Lesson
Title: Ratio, Proportion, and Rate.
Objective:
At the end of this lesson, you should be able to:
solve problems related to Ratio, Proportion, and Rate.
What you should know:
You should be familiar with,
1. Conversion of a scientific or mathematical unit to another.
2. Finding LCM of numbers.
3. Multiplication of fractions and other basic arithmetic operations.
Introduction:
Ratio is a term used to compare two numbers, that is, it shows how many times one number contains the other.
The ratio of the two numbers can be compared as the following:
1. a:b to be compared as n:1. This means how many times b is in a a/b : b/b
2. a:b to be compared as 1:n. This means how many times a is in b, a/a : b/a
N:B ratio can be presented as a fraction of a/b
Proportion: In proportion, a ratio can be used to compare another ratio, that is, which ratio is greater or less than another, a:b or c:d.
Proportional Division: This means dividing some quantity of items into a given ratio.
Presentation /Steps:
Ex. 1 Express 6m to 8m in the form of n:1.
=> n:1 means, 6/8 : 8/8 = 0.75: 1.
Ex. 2. Express the ratio 18cm: 946.4m in the form of 1:n.
For this example, the ratio values have different rates, so, convert 946.4m to CM.
Step:
100cm = 1 =>100 * 946.4 = 94640cm. We now have the same unit, 18cm: 94640cm.
=> 1:n means, 18/18 : 94640/18 = 1:5257.8.
Ex. 3. Find which of the pairs of ratios is lesser, I 1:5, 4:3.
Step:
1:5, 4:3 => 1/5 , 4/3
When two or more ratios are to be compared,
Find the LCM of the denominators of the fractions: LCM of 5 and 3 = 15.
First fraction :
=> Use 15 to divide the denominator of 1/5 (15 ÷ 5 = 3) and multiply the result by the numerator and denominator 1*3/5*3 = 3/15
Second fraction :
=> Use 15 to divide the denominator of 4/3 (15 ÷ 3 = 5) and multiply the result by the numerator and denominator 4*5/3*5 = 20/15
=> The final proportional ratios are 3/15 : 20/15
=> Therefore, 3/15 is lesser.
Ex. 4. A mother is to share a carton of noodles between John and Idara so that their shares are in the ratio 7 : 3 respectively.
Step:
N:B. A carton of noodles contains 40 sachets of noodles.
=> To solve problems like this, sum the ratios, 7 + 3 =10.
=> Use the ratio sum (10) as the denominator for each of the ratios (7,3) 7/10, 3/10, and multiply each by the item (40 sachets of noodles) to be shared.
=> (7/10) * 40 = 28
=> (3/10) * 40 = 12
=> Therefore, John and Idara will get 28 and 12 sachets of noodles respectively.
Ex. 5. Adams, Musa, and Zainab are to share ₦68 so that for every ₦1 that Zainab gets, Musa gets ₦2, and for every ₦3 that Musa gets, Adam gets ₦4. How much does Musa get?
Step 1: Interpretation of the question.
=> If Zainab has 1 share, then Musa has 2 shares.
=> For every 3 shares Musa gets, Adam gets 4; this means that to get Adam's share, divide Musa's initial share by his new share and multiply by 4 (Adam's initial shares).
2/3 * 4 = 8/3
=> The ratio is now 1: 2: 8/3, Zainab, Musa, and Adam.
If the ratio is simplified further, it'll be 3:6:8 (the denominator-3 is used to multiply all through.).
Step 2: To determine how much Musa gets.
=> Add all the numbers of the ratio, 3.6:8.
3 + 6 + 8 = 17.
=> Musa part of the ratio is 6, so, 6/17 * 68 = ₦24.
=> Therefore, Musa's share is ₦24.
Summary / Conclusion :
The ratio is used to compare two numbers and can be presented as fractions.
Proportion is used to compare a ratio with another ratio.
Rates are the difference in units of a ratio or proportion.
Exercise:
1. Divide 1170 between Kola and Emma so that their shares are in the ratio of 8:5.
2. Three students share ₦59920, the first student gets 2 times the second student, and the second student gets 2 times as much as the third student. What is the first student's share of the money?