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 1 :

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 2 :

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 3 :

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 4 :

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.