6.1 Ratio
Answer the following questions:

A. Reduce the fractions to the lowest terms
1. 15/27 5. 256/336
2. 35/20 6. 264/360
3. 48/30 7. 465/527
4. 99/ 121 8. 1050/1425

B. 1. Express the ratio of the number of red marbles to the number of blue marbles using both the colon form and the fraction form.

2. There are 15 fruits in a basket composed of apples and oranges. For every apple, there are four oranges. If an additional six apples were placed in the basket, what would be the new ratio of apples to oranges?

3. In a kitchen, the combined number of plates and glasses is 60. If the ratio of the number of plates to glasses is 2 ∶ 3, how many plates should be added so that the ratio of plates to glasses is 1 ∶ 1?

4. Fred has a collection of movie CDs. The ratio of fantasy movies to drama movies is
3 ∶ 2. The ratio of drama movies to comedy movies is 4 ∶ 3. If Fred has 24 fantasy movie CDs in his collection, how many comedy movie CDs does he have?

C. 1. A pastel-colored tile is subdivided into smaller squares
colored pink, light yellow, and light orange.

Write the indicated ratio in the simplest form.
a. ratio of pink squares to the total number of squares
b. ratio of pink squares to light orange squares
c. ratio of light orange squares to light yellow squares
d. the ratio of pink squares to light yellow squares

2. Solve what is asked in each problem. Show your complete solution.

a. In a school’s glee club, the number of male singers is twice as many as the number
of female singers. If the female singers are divided into sopranos and altos, and
there are twice as many sopranos as there are altos, find the ratio of male singers
to altos in the club.

b. In Cherry’s playlist, there are 256 songs. Fifty of these songs are instrumental, while the rest are not. What is the ratio of instrumental songs to those that are not?

c. There are initially 360 chairs arranged in columns and rows in an auditorium. The
ratio of columns of seats to rows of seats is 1 ∶ 5. How many columns of chairs must
be added to make the ratio of columns to rows 5 ∶ 4?

d. In a huge basket, there are fruits comprised of apples, oranges, and pears. The
ratio of apples to oranges is 2 ∶ 1. The ratio of oranges to pears is 5 ∶ 4. If there are
30 apples, how many pears are there in the basket?

6.2 Direct Proportion'
Answer the following questions:

A. Determine the value of N that will make each statement correct.
1. N × 4 = 12
2. 9 × N = 72
3. 133 = 7 × N
4. N × 14 = 182
5. N × N = 25

B. 1. Find the value of N if 5 ∶ 6 = N ∶ 36.

2. Complete the following direct proportion: N/8 = 126/144

3. For a triangle oriented similar to the triangle in Example 3, find the value of h if a = 6 and b = 24.

4. Leo is inspecting a 1 cm ∶ 1.5 m scale floor plan of his new house. The dimensions of his bedroom in the scaled plan are 2 cm by 3 cm. What is the area of Leo’s actual bedroom in square meters?

C. Find the value of N to form a direct proportion.
1. N/6 = 11/3
2. 44/121 =N/11
1 1
3. 2/2 : 3/2 = N:2
d. 24 : 1/4 = N : 1/3

D. Solve the following problems. Show your complete solution.

a. You jogged 2.4 miles in 30 minutes. At that rate, how long will it take you to jog 3.2
miles?

b. An airplane flies 100 miles in half an hour. How far can it fly in 1 1⁄4 hours at the
same speed?

c. The currency in Tajikistan is the Somoni. The exchange rate is approximately 0.17
Somoni = 1 Philippine peso. How much money in Somoni would you get with ₱500?

d. A map scale designates 1 inch = 25 km. The distance between the two towns on
the map is 3 inches. If a liter of gasoline can last you for 50 kilometers, how many
liters of gasoline would you need to drive from the first town to the second?