Ratio and Proportion

Ratios

Ratios are equivalent to fractions.

Ahmed has $30 and Jane has $60.

The ratio of Ahmed’s money to Jane’s money is 30 : 60 = 1 : 2 in simplified form.

The ratio of Ahmed’s money to total sum is 30 : 90 = 1: 3 in simplified form.

The ratio of Jane’s money to total sum is 60 : 90 = 2 : 3 in simplified form.

Ratios in simplest form

Write 2/3 : 3/4 in simplest form

The LCM of the denominators 3 and 4 is 12.

So multiplying by 12, we get 12 x (2/3) : 12 x (3/4) = 8 : 9 in simplest form

Write 80 cm : 1 m in simplest form

We need to write both quantities in the same unit, 80 cm : 1 m = 80 cm : 100 cm

80 : 100 = 4 : 5 in simplest form

Ratio Questions - Interactive Practice

Questions

1. In what ratio must 21 be increased to become 35?
2. In what ratio must 48 be decreased to become 20?
3. Three friends shared $1080 in the ratio 2 : 3 : 4. Find the smallest share of the money
4. A shop owner mix four types of Candies P, Q, R, S in a bag in the ratio 2 : 3 : 4 : 5. (a) How much is the weight of Candy P in a bag that weights 7 kg. (b) Candy P cost $8/kg, Candy Q cost $10/kg, Candy R cost $4/kg and Candy S cost $6/kg. Find the cost of a bag of 7 kg of mixture.
5. A machine fills 20 bottles in 1 minute. Find the number of bottles it can fill in 2 hours.
6. Ali buys 200 pencils for $40. How much he need to pay of he buys 120 such pencils?
7. Two pipes A and B can fill a Tank in 4 hours. Pipe A alone will take 6 hours to fill the Tank. Find the time that Pipe B will take alone to fill the Tank.