JSS2: MATHEMATICS - 1ST TERM
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Properties of Whole Numbers I | Week 14 Topics|1 Quiz
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Properties of Whole Numbers II | Week 24 Topics|1 Quiz
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Properties of Whole Numbers III | Week 35 Topics|1 Quiz
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Indices | Week 42 Topics|1 Quiz
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Laws of Indices | Week 55 Topics|1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics|1 Quiz
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Standard Form | Week 73 Topics|1 Quiz
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Significant Figures (S.F) | Week 84 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics|1 Quiz
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Approximation & Estimation | Week 121 Topic|1 Quiz
Direct Proportion
Topic Content:
- Meaning of Direct Proportion
What is Direct Proportion?
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.
Worked Example 11.2.1:
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:
Number of pens = 20 : 45
cost of pens = ₦100
These 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 × 5
= ₦225
∴ 45 similar pens costs ₦225
Worked Example 11.2.2:
If 9000 g 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
\( \frac{6}{1} = \frac{3150}{x} \\ \scriptsize cross \: multiply \\ \scriptsize 6x = 3150\\ \\ \scriptsize x = \normalsize \frac{3150}{6} \\ \\ \scriptsize x = ₦525\)