Dividing by a fraction is done by multiplying by its reciprocal. First look at the type of numbers we have.
   214 ÷ 34
2. Change the mixed number to improper fraction. A mixed number is a whole number plus a fraction. Multiply the whole number by the denominator, add the numerator, and keep the denominator. This lets us calculate with a single fraction.
   214 = (2 × 4 + 1) over 4 = 94
3. Keep, change, flip. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down). For example, dividing by 1/2 asks "how many halves fit?", which is the same as multiplying by 2.
   94 ÷ 34 = 94 × 43
4. Cancel common factors. Divide a top and a bottom by a number they share, to keep the numbers small.
   94 × 43 = 31 × 11
5. Multiply the numerators, then the denominators. Now it is an ordinary multiplication: top × top and bottom × bottom.
   3 × 1 = 3
   1 × 1 = 1
   31
6. Write the answer. The bottom number is 1, so the answer is a whole number.
   31 = 3

Check. Multiply back: 3 × 34 should give 214. 3 × 0.75 = 2.25 and 214 = 2.25. ✓

Watch out. Only flip the second fraction (the one you are dividing by), never the first.

Method. To multiply fractions, multiply the numerators together and the denominators together (cancel first to keep the numbers small).

1. Read the question and decide the plan. Multiplying fractions does not need a common denominator. First look at the type of numbers we have.
   38 × 49
2. Cancel common factors first. A number on the top of one fraction and a number on the bottom of the other can be divided by a common factor. This keeps the numbers small and gives an answer already in its simplest form.
   38 × 49 = 12 × 13
3. Multiply the numerators, then the denominators. Multiplying fractions is just multiplying across: top × top and bottom × bottom.
   1 × 1 = 1
   2 × 3 = 6
   16
4. Check the answer is in its simplest form. See whether any number except 1 divides into both the top and the bottom. If not, we are finished.
   1 and 6 have no common factor except 1, so 16 is the answer.

Check. A different route, as decimals: 0.375 × 0.4444 = 0.1667, and our answer 16 = 0.1667. ✓

Watch out. Do not find a common denominator when multiplying. That is only for adding and subtracting.

Method. Work out the correct answer, then compare with Dev. Dev's method is a common mistake.

1. Find what Dev did. Dev added the tops (2 + 1 = 3) and the bottoms (3 + 5 = 8) to get 3/8.
   Dev: 23 + 15 = 2 + 13 + 5 = 38
2. Find a common denominator. Fractions can only be added when the pieces are the same size. The LCM of 3 and 5 is 15.
   23 = 1015 (× 5)
   15 = 315 (× 3)
3. Add the numerators and keep the denominator. The pieces are now the same size.
   1015 + 315 = 1315
4. Compare with Dev's answer. The correct answer is 1315, which is about 0.87. Dev's answer 38 is about 0.38.
   1315 ≠ 38
5. Write the conclusion. The answers are different, so Dev is wrong.
   Dev is not correct.

Check. As decimals: 23 + 15 = 0.667 + 0.2 = 0.867, and 1315 = 0.867. Dev's 38 = 0.375, which is less than 23 alone, so it cannot be right. ✓

Watch out. Never add the denominators. The correct method needs a common denominator first.

Method. Do it in two steps, using the amount left after the first step.

1. Find the cost of the book. 38 of £48: divide by the denominator 8, then multiply by the numerator 3.
   £48 ÷ 8 = £6
   £6 × 3 = £18
2. Find the money left after the book. Take the cost away from the starting amount.
   £48 − £18 = £30
3. Find the cost of lunch. It is 13 of the money that is left, which is £30 (not £48).
   £30 ÷ 3 = £10
4. Find the money left at the end. Take the cost of lunch away from what she had before lunch.
   £30 − £10 = £20

Check. A different route: after the book she has 58 of her money. After lunch she has 23 of that: 23 × 58 = 512. 48 ÷ 12 = 4 and 4 × 5 = £20. ✓

Watch out. “Of the money that is left” means use the new, smaller amount.

