Add It Up
What is 1/6 + 1/3?
A. 2/9
B. 1/2
C. 2/3
D. 1/9
B. 1/6 + 2/6 = 3/6 = 1/2
What is 3/4 - 1/4?
A. 1/4
B. 1/8
C. 1/2
D. 1
C. Two fourths simplify to 1/2.
Three sandwiches are shared equally among 4 hikers. How much sandwich does each hiker get?
A. 3/4
B. 1/4
C. 1 1/3
D. 3/7
A. 3 ÷ 4 = 3/4 of a sandwich.
A bottle holds 2 liters of water. Ana pours out 3/4 liter. How much is left?
A. 1 3/4 L
B. 1/4 L
C. 1 1/4 L
D. 3/4 L
C. 2 - 3/4 = 1 1/4 liters.
Place value. Which choice shows 10 x 10 x 10 x 10 in standard form first and exponential form second?
A. 40, 104
B. 10,000, 104
C. 104, 10,000
D. 1,000, 103
B. Four factors of ten give 10,000, written 104 in exponential form.
What is 3/5 + 7/10?
A. 2/3
B. 1 1/5
C. 1 3/10
D. 9/10
C. 6/10 + 7/10 = 13/10 = 1 3/10
What is 5/6 - 1/4?
A. 7/12
B. 1/2
C. 2/5
D. 2/3
A. 10/12 - 3/12 = 7/12
Ten players share 4 pizzas equally. Which pair shows each player’s share?
A. 10÷4 and 2/5
B. 4÷10 and 5/2
C. 4÷10 and 2/5
D. 10÷4 and 5/2
C. Divide the 4 pizzas by the 10 players. Each gets 2/5 of a pizza.
A class has 3 1/2 yards of fabric and uses 1 3/4 yards. How much fabric remains?
A. 1 3/4 yd
B. 2 1/4 yd
C. 1 1/4 yd
D. 2 3/4 yd
A. 3 1/2 - 1 3/4 = 2 6/4 - 1 3/4 = 1 3/4 yards.
Which pair of fractions has a sum of 13/12?
A. 1/2 + 1/3
B. 3/4 + 2/3
C. 1/4 + 2/3
D. 3/4 + 1/3
D. 9/12 + 4/12 = 13/12.
What is 2 1/4 + 3 2/9?
A. 5 17/36
B. 5 3/13
C. 5 1/12
D. 6 1/36
A. The fractional parts add to 9/36 + 8/36 = 17/36.
What is 7 5/6 - 3 1/4?
A. 4 1/2
B. 4 7/12
C. 3 7/12
D. 4 2/3
B. Subtract the wholes to get 4. The fractional difference is 7/12.
Five cups of yogurt are divided equally among 4 bowls. Each bowl also gets 1/2 cup of berries. How much food is in each bowl?
A. 1 1/4 cups
B. 1 3/4 cups
C. 3/4 cup
D. 2 1/4 cups
B. 1 1/4 + 1/2 = 1 3/4 cups.
A jug holds 4 1/2 liters. Sam pours 1 1/4 liters into one pitcher and 2/3 liter into another. How much did he pour out altogether?
A. 2 7/12 L
B. 1 5/12 L
C. 3 1/4 L
D. 1 11/12 L
D. Add the two amounts poured out. 1 1/4 + 2/3 = 1 11/12 liters.
Evaluate (1 ÷ 4) + (2 ÷ 5).
A. 13/20
B. 1/3
C. 3/20
D. 7/10
A. 1/4 + 2/5 = 5/20 + 8/20 = 13/20.
What is 3 5/6 + 2 3/4?
A. 5 4/5
B. 5 7/12
C. 6 1/12
D. 6 7/12
D. 10/12 + 9/12 = 1 7/12. Add the 5 wholes to get 6 7/12.
What is 6 1/5 - 2 3/4?
A. 4 11/20
B. 3 11/20
C. 4 9/20
D. 3 9/20
D. Regroup 6 4/20 as 5 24/20. Then subtract 2 15/20.
A cook divides 7 cups of soup equally among 6 bowls, then adds 3/4 cup of broth to each bowl. How much is in each bowl now?
A. 1 5/12 cups
B. 2 1/12 cups
C. 1 7/12 cups
D. 1 11/12 cups
D. 7/6 + 3/4 = 14/12 + 9/12 = 23/12 = 1 11/12 cups.
A roll has 10 1/2 feet of paper. A small poster uses 2 1/4 feet. A large poster uses 1 1/2 feet more than the small poster. How much paper is left after both posters?
A. 6 3/4 ft
B. 4 1/2 ft
C. 6 ft
D. 3 3/4 ft
B. The large poster uses 3 3/4 feet. Together the posters use 6 feet, leaving 4 1/2 feet.
Evaluate (4 1/2 - 7/4) + 2 2/3.
A. 4 5/12
B. 5 1/12
C. 5 5/12
D. 6 5/12
C. Inside the parentheses, 4 1/2 - 1 3/4 = 2 3/4. Then 2 3/4 + 2 2/3 = 5 5/12.
FRQ · Find the error. Susan writes 3/4 + 5/6 = 9/12 + 10/12. On her next line, she writes 19/24.
(a) Is her first line correct? Explain.
(b) Is her second line correct? Explain and give the sum.
(a) Yes. Both fractions were renamed in twelfths so the pieces are the same size. (b) No. Nine twelfths plus ten twelfths is nineteen twelfths. The sum is 19/12 = 1 7/12.
FRQ · Show and explain. Eli says 5 1/8 - 2 5/6 must be greater than 3 because 5-2=3.
(a) Do you agree? Explain without finding the exact difference.
(b) Find the exact difference and show your work.
(a) No. The starting number has only 1/8 beyond 5, but Eli is taking away an extra 5/6 beyond 2. The difference must be less than 3. (b) 4 27/24 - 2 20/24 = 2 7/24.
FRQ · Two batches. Six friends share 5 pans of cornbread equally at lunch. Later, the same friends share 2 more pans equally. All pans are the same size.
(a) How much does each friend get at lunch?
(b) How much does each friend get altogether? Show how you know.
(a) 5/6 of a pan. (b) Each gets another 2/6 = 1/3 of a pan. Altogether, 5/6 + 2/6 = 7/6 = 1 1/6 pans per friend.
FRQ · The class mural. A bucket starts with 6 1/4 gallons of paint. The class uses 1 5/6 gallons on Monday and 2 1/3 gallons on Tuesday.
(a) How much paint did the class use altogether? (b) How much is left? Show your work and explain how you know.
(a) 1 5/6 + 2 1/3 = 3 7/6 = 4 1/6 gallons used. (b) 6 1/4 - 4 1/6 = 2 1/12 gallons left. The amount used plus the amount left equals the starting amount.
FRQ · Beat the weight limit. A box can hold up to 3 pounds. Three books weigh 7/8 lb, 5/6 lb, and 9/10 lb.
(a) Without finding the exact sum, explain whether all three books fit within the weight limit.
(b) Would your conclusion still hold if the third book weighed exactly 1 lb? Explain.
(a) Yes. Each book weighs less than 1 lb, so together they weigh less than 3 lb. (b) Yes. The first two books together weigh less than 2 lb. Adding exactly 1 lb still leaves the total below 3 lb.