Question

1. express each ratio as a fraction in simplest form.

(a) 2:5
(b) 4:6
(c) 9:7
(d) 15:10

1. the ratio of the volume of a small bottle of soda to the volume of a large bottle of soda is 3:8.

(a) express the volume of the small bottle as a fraction of the volume of the large bottle.
(b) express the volume of the large bottle as a fraction of the volume of the small bottle.

1. the ratio of the distance jeannie walked on monday to the distance she walked on tuesday is 7:5. how many times as far did she walk on monday than on tuesday?
2. in a bag of beads sold at the store, the ratio of red beads to blue beads is 8:9.

(a) what fraction of the beads are red beads?
(b) what fraction of the beads are blue beads?

1. the ratio of the number of dogs to the number of cats in a pet store is 7:12. if there are 48 cats, how many dogs are there?
2. the ratio of the amount of chocolate syrup to the amount of milk required to make chocolate milk at a dairy is 2:7. how many gallons of milk are needed for 32 gallons of chocolate syrup?

Explanation:

Problem 1

(a)

Step1: Recall ratio to fraction

A ratio \(a:b\) as a fraction is \(\frac{a}{b}\). For \(2:5\), numerator is 2, denominator is 5.

Step2: Check simplification

2 and 5 have no common factors other than 1, so it's already simplest.

Step1: Ratio to fraction

For \(4:6\), fraction is \(\frac{4}{6}\).

Step2: Simplify fraction

Divide numerator and denominator by GCD(4,6)=2. \(\frac{4\div2}{6\div2}=\frac{2}{3}\).

Step1: Ratio to fraction

\(9:7\) as fraction is \(\frac{9}{7}\).

Step2: Check simplification

9 and 7 are coprime, so simplest.

Answer:

\(\frac{2}{5}\)

(b)