MA.7.G.4.4 Compare, contrast, and convert units of measure between different measurement systems (US
customary or metric (SI)), dimensions, and derived units to solve problems.
CONVERTING MEASURES WITHIN A SYSTEM OF MEASUREMENT
Converting metric measurements
These problems can be solved similar to the “Scale Drawing” problems. Use your reference sheet for this type of problem.
It shows:
1 gram = 1000 milligrams and 1 kilogram = 1000 grams
This information is very similar to the scale on a map. Make a proportion.
Therefore, if you are told that your pencil weighs 5 grams and they ask for the weight in milligrams, simply make a ratio
using the correct information from the reference sheet. Then make a proportion using the info from the problem.
Cross multiply
1gram
1000milligrams
5 grams
1gram
=
x
1000milligrams
1000·5=1x = 5000=x
Therefore, 5 grams = 5000 milligrams
Carleta needs 450 centimeters of material to make a banner for a parade. How many meters of material does she need?
Converting customary measurements
Use your reference sheet to find the necessary information.
Tina was making punch for a party. She mixed 7 cups of apple juice, 4 cups of pineapple juice, 8 cups of ginger
ale, and 1 cup of lemon juice. How many gallons of punch did she make?
First, add all the cups together: 7 + 4 + 8 + 1 = 20 cups
Then, use your reference sheet to find how many cups are in 1gallon. It shows:
1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts
This means that there are 16 cups in a gallon. (you need to multiply the 2 x 2 x 4 = 16)
20cups
16cups
So, form a proportion:
=
x
1gallon
1.25
Cross multiply: 1· 20 = 16x or 20=16x 16 20.00 or 1 ¼ gallons
CONVERTING MEASURES BETWEEN DIFFERENT MEASUREMENT SYSTEMS
Each of the relationships in the table above can be written as a unit ratio. A unit ratio is a ratio in which the denominator is
1 unit.
Examples of unit ratios:
So, you can use unit ratios to convert measures between measurement systems in the same manner as converting within
measurement systems.
Convert 9 cm into inches:
Convert 1 lb into kg:
MA.7.G.4.4 Practice Problems
1. Convert the following measurements:
d.
e.
f.
2. The average weight of bass in a certain pond is 40 ounces. About how many pounds does a bass weigh?
3. The height of Niagara Falls is 182 ft. How many yards high is it?
4. The Statue of Liberty weighs 450,000 lbs. How many tons is this?
5. The ceilings of most classrooms are about 2.5 meters above the floor. How many centimeters high is the ceiling?
6. Paul had a bowl of cereal that weighed 35 grams. How many milligrams would this be?
7. Marta’s puppy weighed 4 kilograms. How many grams would this be?
8. Emilio wants to order enough wallpaper to decorate 3 walls in his dining room. Each wall measures 10 feet by 15 feet.
How many square yards of wallpaper does he need?
9. Convert the following measurements:
a.
b.
c.
d.
f.
e.
10. The Chicago marathon is run in October. The distance is 26.2 miles. How far is this in kilometers? Round to the
nearest hundredth if necessary.
11. A snake on display at the zoo is 54 centimeters long. About how many inches is the snake?
12. Leola ran a 10 km race. How many miles did she run?
13. The length of Yuan’s math book is 10.5 inches. What is the length in centimeters?
14. Leatrice bought two one-quart containers of frozen yogurt. How many liters of frozen yogurt did she buy?
15. Mr. Shelton’s car weighs 1.75 tons. How many kilograms does the car weigh?
16. Which is greater, a bottle containing 64 fluid ounces of water or a bottle containing 2 liters of water?
17. Which is greater, a 1.5 pound box of raisins or a 650-gram box of raisins?
18. Which is heavier, a ton of feathers or a ton of bricks?
19. Mrs. Black is making a punch recipe. She used 2 cups of pineapple juice, 1 pint of orange juice, 2 liters of Sprite, and
1 quart of raspberry sherbet. About how many gallons of punch did she make?
20. Rebecca bought a rectangular throw blanket.
Which is closest to the dimensions of Rebecca’s throw
blanket?
A. 59 inches by 32 inches
B. 59 inches by 80 inches
C. 75 inches by 40 inches
D. 80 inches by 150 inches