Adding and Subtracting Fractions with Unlike Denominators — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A painter used 213 gallons on Monday and 134 gallons on Tuesday from 5 gallons. How much is left?
A) 1112 gallon
B) 1112 gallons
C) 1 gallon
D) 712 gallon
First add the paint used: 213 + 134 = 2412 + 1912 = 31312 = 4112. Then subtract from 5: 5 − 4112 = 1112 gallon remaining.
2. A rope is 812 feet long. Cuts of 238 ft and 316 ft are made. What length remains in simplest form?
A) 22324 feet
B) 314 feet
C) 21112 feet
D) 3 feet
Add the two cuts: 238 + 316 = 2924 + 3424 = 51324. Then subtract from 812 = 81224: the result is 81224 − 51324, which requires borrowing to get 73624 − 51324 = 22324.
3. Which expression equals 116?
A) 23 + 12
B) 34 + 512
C) 58 + 13
D) 12 + 13
Convert 34 to 912 and add 512 to get 1412 = 1212 = 116. The other choices do not simplify to 116.
4. Emma ran 325 miles and Zoe ran 2710 miles. How much farther did Emma run?
A) 710 mile
B) 12 mile
C) 1310 miles
D) 110 mile
Convert 25 to 410, then subtract: 3410 − 2710. Borrow 1 from 3 to get 21410 − 2710 = 710 mile.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A baker needs 214 cups of flour and 123 cups of sugar. She needs 31112 cups of dry ingredients in all.
The LCD of 4 and 3 is 12. Convert to 2312 + 1812 = 31112 cups total, since 3 + 8 = 11 and 1112 needs no simplifying.
2. A board is 638 feet. After cutting 256 feet, the remaining length is 31324 feet.
The LCD of 8 and 6 is 24. Convert to 6924 − 22024. Borrow 1 from 6 to get 53324 − 22024 = 31324 feet.
3. Jake practiced piano for 34 hour and guitar for 56 hour. He practiced 1712 hours total as a mixed number.
The LCD of 4 and 6 is 12. Convert to 912 + 1012 = 1912. Since 1912 > 1, rewrite as 1712 hours.
4. A recipe calls for 78 cup of oil. If 13 cup has been added, 1324 cup more is needed.
Subtract 78 − 13 using the LCD of 24: 2124 − 824 = 1324 cup still needed. Since 13 is prime, the fraction is already in simplest form.
5. Two containers hold 415 liters and 234 liters. The difference is 1920 liters.
The LCD of 5 and 4 is 20. Convert to 4420 − 21520. Borrow 1 from 4 to get 32420 − 21520 = 1920 liters.