JSS2: MATHEMATICS - 1ST TERM
-
Properties of Whole Numbers I | Week 14 Topics|1 Quiz
-
Properties of Whole Numbers II | Week 24 Topics|1 Quiz
-
Properties of Whole Numbers III | Week 35 Topics|1 Quiz
-
Indices | Week 42 Topics|1 Quiz
-
Laws of Indices | Week 55 Topics|1 Quiz
-
Whole Numbers & Decimal Numbers | Week 64 Topics|1 Quiz
-
Standard Form | Week 73 Topics|1 Quiz
-
Significant Figures (S.F) | Week 84 Topics|1 Quiz
-
Fractions, Ratios, Proportions & Percentages I | Week 96 Topics|1 Quiz
-
Fractions, Ratios, Proportions & Percentages II | Week 104 Topics|1 Quiz
-
Fractions, Ratios, Proportions & Percentages III | Week 113 Topics|1 Quiz
-
Approximation & Estimation | Week 121 Topic|1 Quiz
Ratio
Topic Content:
- Equivalent Ratio
- Simplifying Ratio
A ratio is a way of comparing two or more quantities. The ratio is a relationship between two numbers indicating how many times the first number contains the second for example, if a basket contains, 8 oranges and 5 mangoes the ratio of oranges to mangoes is 8 ratio 5, written as 8:5 or 8 to 5.
‘Ratio’ can be written in the following form.
1. m : n
2. m to n
3. \( \frac{m}{n} \) (as fraction)
Equivalent Ratio:
Equivalent Ratios are Equal Ratios
Example:
a. 3 : 4, 6 : 8, 9 : 12, 12 : 16 are equivalent ratios because:
3 : 4 = 3 × 2 : 4 × 2 = 6 : 8
= 3 × 3 : 4 × 3: 4 × 2 = 9 : 12
= 3 × 4 : 4 × 4 = 12 : 16
b. 100 : 50, 50 : 25, 20 : 10, 10 : 5 are equivalent because
100:50 = (100 ÷ 2) : (50 ÷ 2) = 50 : 25
= (100 ÷ 5): (50 ÷ 5) = 20 : 10
= (100 ÷ 10) : (50÷ 10) = 10: 5
Simplifying Ratio:
This is writing a ratio in its simplest form or smaller numbers. To simplify any given ratio, divide both its numerator and denominator by the same number until it can no longer be simplified.
Worked Example 10.1.1:
Express the following ratios in their simplest forms
a. 21 : 14
b. 6 : 15
c. 5 : 1\( \frac{1}{2} \)
d. 0.5 : 25
Find the factor that can cancel each number in the simplification process.
Solution
a. 21 : 14 = \( \frac{21}{14}\\ \scriptsize divide \: by \: 7\\ = \frac{3}{2} \\ = \scriptsize 3 : 2 \)
b. 6 : 15 = \( \frac{6}{15}\\ \scriptsize divide \: by \: 3 \\ = \frac{2}{5} \\= \scriptsize 2:5 \)
c. 5 : 1\( \frac{1}{2} \) = \(\frac{5}{1\frac{1}{2}} \\ = \frac{5}{\normalsize \frac{3}{2}} \\ = \frac{5}{1} \: \div \: \frac{3}{2}\\= \frac{5}{1} \: \times \: \frac{2}{3} \\ = \frac{10}{3}\\= \scriptsize 10 \: : \:3\)
d. 0.5 : 25 = \( \frac{5}{10} \scriptsize \: \div \: 25 \\ = \frac{5}{10} \: \times \: \frac{1}{25} \\ = \frac{5}{250} \\ = \frac{1}{50} \\ = \scriptsize 1\: : \: 50 \)