MATHEMATICS PRIMARY SIX – FRACTIONS

Exercise 01          Revision questions on fractions

1. Change 5 to a mixed number.

                  2

2. What is 1 ½ as an improper fraction.
3. (a) Reduce  6 to its lowest terms.

                         9

(b) Reduce  48 to its lowest terms

                    108

4. Change (a) ¾ to a decimal fraction (b) 2 ¼ to a decimal fraction.
5. Convert (a) 0.25 to a common fraction

(b) 1.25 to a common fraction.

6. Change ²/₃ to a decimal fractions
7. What is 0.333—as a common fractions
8. Change (a) 0.3636 (b)           2727 to common fractions.
9. Write (a) 0.122 ——- (b)           24555— to common fractions
10. Arrange the following fractions in ascending order.

(a)           1,   1,   1,   1                           (b)           3,     5     1     2

               4    6    2    3                                           5      6     5     3

1. Arrange the following fractions in descending order.

(a)           2,   5,     5,                              (b)           3,     2 ,    1

               5    12    6                                              4       3      6

2. Add: (a)           3     +     1               (b)           1  ²/₂ + 2  ¼

                            8              4

3. (a) What is the sum of a quarter and a third?

Moses bought a half litre of milk and later bought three quarter litres of milk because the milk was not enough. How much milk did he buy altogether?

Exercise 02          Revision Exercises on Fractions

1. Subtract: (a)           1    –    1                  (b)    2  ½  –  1 ¾

                                     2         4                  (c)           1  –   ¾

(c)           5  –   3                     (d) 3  ¼  –   1  2/3

               6      8

2. (a) What is the difference between three – quarters and a half

    (b) Subtract a quarter from ½

3. A farmer uses a half of his shamba for tomatoes, ²/₃ to grow onions

(a)           How much land does he use for farming?

(b)           How much land remained unused?

4. A quarter of the pupils in my class are girls. one day ½ of the girls number           didn’t attend  lessons. What fraction of  the girls was absent.
5. Simplify: (a)           1  –    1    +    2                       (b)           2   +   1  –  2

                                    4       2          3                                      5         3     3

(c)           1   +    1    +     4

               3         6          4

6. Find the value of 2 ¼ –  2  –    5

                                             3        6

7. Work out (a) 4  ¸  ¹/₃                                   (b)      ³ /₈  ¸ 6

8. Simplify: (a)           3    ¸    3                 (b)           3  ¹/₈  ¸  3  ¾

                                   4          5

9. Work out 4 ¹/₅ ¸ (1 ¹/₆ + 2 ¹/₃)
10. Simplify: (2 ½ + ⁵/₆) ¸ 1 ²/₃
11. Find the value of 1 ½ – 2 ¹/₃ + 1 ¼
12. Work out (a)           1  +  1   ¸   1          (c)           5   ¸  2  –  1  x   1

                                     2      4        3                        6      3      2       3

(b)           2  –   1   of 1           (d)           3  of 4  –  1   ¸  1

               3      2        3                           4      5      6      2

(e)           1  ¸   1   of  2

               3       2         3

3. A club spent a quarter of its earnings and saved the rest. What fraction was saved?

Exercise 03          Revision Exercise on Fractions

1. What is the reciprocal of (a)           2?            (c)           y?            (e)   5?

(b)           3 ?         (d)   1  ½ ?

               5

2. Use the reciprocal method and work out:

(a)           3    ¸   1                  (b)           1 ¹/₃ ¸  2  ¹/₃

              4         4

3. Use the LCM method and simplify:

(a)           2 ½ ¸ 1 ¼                (b)         3    ¸    1

                                                            5         10

4. How many quarter litre bottles can be got from 5 litres?
5. A sixth of my salary is 50,000/=. How much is my salary?
6. I spent 20,000/= out of my salary amounting to 40,000/=. What fraction of my salary did I spend?
7. Add: (a)           5  + 0.6               (b)           8.03 + 2 .1        (c)  0.05 + 22.5
8. Subtract: (a) 12.5 – 1.2 (b) 0.86 – 0.07                (c)   4  – 0.9
9. Add: 2.05 to 30.6
10. Subtract: 1.4 from 34
11. Work out (a) 7 – 4.27 + 3.14 (c)           (3.021 – 2.2) + 0.04

(b) 6 – (0.43 + 1.62              (d)           5.23 + 4 – 6.02

2. Maurice bought 6.4 litres of paraffin for some of his wall paint. He later bought 2.6 litres to mix all the remaining paint. How many litres of paraffin did he buy altogether?
3. Morgan was given 3.5 grammes of juice powder but 2.6 grammes got spoilt. How many grammes remained?
4. Multiply:(a) 9 by 0.2              (b)1.23 by 3.2       (c) 2 x 0.75
5. Divide: (a) 6 by 0.04 (b)           02 by 2

Exercise 04          Revision Exercise on Fractions

1. Divide: (a)           1.2 by 0.03            (b)           0.064 ¸ 0.06
2. Work out: (a)           0.8 x 0.4                                (b)           0.04 x 2

                                           0.2                                                        0.8

3. The length of one side of a square is 4.5 metres.

(a)           What is the perimeter of the square?

