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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
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Two quantities are in inverse proportion if one increases and the other decreases at the same rate.

Example 1

35 workers can build a house in 16 days. How many days will it take 28 workers working at the same rate to build the same house?

Solution

1. Let x represent the number of days it will take 28 works.

No of workersNo of days
3516
28 (the number of workers decreased)x (the number of days will increase)
\( \scriptsize x \: \times \: 28 = 35 \: \times \: 16 \)

28    =   35 x 16

Divide both sides by 28

\( \frac{28x}{28} = \frac{35 \; \times \; 16}{28} \)

\( \scriptsize x = \normalsize \frac{35 \; \times \; 16}{28} \)

\( \scriptsize x = \normalsize \frac{5 \; \times \; 16}{4} \)

\( \scriptsize x = 5 \; \times \; 4 \)

\( \scriptsize x = 20 \; days\)

Example 2

20 men can do a certain job in 10 days. How long will it take

a. 1 man

b. 4 men

c.  x men

Solution:

a. 1 man

No of menNo of days
2010
1 (the number of men decreased)y (the number of days will increase)

y   x  1  =   20 x 10

y  =  200 days

It will take 1 man 200 days

b. 4 men

No of menNo of days
2010
4 (the number of men decreased)b (the number of days will increase)

4 x b =  20 x 10

4b  = 200

Divide both sides by 4

\( \frac{4b}{4} = \frac{200}{4} \\ \scriptsize b = 50 \)

It will take 4 men 50 days 

c. x men

If it takes 1 man 200 days

It will take x men \( \frac{200}{x} \) days

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