Express the ratio below in its simplest form.

3 and 1 half :4.5

3 1/2 : 45 = 7 : 90

Solution:
Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/2
3 1/2 = 7/2

We now have:
3 1/2 : 45 = 7/2 : 45

Convert the whole number 45 to a fraction with 1 in the denominator.

We then have:
3 1/2 : 45 = 7/2 : 45/1

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(7/2, 45/1) = 2

We now have:
3 1/2 : 45 = 7/2 : 90/2

Our two fractions now have like denominators so we can multiply both by 2 to eliminate the denominators.

We then have:
3 1/2 : 45 = 7 : 90

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 7 and 90 is 1

Divide both terms by the GCF, 1:
7 ÷ 1 = 7
90 ÷ 1 = 90

The ratio 7 : 90 cannot be reduced further by dividing both terms by the GCF = 1 :

Therefore:
3 1/2 : 45 = 7 : 90