Guided Practice

Use the terms **drawing** and **actual** to correctly complete the sentence.

A scale is a ratio of length to length.

Write **less than**, **equal to**, or **greater than** to correctly complete each sentence.

A scale of 1 : 1 means that the lengths in the drawing are the lengths of the actual object.

In the video, the width of the horizontal base of the triangle is 8 units. The height of the triangle is 4 units. What are the new width and height of the triangle at a 1 : 4 scale?

New width: unit(s)

New height: unit(s)

Study the map on the left.

The scale for the map is 1 unit : mi

Study the map on the left.

The drawing distance between points A and C is unit(s).

The actual distance between points A and C is mile(s).

Study the map on the left.

The actual distance between points C and D is mile(s).

Study the map on the left.

The actual distance between points B and D is about mile(s).

Study the map on the left.

The actual distance between points C and E is about 25.6 miles. So, the drawing distance between the points is about unit(s).

The continent of Africa is about 5000 miles long from north to south. What is the approximate scale for the map of Africa?

Scale: unit(s) : mile(s)

Use the scale you calculated to determine the approximate length of Africa from east to west.

Length from east to west: miles

The large island off the east coast of Africa is Madagascar. It is the fourth largest island in the world. What is the approximate length of Madagascar from north to south?

Length from north to south: miles

What is the approximate length of Madagascar from east to west?

Length from east to west: miles

Determine the length of the horizontal base of each triangle in the video. Write the scale factor used to enlarge the triangle.

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Use the scale factor to determine the height of the enlarged triangle. Write your answer as a decimal to the nearest hundredth.

New height: units

Determine the radius lengths of the original and enlarged circles in the video. Write the scale factor used to enlarge the circle.

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What scale factor was used to shrink the circle?

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Write the scale factor that was used to enlarge or shrink the shaded figure to create the unshaded figure.

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A triangle with a height of 4 units and a base length of 10 units is shrunk using the scale 2 : 5.

The base length of the new triangle is units.

A rectangle which has an area that is 24 square units is enlarged using the scale 4 : 2.

The area of the new rectangle is square units.

Write the scale factor that was used to enlarge or shrink the shaded figure to create the unshaded figure.

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A rectangle whose perimeter is 18 units is shrunk using the scale 1 : 6.

The perimeter of the new rectangle is units.

A circle with a radius of 6 in. is altered using the scale 1 : 3.

The radius of the new circle is inches.

Write the scale factor that was used to enlarge or shrink the shaded figure on the left to create the unshaded figure on the right.

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Write the word that best completes the sentence.

Altering a figure using the scale 1 : 1 produces a figure.

Recall that a unit rate is a rate with a denominator of 1. You can write unit rates with fractions in both the numerator and denominator to represent problem situations.

For example, if you ran 3/8 mile in 1/3 hour, that could be represented by this unit rate:

Multiply both the numerator and denominator by the reciprocal of the denominator to get the unit rate.

Suppose you walked slowly at 3/8 mile in 1/3 hour. What is your unit rate as a fraction?

You walked mile(s) per hour.

Suppose that after the sun goes down, the temperature decreases half a degree Fahrenheit every 40 minutes. What is the unit rate, as a fraction, of decrease in the temperature per hour?

The temperature decreases degree(s) Fahrenheit per hour.

If 3/8 of a gallon of paint can cover 1/10 of a fence, how much paint is needed to paint the whole fence, as a decimal?

gallons of paint are needed to paint the whole fence.

A turtle walks 0.875 mile in 5/6 hour. How fast does it walk in miles per hour, as a decimal?

The turtle walks miles per hour.

A cookie recipe uses 2.5 cups of sugar for every 2/5 cup of flour. How much sugar per cup of flour does the recipe call for, as a decimal?

The recipe calls for cups of sugar for every cup of flour.

Your water faucet leaks 31/2 liters of water every 10 minutes. How much water do you lose each hour?

You lose liters of water per hour.

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These images were drawn at two different scales: 1 to 3 (left) and 1 to 2 (right).

When we divide 1/3 ÷ 1/2 = 2/3, this tells us the scale from left to right. The image on the left is 2/3 the size of the one on the right. When we divide 1/2 ÷ 1/3 = 3/2, this tells the scale from right to left. The image on the right is 3/2, or 1.5 times, the size of the one on the left.

Another way to convert between scales is to first multiply to make one scale equal to 1 : 1. Then multiply the other scale by that same number.

We can multiply 2/3 × 3/2 = 1, and 3/4 × 3/2 = 9/8. So, the image on the right is 9/8 times larger than the image on the left. The scale from right to left is 9 : 8. From left to right, it is 8 : 9.

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For every 2 units of length on the left image, there are units of length on the right image.

The image on the left is times the size of the image on the right.

For every 3 units of length on the right image, there are units of length on the left image.

The image on the right is times the size of the image on the left.

Determine the horizontal width and vertical height of the actual object that these drawings represent.

Width: units

Height: units

For every 9 units of length on the right image, there are units of length on the left image.

The image on the right is times the size of the image on the left.

Determine the horizontal width and vertical height of the actual object that these drawings represent.

Width: units

Height: units

The image on the right is times the size of the image on the left.

The vertical height of the actual object must be units.

The image on the right is times the size of the image on the left.

The horizontal width of the actual drawing must be about units.

The image on the right is about times the size of the image on the left.

The vertical height of the actual drawing must be about units.

The trapezoid on the left is a scale drawing of the trapezoid on the right. Given this information, you can compare the base lengths to determine the scale.

new length → 4 : 5 ← old length

You can determine the new height by multiplying the old height by the scale: 3 × 4/5 = 2.4. You can multiply any length on the new unshaded figure by 5/4 to figure out the corresponding length on the old figure.

The length of each slanted side on the new unshaded trapezoid is approximately 2.53 units. What is the approximate corresponding length on the original shaded trapezoid? Round your answer to the nearest thousandth.

Original length: units