Question

Express the ratio below in its simplest form.
4.5
:
3
1/2

Answer 1

9:7

Explanation:

Convert all the numbers to either decimal or fraction. The operation becomes simple.

Simplifying after converting to decimal

Convert 3 1/2 to decimal 3 1/2 = 3 + 1/2

1/2 = 0.5

3 + 1/2 = 3 + 0.5 = 3.4

Ratio 4.5:3.5 = 4.5/3.5

Divide by 5 to give

`(4.5 /5 )/(3.5/5) = 0.9/0.7\\\\`

Multiply both numerator and denominator by 10
0.9 x 10 = 9

0.7 x 10 = 7

So the ratio becomes 9/7 = 9:7

Simplifying after converting to fraction

4.5 = 4 + 0.5

0.5 = 1/2

5.5 = 4 + 1/2 = 4 1/2

Convert to mixed fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2

Convert 3 1/2 to fraction

3 1/2 = (3 x 2 + 1)/2 = 7/2

So 4.5 : 3 1/2 = 9/2 : 7/2

Multiplying by 2 we get the same answer: 9:7

Choose whichever approach you feel comfortable with

Answer 2

9 : 7

Explanation:

given the ratio

4.5 : 3
`(1)/(2)` , that is in decimal form

4.5 : 3.5 ( multiply both parts by 10 to clear the decimal )

= 45 : 35 ( divide both parts by 5 )

= 9 : 7 ← in simplest form