Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
RATIOS & RATES
R e ct iv ide
In a Rectivide puzzle, the goal is to divide a single rectangle into three smaller
rectangles so that each small rectangle has the same ratio of gray squares to white
squares as the original rectangle.
EXAMPLE
Solve the Rectivide puzzle below.
6JGTCVKQQHITC[USWCTGUVQYJKVGUSWCTGUKPVJGQTKIKPCNTGEVCPINGKU
5QYGECPOCMGITQWRUQHUSWCTGUKPGCEJQHVJGUOCNNGTTGEVCPINGUYKVJITC[
CPFYJKVGUSWCTGU6JGTGHQTGVJGCTGCQHGCEJUOCNNTGEVCPINGKUCOWNVKRNGQH
We can split the rectangle into three smaller rectangles as shown below so that the
ratio of gray squares to white squares is 1:2 in each smaller rectangle.
1:2
This is the
only solution.
PRACTICE
Solve each Rectivide puzzle below.
43.
44.
45.
46.
46
Beast Academy Practice 5C
Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
RATIOS & Rect
R ATES
i vi de
PRACTICE
Solve each Rectivide puzzle below.
47.
48.
49.
50.
51.
52.
53.
54.
Beast Academy Practice 5C
47
Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
RATIOS & RATES
P rop ort ions
We often use fractions when working with ratios. For example, a boy:girl ratio
QHECPDGYTKVVGPCU
boys 2
.
girls This means that the number of boys divided by the number of girls equals 2 .
A proportion is an equation showing that two ratios are equal. There are many ways
VQſPFVJGOKUUKPIXCNWGKPCRTQRQTVKQP
x
To solve for xKPVJGRTQRQTVKQPx :21, we can solve for x in the equation 21 .
EXAMPLE
What is the value of x in the equation below?
x
21
We can convert the fraction.
12
,
21
On the left side, we get •5Qx12.
59.
•
•
x
21
x
21
•
21
•
21
x
Fill in the missing value in each equation below.
2
15
PRACTICE
•
or
To isolate the variable x, we multiply both sides of
the equation by 21.
55.
so x12.
We can isolate the variable.
PRACTICE
•
x
21
We can write with a denominator of 21 by
OWNVKRN[KPIVJGPWOGTCVQTCPFFGPQOKPCVQTD[
56.
15
5
12
8
57.
58.
19
11 88
Solve for the variable in each equation below.
x
60.
a
9
59. xAAAAA
60. aAAAAA
61.
w
21
15
62.
m
9
21 61. wAAAAA
62. mAAAAA
48
)WKFG2CIGU
Beast Academy Practice 5C
Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
EXAMPLE
RATIOS Prop
& RoATES
rt i o n s
What is the value of x in the equation below?
5
8
x
9
5
9
We can eliminate the denominators.
8
5
•
5 • x8 • 9
We eliminate the denominators of 9 and x by
multiplying both sides of the equation by a common
multiple of their denominators: 9x.
5x
x
5
This gives 5x
72
2
x 25
We divide both sides by 5 to get x 5 14 5 .
a
8
9x x • 9x
c
For any equation b = d ,
we have ad=bc.
PRACTICE
63.
Solve for the variable in each equation below.
Write your answer in simplest form.
2 15
m
64.
12
5
s 8
63. mAAAAA
64. sAAAAA
65.
15
c
66.
a 9
65. cAAAAA
66. aAAAAA
67.
2 15
z
5
68.
10
10
v
67. zAAAAA
68. vAAAAA
69.
8
11
n 6
70.
10
6
r
69. nAAAAA
70. rAAAAA
Beast Academy Practice 5C
)WKFG2CIGU
49