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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 said to be in direct proportion if their ratios always remain the same as the quantities increase or decrease. In other words, as one quantity increases, the other increases, and vice-versa, at the same rate.

Example 1

If 20 pens cost ₦100, what is the cost of 45 similar pens?

Solution

Let the cost of 45 pens be ₦x 

Express each quantity as a ratio:

No of pens =  20: 45

cost of pens = 100  

This ratios are equivalent for direct proportion

20  : 45    =  100 :   x

\( \frac{20}{45} = \frac{100}{x} \)

cross multiply

\( \scriptsize 20 \: \times \: x = 45 \: \times \: 100 \)

Divide both sides by 20

\( \frac{20x}{20} = \frac{45 \: \times \: 100}{20} \)

x = 45 x 5  

=   225

Example 1

If 9000g of meat cost ₦3150, what is the cost of \( \scriptsize 1 \normalsize \frac {1}{2}\scriptsize kg\)?

Solution

Let the cost of  \( \scriptsize 1 \normalsize \frac {1}{2}\scriptsize kg\) be x

Mass of meat   =  9000g :  \( \scriptsize 1 \normalsize \frac {1}{2}\scriptsize kg\)

= 9000g : \( \frac {3}{2}\scriptsize kg\)

convert kg to g

= 9000g : \( \frac {3}{2}\scriptsize \: \times \: 1000g\)

= 9000g : 1500g

= 90 : 15

= 6 : 1

Cost of meat = 3150 :  x

Both ratios are equivalent

6 : 1   =  3150 :  x

\( \frac{6}{1} = \frac{3150}{x} \\ \scriptsize cross \: multiply \\ \scriptsize 6x = 3150\\ \\ \scriptsize x = \normalsize \frac{3150}{6} \\ \\ \scriptsize x = ₦525\)
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