Express the ratio in simplest form. the ratio of 500 m to 3 km a. 500 : 3 b. 1 : 6 c. 5 : 3 d. 3 : 500

1)Express the following ratios in the simplest form.
a)150 : 400 
Solution : 
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 
Solution : 
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 
Solution : 
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 
Solution 
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.

9/12 is the answer because 3/4 times 3 each is 9/12