Fractions

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 245

5. A gar­dener pre­pares a mix com­pro­mis­ing of 545 kgs of top­soil, ¾ kgs of fer­til­izer and 157kgs of sand. What is the total weight of this mix­ture? Write you answer as a mixed num­ber in its sim­plest form.

6. What is 957 — 389? Write your answer as a mixed num­ber in its sim­plest form.

7. Cal­cu­late the area of this shape:

Multiplying fractions to calculate area of irregular 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 = 138

3. 434 ÷ 212 = 19/4 ÷ 5/2 = 19/4 x 2/5 = 19/2 x 1/5 = 19/10 = 1910

4. 734 x 245 = 31/4 x 14/5 = 155/20 x 56/20 =

8680/400 = 868/40 = 434/20 = 217/10 = 21710

5. 545 + 34 + 15= 812/140 + 105/140 + 240/140 = 1157/140 = 8 37140

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

6. 95- 38= 68/7 — 35/9 = 612/63 — 245/63 = 367/63 = 5 5263 

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

7. Shape = 2 rec­tan­gles 4 78 x 3 56 and  8 35 x (4 78 — 2 89)

4 78 x 3 56  = 39/8 x 23/6 = 897/48 = 299/16 = area of first rectangle

4 78 — 2 89 = 39/8 — 26/9 = 351/72 — 208/72 = 143/72

Sec­ond rectangle =

8 3x 143/72 = 43/5 x 143/72 = 6149/360 = 17 29360 

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

= 35 553720  

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.

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