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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4 Topics
    |
    1 Quiz
  2. Properties of Whole Numbers II | Week 2
    4 Topics
    |
    1 Quiz
  3. Properties of Whole Numbers III | Week 3
    5 Topics
    |
    1 Quiz
  4. Indices | Week 4
    2 Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5 Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4 Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3 Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4 Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6 Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4 Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3 Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1 Topic
    |
    1 Quiz
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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 = \( \frac{5}{10} \scriptsize \: \div \: 25 \\ = \frac{5}{10} \: \times \: \frac{1}{25} \\ = \frac{5}{250} \\ = \frac{1}{50} \\ = \scriptsize 1\: : \: 50 \)

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