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
Increasing or Decreasing a Quantity in a Given Ratio
Topic Content:
- Increasing or Decreasing a Quantity in a Given Ratio
- End of Lesson Evaluation Questions
1. To increase a given quantity by a given ratio, use the ratio as a multiplying factor such that the numerator is greater than the denominator.
2. To decrease a given quantity by a given ratio, use the ratio as a multiplying factor such that the numerator is less than the denominator.
Multiplying Factor = \( \frac{new \; quantity}{old \; quantity} \)
Worked Example 10.4.1:
Increase the following quantities in the given ratio:
a. 180 km in the ratio of 3:2
b. ₦500 in the ratio of 7:5
Solution
a. New quantity = \( \scriptsize 180 \; \times \; \normalsize \frac{3}{2} \scriptsize = 270 \)
b. New quantity = \( \scriptsize ₦500 \; \times \; \normalsize \frac{7}{5} \scriptsize = ₦700\)
Worked Example 10.4.2:
Decrease the following quantities in the given ratio
a. 180 km in the ratio 2:3
b. ₦500 in the ratio 3:5
Solution
a. New quantity =\( \frac{2}{3}\scriptsize \; \times \; 180 km = 120km \)
b. New quantity = \( \frac{3}{5}\scriptsize \; \times \; ₦500 = ₦300\)
Evaluation Questions:
1.
a. What percentage of 300 kobo is 120 kobo
b. What percentage of 10m is 200cm?
c. Express ₦600 as a percentage of ₦2400
d. Express 50 as a percentage of 150?
e. What percentage of 200km is 40000m?
2. Express the following ratios in their lowest forms.
a. 16: 36
b. \( \frac{3}{5} \scriptsize \: : \: 2 \)
c. \( \scriptsize 0.2 \: : \: \normalsize \frac{1}{2} \)
d. 200: 600
e. 30: 150
f. 6hrs : 1 day
View Answers3. Find the missing numbers in the following equivalent ratios
a. \( \scriptsize 4\: : \: \square = 6 \: : \: 21 \)
b. \( \scriptsize 2\: : \: \square = 14 \: : \: 35 \)
c. \( \scriptsize 3\: : \: 5 = \square \: : \: 1000 \)
d. \( \scriptsize 12 \: : \: 15 = \square \: : \: 25 \)
View Answers4.
a. Share ₦900 between Mary and Martha in the ratio 4:5 respectively.
b. Share each of the following in the given ratio
i. 6000m in the ratio 2:3
ii. ₦450 in the ratio 7:8
iii. 75 oranges in the ratio 2:3
c. The ratio of the cost price to the selling price of a car is 3:4. If the car costs ₦2,100,000 find the selling price.
View Answers5.
a. Increase ₦150 in the ratio 5:1
b. Increase 800kg in the ratio 8:5
c. Decrease 150 oranges in the ratio 1:5
d. Decrease 800kg in the ratio 5:8
e. Work out the multiplying factors which change 750m to 900m