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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4Topics
    |
    2 Quizzes
  2. Properties of Whole Numbers II | Week 2
    4Topics
    |
    2 Quizzes
  3. Properties of Whole Numbers III | Week 3
    4Topics
    |
    1 Quiz
  4. Indices | Week 4
    2Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1Topic
    |
    1 Quiz
Lesson Progress
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To find the unknown term in a ratio:

1. Write the ratio as a fraction

2. Cross multiply to find the unknown value

Example 1

Find the missing numbers in the following:

a. 12 : x = 20 : 35

Solution

\( \frac{12}{x} = \frac{20}{35}\; \; \; \; \; \scriptsize \; (cross \; multiply) \\ \scriptsize 20x\: = \: 12 \: \times \:35 \\ \scriptsize x = \normalsize \frac{12 \; \times \; 35}{20} \\ \scriptsize x = 21\)

b. 4 : 9 = x : 99

\( \frac{4}{9} = \frac{x}{99}\; \; \; \; \; \scriptsize \; (cross \; multiply) \\ \scriptsize 9x = 4 \: \times \: 99 \\ \scriptsize x = \normalsize \frac{4 \: \times \: 99}{9} \\ \scriptsize x = \normalsize \frac{4 \: \times \: 11}{1} \\ \scriptsize x = 44\)

Example 2

Find the missing numbers in the following equivalent ratio:

a. \( \scriptsize 12 : \square = 20 : 35 \)

b. \( \scriptsize 4 : 9 = \square : 99 \)

c. \( \scriptsize 3 : 4 =21 : \square \)

Solution

a. \( \scriptsize 12 : \square = 20 : 35 \)

\( \frac{12}{\square} = \frac{20}{35} \\ \frac{12}{\square} = \frac{4}{7}\scriptsize \; \; \; \; \; (cross \: multiply) \\ \scriptsize 4 \: \times \: \square = 12 \: \times \: 7 \\ \scriptsize \square = \normalsize \frac{12 \: \times \: 7}{4} \\ \scriptsize \square = \normalsize \frac{84}{4} \\ \scriptsize \square = 21\)

 b. \( \scriptsize 4 : 9 = \square : 99 \)

\( \frac{4}{9} = \frac{\square}{99} \; \; \; \; \; \scriptsize \; (cross \; multiply) \\ \scriptsize 9 \: \times \: \square = 99 \: \times \: 4 \\ \scriptsize \square = \normalsize \frac{99 \: \times \: 4}{9} \\ \scriptsize \square = 11 \: \times \: 4 \\ \scriptsize \square = 44\)

c. \( \scriptsize 3 : 4 =21 : \square \)

\( \frac{3}{4} = \frac{21}{\square} \; \; \; \; \; \scriptsize \; (cross \: multiply) \\ \scriptsize 3\: \times \: \square = 21 \: \times \: 4 \\ \scriptsize \square = \normalsize \frac{21 \: \times \: 4}{3} \\ \scriptsize \square =7 \: \times \: 4 \\ \scriptsize \square = 28\)

Example 4

In a car park, there are 30 white cars and 20 blue cars. 

a. What is the ratio of the white car to the blue car?

b. What is the ratio of the blue car to the white car?

Solution

a. Number of white cars =  30

Number of blue cars    =  20

Ratio of white cars to blue cars  =

White car   :   blue car

30 : 20   =  3 : 2

b. Ratio of blue car to white car =

Number of blue cars:   Number of white cars =  20 : 30

= 2 : 3

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