(b)          What is its area

4. A rectangular garden measures 2.8 cm by 1.2 cm. Find its

(a)           perimeter               (b)           Area

5. A parcel weighting 8.5 kg contains packets of salt each weighting 0.25 kg.           how many packets of salt are in the parcel?
6. There are 20 boys and 30 girls in a class. What is the ratio of

(a)           Boys to girls          (b)           girls to boys

7. Express the following rates as fractions

(a)           1 : 6        (b)           2 : 4        (c)           ½ ¸ ¼     (b)           0.2 : 0.4

8. Change the following fractions to ratios

(a)           3              (b)           1 ¼                         (c)           8

               4                                                                            4

9. Peter and Sseku shared 32 sweets in the ratio 3 : 5. How many sweets did each get?
10. A man and his wife shared an amount of money in the ratio 2 : 3 respectively if his wife got 9,000/=

(a)           How much money did they share?

(b)           How much money did the man get?

1. 120 oranges were shared by Amos, John and Mary in the ratio 1 : 2 : 3 respectively. How many oranges did each get?
2. The ratio of sharing 24 goats by A, B and C is 2 : 3 : 7. If B got 6 goats how many goats did each of the rest get?

Exercise 05          Revision Exercise on Fractions

1. The ratio of boys to girls in a class is 2 : 5 If there are 14 boys, how many pupils are in the class?
2. Increase 320 in the ratio (a) 4 : 2 (b)           3 : 2
3. Decrease 480 in the ratio (a) 2 : 4                  (b) 1 : 2
4. The price of an article was reduced from 18,000/= in the ratio 2 : 3. Find the new price.
5. The cost of an item was increased to 4000/= in the ratio 4 : 3. What was its original cost?
6. The price of a plastic basin was reduced to 12,000/= in the ratio 2: 3 Calculate its original price.
7. The number of pupils in Kasanke Primary School rose from 400 to 480 pupils. What is the ratio of increase?
8. In what ratio did the enrolment of school C fall from 60 pupils to 25 pupils in the previous year?
9. If one exercise book costs shs 300/=, what is the cost of 4 similar exercise books?
10. Three pencils cost 2400/=, what is the cost of 2 pencils of a similar kind?
11. Shs 3600/= can buy 2 pairs of socks.
12. 2 men can do a piece of work in 4 days. How many days will 6 men take to do the same piece of work at the same rate?
13. 5 women can did a garden in 15 days. How many woman can dig the same garden in 5 days at the same working rates?
14. A bus moving at a speed of 60 km/hr takes 2 hours to cover a certain distance. How long will the car take to cover the same journey at 120 km/hr?

Exercise 06          Revision Exercise on Fractions

1. Express (a) 4% as a fraction.           (b)           12 ¼ % as a fraction

• Change the following fractions to percentages.

(a)           2              (b)           3              (c)               1

               5                              4                                 2

3. Change the following as decimal fractions

(a)           0.5          (b)           1.25        (c)           0.075      (d)           0.014

4. Express the following as decimal fractions.

(a)           0.2 %      (b)           0.25%    (c)           2.45%

5. Change the ratios below to percentages.

(a)           1 : 4        (b)           3 : 8        (c)           2 : 3

6. Convert the following percentages to ratios

(a)           25 %                       (b)           75%                        (c)           125%

7. If 25% of a choir are female, what percentage are the male?
8. There are 50 children in our poultry house. We sold 15 of them yesterday.

(a)           What percentage of chicken was sold?

(b)           Calculate the percentage of chicken that remained

9. What is 20% of 1800/=?
10. Find 15% of an hour.
11. Find 12 ½ of 800/=
12. A school enrolled 600 pupils of which 250 are boys.

(a)           How many are the girls?

(b)           What percentage are the (i)   boys                    (ii)           girls

3. (a) Express 500g as a percentage of 1 kg

(b)           Express 30 minutes as a percentage of 2 hours

(c)           Express 15 goats as a percentage of 90 goats

(d)           What percentage are 125 g of a kg?

Exercise 07          Revision Exercise on Fractions

1. 15% of a number is 60. find the number
2. 10% of my cattle are bulls. The bulls are 45. How many cattle are in my kraal?
3. Increase 400 by 20%
4. The number of children in a school last year was 360. This year the number increased by 25%. What is the number of the pupils in the school this year?
5. Decrease 280 by 14%.
6. An officer’s salary is shs 80,000/=. How much will his salary be

(a)           If its decreased by 20%      (b)           If  its increased by 25%

7. (a) Maizi bought a book at 450/= and sold it at 480/=. What was his profit?

(b)           Find his percentage profit.

8. Mugerwa bought a radio at shs 9450/- and sold it at 9000/=. What was his loss?
9. What is the percentage loss of buying an item at 800/= and selling it at 600/=.
10. The marked price of an article is 4000/=. If a trader allows a discount of 2% find: (a)  The discount allowed

(b)  The actual price after the discount

1. Mukasa bought a book at 400/=, a pen at 500/= and a set mathematical instruments at 600/= and was offered a discount of 5%. How much did he pay altogether?

Exercise 08          Revision Exercise on Fractions 

1. Calculate the simple interest on 20,000/= at a rate of 5 % per annum for 2 years.
2. Find the simple interest on 12,000/= at a rate of 4% per year for 2 ½ years.
3. Find the amount of money a trader will withdraw at a principle of 50,000/= at a rate of 2 % per annum for 5 years.
4. Calculate the time taken for 15,500/= to yield 15000/= at a rate of 5 % per year.
5. Find time taken on

6. Find the rate at which 40,000/= will yield 3,600/= after 2 years.
7. What principal will give an interest of 2,800/= at 10% interest for 2 years?