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Mathematics: Ratio and Rates by Abioye T

This document provides examples and explanations of ratios and rates. It defines a ratio as comparing two quantities of the same kind numerically. Examples given include using ratios to solve problems involving dividing money paid to workers based on hours worked. Another example shows using a ratio to calculate the number of women in a village given the ratio of men to women and the number of men. The document also provides a brief example of calculating density using mass, volume, and the formula of density.

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Ekemini-Abasi
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81 views9 pages

Mathematics: Ratio and Rates by Abioye T

This document provides examples and explanations of ratios and rates. It defines a ratio as comparing two quantities of the same kind numerically. Examples given include using ratios to solve problems involving dividing money paid to workers based on hours worked. Another example shows using a ratio to calculate the number of women in a village given the ratio of men to women and the number of men. The document also provides a brief example of calculating density using mass, volume, and the formula of density.

Uploaded by

Ekemini-Abasi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Mathematics

Ratio and Rates

By Abioye T.
Objectives

The students should be able to:

(i) solve problems involving ratios.

(ii) apply the knowledge of ratio in solving


problems on rates.
Two quantities are said to be in the ratio A:B if
the first quantity can be divided into A equal
parts and the second into B equal parts, each
part of the first being equal to each part of the
second.

A ratio is a numerical way of comparing


quantities of the same kind i.e. the quantities
must be expressed in the same units.
Example
(a) In a certain village, the ratio of men to women is
40:43. If there are 6 000 men in the village, find the
number of women.
Solution

Let the number of women be x


Then 40:43=6000: X

x= (6000 x 43) ÷ 40= 6450


women are 6450.
Dantala, Uche and Lekan work on a farm for 5, 7
and 8 hours respectively. For this they are paid a
total of NI 200.60. How should the money be
divided?

The money should be divided according to the


number of hours worked i.e. in the ratio 5:7:8.
The total number of shares 5+7+8 = 20
Then 1 share =1 200.60 ÷20 = N 60.03
Dantala should receive N(5 x 60.03)3 N300.15.

Uche should receive N(7 x 60.03)=N420.21.

Lekan should receive N (8 x 60.03)% N480.24.


(a) If 11 people paint a building in 21 days,
how long would 7 people take?
Solution
7 people take more days than 11 people. Then
the number of people decrease in the ratio 7:
11. Thus, the time taken is increased in the
ratio 11:7. Since time is to be found, then 11
people take 21 days.

: 7 people take (21×11÷7) days


= 33 days
Example
A wooden cube has a mass of 504.8 g. If onset of
the cube measures 5 cm, calculate the density of
the wood correct to 2 s.f.

Solution
Volume of cube = 5 x 5 x 5 cm’= 125 cm
Density of wood =504.8÷125
= 4.038 4
= 4.0 g/cm³ (2 s.f.)
Evaluation.
1. Okoh, Abdul and Ola share N73.00 such that
Ola gets N5.00 more than Abdul and Okoh gets
N2.00 more than Abdul. In what ratio did they
share the amount?

2.The ages of a parent and child are in the ratio


7:2. If the child's age now is 16, what will be the
ratio of their ages in 4 years time?

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