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Properties of Whole Numbers I | Week 14 Topics1 Quiz
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Properties of Whole Numbers II | Week 24 Topics1 Quiz
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Properties of Whole Numbers III | Week 35 Topics1 Quiz
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Indices | Week 42 Topics1 Quiz
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Laws of Indices | Week 55 Topics1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics1 Quiz
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Standard Form | Week 73 Topics1 Quiz
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Significant Figures (S.F) | Week 84 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics1 Quiz
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Approximation & Estimation | Week 121 Topic1 Quiz
Topic Content:
- Sharing Quantities in Given Ratios
To share quantities in a given ratio:
1. Add the ratios together.
2. Find the fraction of the given ratio that is the total ratio.
3. Use these to multiply the quantities respectively.
Worked Example 10.3.1:
Divide ₦120 between Bola and Ade in the ratio 2 : 3
Solution
The given ratio = 2 : 3
Total ratio = 2 + 3 = 5
Bola gets \( \frac{2}{5}\scriptsize \: of \: N120 \\ \scriptsize = 2 \: \times \: 24 = N48 \)
Ade gets \( \frac{3}{5}\)of the total amount.
= \( \frac{3}{5}\scriptsize \: of \: N120 \\ \scriptsize = 3 \: \times \: 24 = N72 \)
Bola gets ₦48 and Ade gets ₦72.
Worked Example 10.3.2:
The ratio of maths books to English books in a library is 15 : 2. The total number of books is 170. Find:
a. the number of maths books
b. the number of English books.
Solution
Ratio = maths book : English book
= 15 : 2
total ratio = 15 + 2 = 17
The total number of books is 170
a. Number of Maths books
= \( \frac{Maths \; ratio}{Total \; ratio}\scriptsize \: \times \: 170 \\ = \frac{15}{17}\scriptsize \: \times \: 170 \\ \scriptsize 15 \: \times \: 10 = 150 \: Maths \: books\)
b. Number of Maths books
= \( \frac{English \: ratio}{Total \: ratio}\scriptsize \: \times \: 170 \\ = \frac{2}{17}\scriptsize \: \times \: 170 \\ \scriptsize 2 \: \times \: 10 = 20 \: English \: books\)
Worked Example 10.3.3:
Two girls shared oranges in the ratio of 3 : 5. The girl with the smaller share got 45 oranges. How many oranges did the other girl get?
Solution
Ratio = 3 : 5
total ratio = 3 + 5 = 8
smaller ratio = 3
Let the total number of oranges be x
The girl with smaller ratio gets:
= \( \frac{Smaller \: ratio}{Total \: ratio}\scriptsize \: \times \: x \\ = \frac{3}{8}\scriptsize \: \times \: x \\ \frac{3x}{8} = \frac{45}{1}\\ \scriptsize Cross \: Multiply \\ \scriptsize 3x = 8 \; \times \: 45 \\ \scriptsize Divide \: both \: sides \: by \: 3\\ \frac{3x}{3} = \frac{8 \: \times \: 45}{3}\\ \scriptsize x = 8 \: \times \: 15 = 120\)
120 oranges were shared
The other girl gets:
= \( \frac{5}{8}\scriptsize \: \times \: 120 \\ \scriptsize Divide \: by \: 2\\ \frac{5}{4}\scriptsize \: \times \: 60 \\ \frac{300}{4} \scriptsize = 75 \: oranges\)
Or
The other girl gets (120 – 45) = 75 oranges
