Guided Practice

1 inch is equal to exactly 2.54 centimeters. How many centimeters are in 1 foot?

The ratio of inches to centimeters is 1 in. : 2.54 cm. And 1 foot is equal to 12 inches. So find the equivalent ratio with 12 inches.

1 in. : 2.54 cm = 12 in. : ?

There are 2.54 × 12, or 30.48, centimeters in 1 foot.

Sam bought 45 half-gallons of chocolate ice cream, because this is a word problem. How many liters of ice cream did Sam buy?

1 gallon is equal to 3.8 liters, so 1/2 gallon is equal to 1/2 × 3.8, or 1.9, liters.

1 half-gal : 1.9 L = 45 half-gal : ? L

Sam bought 1.9 × 45, or 85.5, liters of chocolate ice cream.

Corinne makes a light-green paint by combining 2 gallons of blue paint with 4 gallons of yellow paint. How much yellow and blue paint does she need to make a total of 1 quart of the light-green paint?

1 gallon = 4 quarts

So, Corinne combines 8 quarts of blue paint with 16 quarts of yellow paint (24 quarts total) to make the light-green paint.

8 qt : 24 qt = 1/3 qt : 1 qt
16 qt : 24 qt = 2/3 qt : 1 qt

Corinne needs 1/3 quart of blue paint and 2/3 quart of yellow paint to make 1 quart of the light-green paint.

How many kilometers are in 1 mile? Round to the nearest hundredth.

1 mile = kilometers

How many centimeters are in 6 inches?

How many centimeters are in 11/2 inches?

6 inches   = centimeters

11/2 inches = centimeters

1 gallon is equal to 3.8 liters. How many liters are in a 2-gallon bottle?

2 gallons = liters

There are 16 ounces in 1 pound.

How many pounds are in 48 ounces?

48 ounces = pounds

1 cup is equal to a half pint. How many half pints are in 40 cups?

40 cups = half pints

1 mile is equal to approximately 1.61 kilometers.

If a car drives 50 kilometers per hour, what is its speed in miles per hour? Round to the nearest hundredth.

The speed is miles per hour.

A liter of water weighs about 1 kilogram, or about 2.2 pounds. Ryan's class bought thirty 2-liter bottles of water. Describe the weight of the 30 bottles.

pounds

kilograms

1 kilogram is equal to about 2.2 pounds. How many pounds are in 11/4 kilograms? Write your answer as a decimal.

11/4 kilograms = pounds

Saul drew a picture and reasoned about the problem this way: The light-green paint contains 2/4 as much blue paint as yellow paint.

of a quart is blue paint.

of a quart is yellow paint.

Sal's fruit punch uses 5 quarts of juice to 2 quarts of soda. How much juice and soda does Sal need to make 35 cups of fruit punch for his class?

Sal needs cups of juice and cups of soda.

0.85 mi/? ft = 1 mi/5280 ft

0.85 mi = ft

A race is 33,000 feet long. How many miles long is the race? Write your answer as a decimal.

33,000 ft = mi

Dolly is making bows from 12 yards of ribbon. If a yard is equal to 3 feet, how many inches of ribbon does Dolly have?

Dolly has inches of ribbon.

Chas owns 5 square kilometers of farmland. How many acres does he own if 1 square kilometer is approximately equal to 247.105 acres? Write your answer as a decimal.

Chas owns acres.

A pool holds 14,360 gallons of water. About how many cubic feet of water does it hold if 1 cubic foot is about 7.5 gallons? Round the answer to the nearest whole number.

The pool holds cubic feet of water.

A limousine is 4.5 meters long. How many yards long is the limousine if 1 yard is about 0.91 meters long? Round your answer to the nearest hundredth.

The limousine is yards long.

The diameter of a plain M&M® candy is approximately 0.5 inch. About how many M&M candies would you have to place end to end to form a line a mile long? Use a comma in your answer.

You would need M&Ms.

A tree is measured and found to be 16.9 meters tall. How many centimeters tall is the tree?

The tree is cm tall.

Francis purchased enough powdered formula to make 34 quarts of liquid for her infant son. How many liters of formula will the powder make if 1 liter is about 1.06 quarts? Round to the nearest hundredth.

34 quarts = liters

A book cover has an area of 72 square inches. What is its area in square centimeters? Round to the nearest tenth.

The cover measures cm2.

These number lines show some equivalent measures in the metric system.

For lengths, the metric system has units called millimeters (mm), centimeters (cm), meters (m), and kilometers (km).

There are 12 inches in 1 foot. How many feet are in 36 inches?

Multiply the numerator and denominator of the ratio 12 : 1 by the same number. This doesn't change the value of the ratio.

12 × 3 is equal to 36, and 1 × 3 is equal to 3. There are 3 feet in 36 inches.

You can convert fraction and decimal measurements just like you convert whole-number measurements. Recall the inches-to-feet ratio of 12 : 1.

12 ÷ 2 is equal to 6, and 1 ÷ 2 is equal to 1/2. So, this work shows that there is 1/2 foot, or 0.5 foot, in 6 inches.

Often, when converting measurements, you can do more than one conversion. To convert 60.96 centimeters to feet, you can first convert to inches. There are 2.54 cm in 1 in.:

2.54 : 1 = 60.96 : ?

60.96 ÷ 2.54 = 24, so there are 24 inches in 60.96 centimeters. Now convert 24 inches to feet:

12 : 1 = 24 : ?

24 ÷ 12 = 2, so there are 2 feet in 60.96 centimeters.

