Converting with Scale Factors

What does it mean when two things are proportional?

• When two things are proportional, it means that they change together in a predictable way.

• When two things are proportional, it means that they change differently from each other.

• When two things are proportional, it means that they change independently of each other.

• When two things are proportional, it means that they are compared to each other.

Answer explanation

When two things are proportional, it means that as one thing increases or decreases, the other thing also changes, and they do so in a predictable manner. For example, if you double one thing, the other thing will also double. Proportional relationships are important in mathematics, science, and everyday situations where you want to predict how things change together.

Tags

CCSS.7.RP.A.2D

A model train is 8 cm long. If it was built with a scale of 4 cm = 5 m, how long is the actual train?

• 5 m

• 10 m

• 15 m

• 20 m

Answer explanation

The scale of 4 cm = 5 m means that for every 4 centimeters on the model, it represents 5 meters in reality. To find the length of the actual train, set up a proportion: 4 cm / 5 m = 8 cm / x m. Cross-multiplying, you get 4x = 40, and dividing by 4, you find that x = 10. Therefore, the actual train is 10 meters long.

Tags

CCSS.7.G.A.1

On a map, 5 inches represent 10 miles. How many inches would be between two cities that are 25 miles apart?

• 12.5 inches

• 5 inches

• 10 inches

• 15 inches

Answer explanation

According to the scale, 5 inches represents 10 miles. To find the distance between the cities on the map, set up a proportion: 5 in / 10 mi = x inches / 25 mi. Cross-multiplying, you get 10x = 125, and dividing by 10, you find that x = 12.5. Therefore, the distance between the cities on the map is 12.5 inches.

Tags

CCSS.6.RP.A.3B

Lisa is traveling from one city to another. She is looking at a map with a scale where 4 cm represents 50 miles. She then uses a ruler to measure the distance on the map between the two cities she is traveling. The distance between them is 120 cm. How many miles apart are the two cities?

• 600 miles

• 1900 miles

• 750 miles

• 1500 miles

Answer explanation

According to the scale, 4 centimeters on the map represents 50 miles in reality. To find the distance between the actual cities, set up a proportion: 4 cm / 50 mi = 120 cm / x miles. Cross-multiplying, we get 4x = 6000, and dividing by 4, we find that x = 1,500. Therefore, the two cities are 1,500 miles apart.

Tags

CCSS.6.RP.A.3B

A farmer is making a scale model of his field. The field measures 200 meters in length. On the model, 5 centimeters will represent 10 meters. How long does the model need to be?

• 200 cm

• 250 cm

• 100 cm

• 140 cm

Answer explanation

According to the scale, 5 cm represents 10 meters. To find the length of the model, set up a proportion: 5 cm / 10 m = x cm / 200 m. Cross-multiplying, you get 10x = 1000, and dividing by 10, you find that x = 100. Therefore, the model needs to be 100 cm long.

Tags

CCSS.7.G.A.1