Ratios and Proportions Practice

A ratio is

• two equal fractions

• a comparison between 2 quantities

• an estimation of an amount

• a variable

Answer explanation

A ratio specifically refers to a comparison between 2 quantities, showing the relative size of one quantity to another. The other options do not accurately define what a ratio is.

Fully simplify the ratio...

18:24

• 3:4

• 9:12

• 2:3

• 3:2

Answer explanation

To simplify the ratio 18:24, divide both numbers by their greatest common divisor, which is 6. Thus, 18 ÷ 6 = 3 and 24 ÷ 6 = 4, resulting in the simplified ratio 3:4. Therefore, the correct answer is 3:4.

Simplify the ratio of

20 to 25

Mathematical Equivalence

OFF

Simplify the ratio of
35 : 14

• 5 : 2

• 2 : 5

• 3 : 1

• 35: 14

Answer explanation

To simplify the ratio 35 : 14, divide both numbers by their greatest common divisor, which is 7. Thus, 35 ÷ 7 = 5 and 14 ÷ 7 = 2, resulting in the simplified ratio of 5 : 2.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.3

The ratio of the measures of the three angles of a triangle is 14:5:11. Find the measure of the angles.

• 80⁰, 90⁰, and 30⁰

• 84⁰, 30⁰, and 66⁰

• 78⁰, 31⁰, and 71⁰

• 58⁰, 45⁰, and 77⁰

Answer explanation

The angles of the triangle can be expressed as 14x, 5x, and 11x. The sum of angles in a triangle is 180 degrees. Solving 14x + 5x + 11x = 180 gives x = 6. The angles are 84°, 30°, and 66°, matching the correct choice.

A triangle’s angle measures are in the extended ratio of 2 : 4 : 9. Find the measures of the angles.

• 20^o, 40^o, 90^o

• 24^o, 48^o, 108^o

• 24^o, 32^o, 124^o

• 20^o, 40^o, 100^o

Answer explanation

The angles in the ratio 2:4:9 can be expressed as 2x, 4x, and 9x. The sum of angles in a triangle is 180°. Thus, 2x + 4x + 9x = 180° gives 15x = 180°, leading to x = 12°. Therefore, the angles are 24°, 48°, and 108°, which matches the correct choice.

What is it called when you set two ratios equal to each other?

• Proportion

• Fraction

• Ratio

• Congruent

Answer explanation

When you set two ratios equal to each other, it is called a proportion. This concept is fundamental in mathematics, particularly in solving problems involving similar figures and scaling.

Solve the proportion:

• 4

• 8

• 14

• 10

Answer explanation

To solve the proportion, set up the equation and cross-multiply. After simplifying, you find that the value that satisfies the proportion is 8, making it the correct answer.

Mathematical Equivalence

ON

There are 80 students in Mr. Bass’ classes.  The ratio of boys to girls is 2 : 3.
How many boys are in the classes?
How many girls?

• Boys: 32
  Girls: 48

• Boys: 48
  Girls: 32

• Boys: 5
  Girls: 15

• Boys: 15
  Girls: 5

Answer explanation

The ratio of boys to girls is 2:3, meaning for every 5 students, 2 are boys and 3 are girls. With 80 students, we have 80 ÷ 5 = 16 groups. Thus, boys = 16 × 2 = 32 and girls = 16 × 3 = 48. The correct answer is Boys: 32, Girls: 48.