Use the number lines to convert each of the metric measurements given.

cm = 1 m

mm = 1 cm

km = 100 cm

There are 3 feet in 1 yard. How many yards are in 300 feet?

There are yards in 300 feet.

There are 16 ounces in 1 pound. How many ounces are in 1/4 pound? How many ounces are in 0.8 pound?

There are ounces in 1/4 pound.

There are ounces in 0.8 pound.

There are 12 inches in 1 foot and 5280 feet in 1 mile. How many miles are in 380,160 inches?

There are miles in 380,160 inches.

There are 12 inches in 1 foot. What does this mean? There are many ways of saying what it means. One way is to say that 12 inches equals 1 foot, or write 12 in. = 1 ft.

Another way of stating the relationship is to say that inches and feet are related by the ratio 12 to 1.

Enter the ratio 12 : 1 on the diagram at the right. Then enter 6 in the bottom left box. This will represent 6 inches. Then press Enter inside the bottom left box to convert 6 inches to feet.

How many feet are equal to 6 inches? How was this calculated using the numbers from the diagram? (Scroll down for more.)

The diagram also shows that one-half foot, or 0.5 foot, is equal to 6 inches. Inches to feet is described by the ratio 12 : 1, but feet to inches is described by the inverse ratio 1 : 12. The ratio 0.5 : 6 is equivalent to the ratio 1 : 12.

To convert feet to inches, type a number into the bottom right box, keeping the ratio 12 : 1 the same. Press Enter inside the bottom right box to convert feet to inches.

How many inches are in 2.5 feet? How was this calculated using the numbers from the diagram? (Scroll down for more.)

If you delete the ratio in the middle of the diagram, enter 30 in the bottom left box and 2.5 in the bottom right box, and then press Enter in the bottom right box, the conversion ratio is calculated for you. You should see the ratio 1 : 0.08333...

But the numbers 30 and 2.5, representing 30 inches and 2.5 are the same from before! They are related by the ratio 12 inches to 1 foot. Why did the ratio change?

Well, actually, the ratio did not change. Can you explain this?

Let's try another conversion. Let's convert 17.78 centimeters to inches.

Enter 17.78 in the bottom left box. (Use the drawing canvas to write "cm" to remember that 17.78 means 17.78 centimeters.) There are 2.54 centimeters in 1 inch, so enter the ratio 2.54 : 1. For every 2.54 cm in the left bar, there will be 1 inch in the right bar.

Make sure the bottom right box is empty (or has just a ? in it). Then press Enter in the bottom left box to convert the centimeters to inches.

How many inches are in 17.78 centimeters? How was this calculated using the numbers from the diagram? (Keep scrolling for more!)

How about another? A plane is flying at 30000 feet. How many miles up is it?

Enter 30000 in the bottom right box. There are 5280 feet in 1 mile, so enter the ratio 1 : 5280. For every 5280 ft in the right bar, there will be 1 mile in the left bar.

Make sure the bottom left box is empty (or has just a ? in it). Then press Enter in the bottom right box to convert the feet to miles.

How many miles are in 30000 feet? How was this calculated using the numbers from the diagram?

Let's do one more example to show how a ratio can be calculated.

A half cup is the same as 8 tablespoons. Determine a conversion ratio between cups and tablespoons.

Enter 0.5 (for cups) in the bottom left box and 8 (for tablespoons) in the bottom right box. Make sure the ratio boxes are empty (or just show question marks). Then, press Enter in the bottom right box.

Play with the tool. How many tablespoons are in 1 cup? How many cups are in 1 tablespoon?

Use the tool to determine each measure. Try to predict the answer before finding out.

• Horses are sometimes measured using a unit called hands. A horse that is 56.4 inches tall would be 14.1 hands tall. What is the conversion ratio between hands and inches?
• In a suburb of New York City, a block is equal to 1/20 of a mile. How many of these blocks do you run if you run 3.1 miles? (You can't enter fractions in the tool. But you can write ratios in different ways, or use decimals.)
• One light-nanosecond (how far light can travel in 1 billionth of a second) is 1 foot. How far, in miles, can light travel in 100 nanoseconds, or 1 ten-millionths of a second?

• A kilometer is approximately 0.6214 mile. About how many kilometers is 10.8 miles?
• A 7.1-pound baby weighs 113.6 ounces. What is the conversion ratio between pounds and ounces?
• An inch is equal to 25.4 millimeters. How many inches are in 700 millimeters?
• Sue has 2.5 times the amount of money that Tom has. If Sue has \$65, how much does Tom have? (Notice that we can do "conversions" like this without having units of measure!)
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Use your keyboard's arrow keys (← ↑ → ↓) to move the image on the grid.

Suppose that each grid square is 40 cm long and 40 cm wide. Determine the area of the figure.

Area = cm2

Use your keyboard arrow keys (← ↑ → ↓) to move the image on the grid.

Suppose that each grid square is 5 m long and 5 m wide. Determine the area of the figure.

Area = m2

Use your keyboard's arrow keys (← ↑ → ↓) to move the image on the grid.

Suppose that each grid square is 2.5 in. long and 2.5 in. wide. Determine the area of the figure.

Area = in.2

Use your keyboard's arrow keys (← ↑ → ↓) to move the image on the grid.

Suppose that each grid square is 1 ft long and 1 ft wide. Determine the area of the figure.

Area = ft2

Use your keyboard's arrow keys (← ↑ → ↓) to move the image on the grid.

Suppose that each grid square is 2 km long and 2 km wide. Determine the area of the figure.

Area = km2