### Overview

Some people are fazed by fractions but if you learn a few rules I think you may be able to pick up some easy marks. You have to be able to add, subtract, multiply and divide fractions. Plus you need to be able to compare fractions, and understand reciprocals and mixed numbers.

### Fractions Questions

1. 1/4 of Arsenal’s revenue comes from commercial activities, 2/5 comes from match day receipts, the rest comes from TV broadcasting rights. What fraction of Arsenal’s revenue comes from TV?

2. What is the reciprocal of 8/11? Give your answer as a mixed number.

3. What is 4¾ ÷ 2½? Give your answer as a mixed number.

4. Calculate 7¾ x 2^{4}⁄_{5}

5. A gardener prepares a mix compromising of 5^{4}⁄_{5} kgs of topsoil, ¾ kgs of fertilizer and 1^{5}⁄_{7}kgs of sand. What is the total weight of this mixture? Write you answer as a mixed number in its simplest form.

6. What is 9^{5}⁄_{7} — 3^{8}⁄_{9}? Write your answer as a mixed number in its simplest form.

7. Calculate the area of this shape:

### Fractions Approach

**1. 5. & 6**. These involve adding and subtracting fractions. To add fractions:-

a) Find a common denominator (bottom of fraction). An easy way to find a common denominator is to simply multiply them. Alternatively you could use the knowledge you gained in Factors, Powers and Roots to find the lowest common multiple.

b) For each fraction, multiply the numerator (top of fraction) by the same amount as you used to convert the denominator to a common denominator.

c) The answer will be the sum of the revised numerators over the common denominator.

d) Simplify (not necessary if you have used the lowest common denominator) and write as a mixed number (integer and fraction) where possible.

To subtract one fraction from another, use the same method but subtract one numerator from the other.

Adding and subtracting fractions is yet another skill that is best learnt and understood by working through some questions and answers.

**2.** To find the reciprocal of a fraction just turn the fraction upside so 1/2 becomes 2/1 =2.

**3. 4. & 7.** To multiply fractions, you just need to multiply out the numerators and denominators. Questions will often involve mixed numbers. Convert any mixed numbers to improper fractions (e.g convert 1 1/2 to 3/2), simplify if possible, multiply the top and bottom. Finally present your answer in the simplest form and if appropriate as a mixed number.

To divide by a fraction simply turn the fraction upside down and multiply. Again if you have mixed numbers, convert to improper fractions as the first step.

a) Convert any mixed numbers to improper fractions.

b) Turn the fraction you are dividing by upside down.

c) Multiple the top and bottom halves of the fractions.

d) Simplify the answer and, where possible, convert to a mixed number.

### Fractions Answers

1. 1 — 1/4 −2÷5 = 1 — 5/20 — 8/20 = 7/20

2. Reciprocal of 8/11 = 11/8 = 1^{3}⁄_{8}

3. 4^{3}⁄_{4} ÷ 2^{1}⁄_{2} = 19/4 ÷ 5/2 = 19/4 x 2/5 = 19/2 x 1/5 = 19/10 = 1^{9}⁄_{10}

4. 7^{3}⁄_{4} x 2^{4}⁄_{5} = 31/4 x 14/5 = 155/20 x 56/20 =

8680/400 = 868/40 = 434/20 = 217/10 = 21^{7}⁄_{10}

5. 5^{4}⁄_{5} + ^{3}⁄_{4 } + 1^{5}⁄_{7 }= 812/140 + 105/140 + 240/140 = 1157/140 = 8 ^{37}⁄_{140 }

NB– This was a rubbish question I devised. I’m sure in “real” exams questions would give more convenient answers!

6. 9^{5}⁄_{7 }- 3^{8}⁄_{9 }= 68/7 — 35/9 = 612/63 — 245/63 = 367/63 = 5 ^{52}⁄_{63 }

Again I’m not sure actual questions would be this awkward!

7. Shape = 2 rectangles 4 ^{7}⁄_{8} x 3 ^{5}⁄_{6} and 8 ^{3}⁄_{5} x (4 ^{7}⁄_{8} — 2 ^{8}⁄_{9})

4 ^{7}⁄_{8} x 3 ^{5}⁄_{6} = 39/8 x 23/6 = 897/48 = 299/16 = area of first rectangle

4 ^{7}⁄_{8} — 2 ^{8}⁄_{9} = 39/8 — 26/9 = 351/72 — 208/72 = 143/72

Second rectangle =

8 ^{3}⁄_{5 }x 143/72 = 43/5 x 143/72 = 6149/360 = 17 ^{29}⁄_{360 }

Total area of shape = 299/16 + 6149/360 = 13455/720 + 12298/720 = 25753/720

= 35 ^{553}⁄_{720 }

Yet again I think actual GCSE questions are likely to have answers that are neater to give you encouragement that you are on the right tracks.