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FRACTIONS, RATIOS, DECIMALS AND PERCENTAGES

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Fractions and Percentages

A fraction can be converted to decimal by dividing the numerator by its denominator. It can be changed to percentage by simply multiplying by 100.

Example 5.1

  • Change 3/8 into a decimal and percentage
  • Convert 0.145 to percentage

Solution

1)         3/8 = 0.375 in decimal

3/8 x 100% = 37.5%

2)         0.145×100=14.5%

 

Example 5.2

To change percentage to decimal fraction, simply divide by 100 and then convert to decimal fraction. E.g. convert 92% to decimal

 

Solution

92

100

920

900

200

200      =0.92

 

 

Example 5.3

  1. Change the following to percentages

(a) 0.125    (b) 0.002

 

Solution

(a) 0.125×100% = 12.5%

(b) 0.002 = 0.002×100% = 0.2%

 

  1. Change the following to decimal fractions

(A) 45 %    ( b) 8/3%

 

Solution

  1. 45/100=0.45
  2. 8/3= 8/3 ÷100/1= 8/3 x 1/100 = 8/300 = 4/150 = 2/75

0.02666

 

75        200

150

500

450

500

450

500

=0.0267

Class work

  1. Change the following to percentage

(a) 0.264 (b) 0.875

 

  1. Change the following to decimal fractions

(A) 60% (b) 52/3%

 

APPLICATION OF DECIMAL FRACTIONS AND PERCENTAGES

Consider the following examples.

    1. Find 15% of 2.8kg
    2. Express 3.3 mass a percentage of 7.5
    3. Find 331/3 % of8.16litres

 

Solution

  1. 15/100 of 2.8kg

15/100 x 2.8 x 1000g

15/100 x 2800

=420g

=420/1000

=0.420kg

 

  1. b. 3.3/7.5 x 100/1

33/75 x 100/1

11×4 = 44%

 

  1. c. 331/3% of 8.16litres

100/3 of 8.16litres

100/3 of 8.16litres

100/3 x 8.16litres

100/3 x 8.16 x 1000 (1litre=1000cm3)

100/3 x 8160

100/3 ÷100/1 x 8160

100/3 x 1/100 x 8160

=2700/1000= 2.720litres

 

Class work

  1. Express1.5 as a percentage of 2.5 m
  2. Find 662/3 % of2.4m

 

Proportion

Proportion can be solved either by unitary method or inverse method. When solving by unitary method, always

  • write in sentence the quantity to be found at the end.
  • decide whether the problem is either an example of direct or inverse method
  • find the rate for one unit before answering the problem.

 

Examples

  1. A worker gets N 900 for 10 days of work, find the amount for (a) 3 days (b) 24 days (c) x days

 

Solution

For 1 day  = N 900

1 day = 900/10 = N90

  1. For 3 days =3 x 90 = 270
  2. For 24 days = 24×90 = N 2,160
  3. For x days =X x 90 = N 90 x

 

Inverse Proportion

Example

  1. Seven workers dig a piece of ground in 10 days. How long will five workers take?

Solution

For 7 workers =10 days

For 1 worker =7×10=70 days

For 5 workers=70/5 =14 days

  1. 5 people took 8 days to plant 1,200 trees, How long will it take 10 people to plant the same number of trees

 

Solution

For 5 people =8 days

For 1 person =8×5=40 days

For 10 people =40/10 =4 days

 

Class Work

  1. A woman is paid N 750 for 5 days, Find her pay for (a) 1 day (b) 22 days
  2. A piece of land has enough grass to feed 15 cows for x days. How long will it last (a) 1 cow (b) y cows
  3. A bag of rice feeds 15 students for 7 days .How long would the same bag feed 10 students

Note on direct proportion: this is an example of direct proportion .The less time worked (3 days) the less money paid (#270) the more time worked (24 days) the more money paid (N N 2,160)

 

Ratio

Ratio behaves the same way as fraction. Ratios are often used when sharing quantities..

 

Example

600/800=600/800=3/4

300-400=600-800=1200-1600=3=4

 

Example

  1. Express the ratio of 96 c: 120c as simple as possible

Solution 96c: 120c=96/120=4/5=4.5

  1. Fill in the gap in the ratio of 2:7=28

 

Solution
       let the gap be X

2/7 = X/28

7X =2 x 28

X=2 x 28/7

X=2 x 4

X = 8

  1. Two students shared 36 mangoes in the ratio 2:3 How many mangoes does each student get?

Solution

Total ratio =2+3=5

First share=2/5×35/1=21 mangoes

 

Rate

Rate is the change in one quantity to the other. Examples are 45km/hr, a km, 1 litre etc

Worked examples

  1. A car goes 160 km in 2 hrs what is the rate in km/hr?

 

Solution

In 2 hrs the car travels 160 km

In 1 hr the car travels 160/2=80km

Therefore the rate of the car is 80km/hr

  1. A car uses 10 litres of petrol to travel 74 km. Express its petrol consumption as a rate in km per litre.

 

Solution

10 litres =74 km

1 litres = 74/10 km

=7.4 km

 

Class work

  1. A car factory made 375 cars in 5 days, Find its rate in cars per day.
  2. A car travels 126 km in 11/2 hrs. Find the rate in km per hr.

 

WEEKEND ASSIGNMENT

  1. 5 men build in 10 days, how long would it take 25 men?

(a) 3 days (b) 2 days (c) 5 days (d) 10 days

  1. A girl buys 7 pens for N How would ten pens cost? (a)#300(b)#30(c)#3(d)#200
  2. Fill in the gap in m: a =16:24 (a) 10 (b) 12 (c) 4 (d) 6
  3. Express 90km /hr: 120km /hr as simple as possible (a) 4:3 (b) 3:4 (c) 2:3 (d) 3:2
  4. A factory makes N 2000 pencils in 10 days, Find its production rate of pencils per day (a) N 20 per day (b) N 100 per day(c) N 50 per day (d) N 200 per day

                                        

THEORY

  1. Find 50% of 3.5m
  2. A bag of corn can feed 100 chicks for 12 days. How long would the same bag feed 80 chickens?

 

See also

H.C.F & L.C.M AND PERFECT SQUARES

WHOLE NUMBERS AND DECIMAL NUMBERS

BASIC OPERATION OF INTEGERS

WEIGHT

VOLUME OF CYLINDER

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