Method. If you know a fraction of the whole, divide by the numerator to find one part, then multiply by the denominator to find the whole.

1. Say what the question gives us. The boys are a fraction of the whole club. We know the number of boys, so we can find the size of the whole club.
   25 of the club = 18 boys
2. Write down what we know. The fraction 25 means the whole is split into 5 equal parts, and 2 of those parts together make 18.
   2 parts = 18
3. Find one part: divide by 2. If 2 parts make 18, then one part is 18 shared into 2.
   18 ÷ 2 = 9
4. Find the whole: multiply by 5. The whole is all 5 parts, so multiply the size of one part by 5.
   9 × 5 = 45
5. Write the answer. This is the whole amount (the number the fraction was taken from).
   The whole is 45.
6. Answer in words. The whole is the number of members in the club.
   There are 45 members in the club.

Check. Work forwards: 25 of 45 = 45 ÷ 5 × 2 = 9 × 2 = 18. ✓

Watch out. Go up to the whole by multiplying by the denominator. A common mistake is to find the fraction of the part instead.

Method. Find the sugar for one biscuit, then multiply for 20 biscuits.

1. Find the sugar for one biscuit. 6 biscuits use 3/4 cup, so share the 3/4 cup between 6 biscuits: divide by 6.
   34 ÷ 6 = 34 × 16 = 324 = 18 cup
2. Multiply for 20 biscuits. Each biscuit needs the same amount.
   18 × 20 = 208
3. Simplify. Divide the top and the bottom by 4.
   208 = 52
4. Write as a mixed number. 5 ÷ 2 = 2 remainder 1.
   52 = 212 cups

Check. A different route: 20 biscuits = 6 + 6 + 6 + 2 biscuits. Three lots of 6 need 3 × 34 = 94 = 214 cups. The 2 extra biscuits need 26 of 34 = 14 cup. 214 + 14 = 212. ✓

Watch out. Find the amount for 1 first. This is called the unitary method.

Method. Add the fractions used, then subtract the total from the whole tank.

1. Find a common denominator. To add fifths and quarters we need pieces of the same size. The LCM of 5 and 4 is 20.
   25 = 820 (× 4)
   14 = 520 (× 5)
2. Add the fractions used. Add the numerators and keep the denominator.
   820 + 520 = 1320
3. Write 1 whole tank as twentieths. A full tank is all 20 of the 20 equal parts.
   1 = 2020
4. Subtract the fuel used from the whole tank. What is left in the tank.
   2020 − 1320 = 720

Check. 1320 used + 720 left = 2020 = 1 whole tank. ✓

Watch out. “What is left” means subtract from 1 whole.

Method. To divide by a fraction, turn the second fraction upside down and multiply: keep, change, flip.

1. Decide the operation. Area of a rectangle = length × width, so width = area ÷ length.
   Width = 34 ÷ 56
2. Keep, change, flip. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down). For example, dividing by 1/2 asks "how many halves fit?", which is the same as multiplying by 2.
   34 ÷ 56 = 34 × 65
3. Cancel common factors. Divide a top and a bottom by a number they share, to keep the numbers small.
   34 × 65 = 32 × 35
4. Multiply the numerators, then the denominators. Now it is an ordinary multiplication: top × top and bottom × bottom.
   3 × 3 = 9
   2 × 5 = 10
   910
5. Check the answer is in its simplest form. See whether any number except 1 divides into both the top and the bottom. If not, we are finished.
   9 and 10 have no common factor except 1, so 910 is the answer.
6. Write the answer with its units. The width is a length, so it is in metres.
   Width = 910 m

Check. Multiply back: 910 × 56 should give 34. 0.9 × 0.8333 = 0.75 and 34 = 0.75. ✓

Watch out. Only flip the second fraction (the one you are dividing by), never the first.