<span>1) Express the following ratios in the simplest form. a) 150 : 400 </span>Solution : <span> The given ratio is 150 : 400 = 150/400 The common factor of 150 and 400 is 50. (150 ÷ 50)/ (400 ÷ 50) = 3/8 = 3 : 8. ---------------------------------------------------------------------- b) A dozen to score </span>Solution : <span> One dozen = 12 and one score = 20. So, a dozen to score = 12/20 = 12 : 20. (12 ÷ 4)/ (20 ÷ 4) [ As the common factor is 4] = 3/5 = 3 : 5. ---------------------------------------------------------------------- c) 200 grams to 4 kg </span>Solution : <span> 200 g to 4 kg As both the quantities are in different units, first make their units same. 1kg = 1000 g ∴ 4 kg = 4000 g. 200 g to 4000 g = 200 / 4000 Common factor of 200 and 4000 is 200. (200 ÷ 200)/(4000 ÷ 200) = 1/20 = 1 : 20. ---------------------------------------------------------------------- d) Sam earned $4000 and paid $500 as income tax and spent $1500 on household expenses. Find the ratio of : 1) income tax to income 2) household expenses to income 3) savings to earnings </span><span>Solution </span><span> Sam’s income = $4000 Income tax = $500 ∴ income tax to income = 500/4000 (500 ÷ 500)/(4000 ÷ 500) = 1/8 Ratio of Income tax to income is 1 : 8 Expenses = $1500 ∴ Household expenses to income = 1500/4000 (1500 ÷ 500)/ (4000 ÷ 500) = 3/8 Ratio of Household expenses to income = 3 : 8. Savings = Income – (expenses + income tax) Savings = 4000 – (1500 + 500) = $2000. ∴ Savings to earnings = 2000/4000 (2000 ÷ 2000)/(4000 ÷ 2000) = ½ Ratio of savings to expenses = 1 : 2.</span>
