Excerpt from Beast Academy Practice 4D. (C) 2015 www.BeastAcademy.com
FRACTIONS
D iv ision
EXAMPLE
'KIJVRQWPFUQHƀQWTCTGFKXKFGFKPVQ
1
RQWPFDCIU*QYOCP[DCIUCTG
5
PGGFGFVQJQNFCNNVJGƀQWT!
1
(TQOGCEJRQWPFQHƀQWTYGECPOCMGſXG 5 RQWPF
bags, so HTQOGKIJVRQWPFUQHƀQWTYGECPOCMG
ª40 bags.
PRACTICE
Answer each question below.
114. The Burger Palace orders a box that contains 12 pounds of
114. ________
1
hamburger patties. Each patty weighs of a pound. How many
patties are in the box?
115. One lap around the track at Kayla’s school is
1
5
of a mile. Kayla runs
OKNGUCTQWPFVJGVTCEM*QYOCP[NCRUFQGU-C[NCTWP!
116. Captain Kraken has sheets of plywood that are
1
116. ________
inches thick. A
stack of these plywood sheets is 18 inches tall. How many sheets
are in the stack?
117. A regular polygon whose sides are
1
5
of an inch long has a perimeter
QHKPEJGU*QYOCP[UKFGUFQGUVJGRQN[IQPJCXG!
118. The Beast Island Candy Shop makes 50 pounds of peppermint bark
1
115. ________
117. ________
118. ________
candy. The candy makers split the bark into 8 RQWPFDCIUYJKEJ
are each sold for $6. How much money will the shop collect if they
sell every bag of peppermint bark?
28
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Beast Academy Practice 4D
The reciprocal
of a number n is the
number we multiply n
by to get 1.
EXAMPLE
9JCVKUVJGTGEKRTQECNQH!
1
1
ª UQCPF are reciprocals.
1
KUVJGTGEKRTQECNQH
7
PRACTICE
119.
1
5
121. 5+6
123.
15
FRACTIONS
R e cip roca ls
Excerpt from Beast Academy Practice 4D. (C) 2015 www.BeastAcademy.com
Find the reciprocal of each number or expression below.
Reciprocal: ______
120. Reciprocal: ______
Reciprocal: ______
122. 6×9
Reciprocal: ______
Reciprocal: ______
124. Reciprocal: ______
125. Does 0 have a reciprocal? If so, what is it? If not, explain why not.
126. Write an expression for the reciprocal of n.
126. ________
(Assume that n is not zero.)
1
127. Write an expression for the reciprocal of a .
127. ________
128. Write an expression for the reciprocal of c+1.
128. ________
(Assume that a is not zero.)
(Assume that cKUPQV
129. What is the sum of the reciprocals of
Beast Academy Practice 4D
1
5
1
and ?
129. ________
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29
Excerpt from Beast Academy Practice 4D. (C) 2015 www.BeastAcademy.com
FRACTIONS
D iv ision b y Unit Fra ctions
EXAMPLE
1
What is 8÷ 5 ?
1
9GEQPUKFGTFKXKFKPIRQWPFUQHƀQWTKPVQ 5 RQWPFDCIU
1
Dividing by n
is the same as
multiplying by
the reciprocal
of n.
(TQOGCEJRQWPFQHƀQWTYGECPOCMGſXG 5 RQWPFDCIU
so HTQOGKIJVRQWPFUQHƀQWTYGECPOCMGª40 bags.
or
1
9GNQQMCVVJGPWODGTNKPGVQſPFQWVJQYOCP[ 5 ’s are in 8.
5KPEGVJGTGCTGſHVJUKPVJGTGCTGª40ſHVJUKP.
For example,
9÷4=9× 41 = 9
4 , and
5÷ 71 =5×7=35.
0
1
2
5
6
8
ſHVJU
1
We write 8÷ 5 ª40.
Dividing by a number is the same as
multiplying by its reciprocal.
PRACTICE
To compute each quotient below, multiply by the reciprocal.
Write your answers in simplest form.
130. 5÷ 1 1
131. ÷ 16
132. 9÷ 1 133.
30
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1
1
÷ 16 8
Beast Academy Practice 4D
Excerpt from Beast Academy Practice 4D. (C) 2015 www.BeastAcademy.com
F RAC TIONS
Division by Unit Fr a ct i o n s
PRACTICE
Write each quotient below in simplest form.
2
1
134. 11
÷2
135. 2 15 ÷ 18 1
136. 5÷(Ò 12
)
1
137. ÒÒ 12
(9÷ 101 )÷ 15 1
1
139. 9÷( 10
÷ 5 )
138.
PRACTICE
140. How many
Answer each question below.
1
EWRUEQQRUQHƀQWTCTGPGGFGFVQGSWCN 2 141. The tallest tree in Ranger Rick’s forest grows
140. ________
cups?
1
8
of an inch every week.
*QYOCP[YGGMUYKNNKVVCMGHQTVJGVTGGVQITQY inches?
142. 6CTCDTQWIJVICNNQPUQHYCVGTQPCJKMG5JGICXG 1 of a gallon
141. ________
142. ________
1
1
gallons of
to each of her hiking companions, which left her with
water. How many companions were on the hike with Tara?
1
YJCVKUVJGXCNWGQHa?
143. If a÷ 16
Beast Academy Practice 4D
143. ________
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31