SIMPLIFYING RATIOS WITH FRACTIONS AND DECIMALS

Simplify Ratios with Fractions

Simplify

Problem 1 :

1 2/3 : 1 1/3

Solution :

1 2/3 : 1 1/3

To convert mixed fractions to improper fractions.

= 5/3 : 4/3

By multiplying both parts by 3, we get

= (5/3) ⋅ 3 : (4/3) ⋅ 3

= 5 : 4

So, the simplest form is 5 : 4.

Problem 2 :

 1/3 : 1/2

Solution :

1/3 : 1/2

Denominators are not same. So we have to find LCM,

= 1/3 × (2/2) : 1/2 × (3/3)

= 2/6 : 3/6

By multiplying both parts by 6, we get

= (2/6) ⋅ 6 : (3/6) ⋅ 6

= 2 : 3

So, the simplest form is 2 : 3.

Problem 3 :

 2 1/2 : 1 1/3

Solution :

2 1/2 : 1 1/3

To convert mixed fractions to improper fractions.

= 5/2 : 4/3

Denominators are not same. So we have to find LCM,

= 5/2 × (3/3) : 4/3 × (2/2)

= 15/6 : 8/6

By multiplying both parts by 6, we get

= (15/6) ⋅ 6 : (8/6) ⋅ 6

= 15 : 8

So, the simplest form is 15 : 8.

Problem 4 :

3 1/4 : 2/3

Solution :

3 1/4 : 2/3

To convert 3 1/4 is improper fractions.

13/4 : 2/3

Denominators are not same. So we have to find LCM,

= 13/4 × (3/3) : 2/3 × (4/4)

= 39/12 : 8/12

By multiplying both parts by 12, we get

= (39/12) ⋅ 12 : (8/12) ⋅ 12

= 39 : 8

So, the simplest form is 39 : 8.

Problem 5 :

1 2/3 : 1 3/10

Solution :

1 2/3 : 1 3/10

To convert mixed fractions to improper fractions.

5/3 : 13/10

Denominators are not same. So we have to find LCM,

= 5/3 × (10/10) : 13/10 × (3/3)

= 50/30 : 39/30

By multiplying both parts by 30, we get

= (50/30) ⋅ 30 : (39/30) ⋅ 30

= 50 : 39

So, the simplest form is 50 : 39.

Express as a ratio in simplest form :

Problem 6 :

0.5 : 0.3

Solution :

0.5 : 0.3

Multiplying both parts by 10, we get

= 0.5(10) : 0.3(10)

= 5 : 3

So, the simplest form is 5 : 3.

Problem 7 :

0.2 : 0.8

Solution :

0.2 : 0.8

Multiplying both parts by 10, we get

= 0.2(10) : 0.8(10)

= 2 : 8

= 2/8

= 1/4

So, the simplest form is 1 : 4.

Problem 8 :

0.6 : 1.5

Solution :

0.6 : 1.5

Multiplying both parts by 10, we get

= 0.6(10) : 1.5(10)

= 6 : 15

= 6/15

= 2/5

So, the simplest form is 2 : 5.

Problem 9 :

0.35 : 0.49

Solution :

0.35 : 0.49

Multiplying both parts by 100, we get

= 0.35(100) : 0.49(100)

= 35 : 49

= 35/49

= 5/7

So, the simplest form is 5 : 7.

Problem 10 :

At a football match the ratio of female supporter to male supporters is 16 : 2. Write this ratio in simplest form.

Solution :

Ratio between female supporters to make supporters = 16 : 2

= 16 / 2

= 8 / 1

= 8 : 1

Problem 11 :

To make purple paint red and blue paint are mixed in the ratio 0.6 : 1.4. Write this ratio in simplest form.

Solution :

Ratio between red paint to blue paint = 0.6 : 1.4

= 0.6 / 1.4

Multiplying both numerator and denominator by 10, we get

= 6/14

= 3 / 7

= 3 : 7

Problem 12 :

Which is the best buy: 50g of cheese for $24 or 70g of cheese for $35?

Solution :

50g of cheese for $24 :

Cost of 1 gram cheese = 24/50

= $0.48

70g of cheese for $35 :

Cost of 1 gram of cheese = 35/70

= 0.5

0.48 is smaller, so first buy is best.

Problem 13 :

Caviar was 22 g for $105 at one store and 10 g for $55 at another store. Convert both of these to a cost per 100g to the nearest cent to find the best buy.

Solution :

Cost of 22 g caviar = $105

Cost of 1 gram = 55/22

= $2.5

Cost of 100 grams = 2.5 x 100

= $250

Cost of 10 g of caviar = $55

Cost of 1 gram = 55/10

= $5.5

Cost of 100 grams = 5.5 x 100

= $550

The first one is the best buy.