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Solving Proporti
ons
Definitions:Proportion – an equation stating that two ratios are equal
Cross Products – are found by multiplying the
denominator of each ratio by the numerator of the other ratio
Using Unit Rates:
2.45 dollars 5 cards
=
Step 1: Find the unit price
Example: Postcards cost $2.45 for 5 cards. How much will 13 cards cost?
$ 0 . 49 per card
Step 2: You know the cost of one card. Multiply to find the cost of 13 card.
$ 0 . 49 per card
x
13 cards
=
$6.37
Using Unit Rates:
84.36 dollars 12 pairs
=
Step 1: Find the unit price
Example: Goggles cost $84.36 for a case of 12. How much will it cost for 17 pairs?
$ 7 . 03 per pair of goggles
Step 2: You know the cost of one pair of goggles. Multiply to find the cost of 17 pairs.
$ 7 . 03 per pair
x
17 pairs
=
$119.51
Using Unit Rates:
7.75 dollars5 notebooks
=
Step 1: Find the unit price
Example: The bookstore sales five notebooks for $7.75. At this rate how much would 7 notebooks cost ?
$ 1 . 55 per notebook
Step 2: You know the cost of one notebook. Multiply to find the cost of 7
notebooks. $ 1 . 55 per notebook
x
7 notebooks
=
$10.85
Using Unit Rates:
144 bricks 3 hours
=
Step 1: Find the unit price
Example: Steven can lay 144 bricks in 3 hours. At this rate, how many bricks can he lay in 8 hours ?
48 bricks per hour
Step 2: You know the number of bricks in 1 hour. Multiply to find the number in 8 hours.
48 bricks per hour
x
8 hours
=
384 brick
s
m 12 =
x 3
x 3
Since 12 x 3 = 36 21
36Find what number times 3 equals 21
m = 7
8 10 =
x 4
x 4
Since 10 x 4 = 40 k
408 x 4 = k
k = 32
Using Mental Math:
3 8 =
x 3
x 3
Since 8 x 3 = 24 b 24
3 x 3 = b
b = 9
5 g =
x 6
x 6
Since 5 x 6 = 30 30
48
g = 8
Find what number times 6 equals 48
Using Mental Math:
Examples:
S4
72
= 1.) Cross Multiply Opposite Numerators and denominators
2s = 7 • 4 2.) Multiply
2s = 28 3.) Divide both sides by 2
2s2
= 282
s = 14
4.) Simplify
Using Cross Products:
Examples:
10 5
u3
= 1.) Cross Multiply Opposite Numerators and denominators
10 • 3
= 5u 2.) Multiply
30 = 5u 3.) Divide both sides by 5
305
= 5u5
u = 6
4.) Simplify
Using Cross Products:
Examples:
20w
123
= 1.) Cross Multiply Opposite Numerators and denominators
20 • 3
= 12w 2.) Multiply
60 = 12w 3.) Divide both sides by 12
6012
= 12w12
w = 5
4.) Simplify
Using Cross Products:
Examples:
930
p 16
= 1.) Cross Multiply Opposite Numerators and denominators
9 • 16
= 30p 2.) Multiply
144 = 30p 3.) Divide both sides by 30
14430
= 30p30
p = 4.8
4.) Simplify
Using Cross Products:
Writing Proportions:Eight out of ten fish are trout. How many trout are there out of 40 fish?
810
n40
=
Trout = 32
8 • 40 = 10n320 10
n32010
10n10
=
=
According to a label, there are 25 calories in a serving of turkey. How many calories are in 2.5 servings?
25 1
x2.5
=
Calories =62.5
25 • 2.5
= 1x62.5 1x
62.51
1x1
=
=
Writing Proportions:
Chris drove 200mi in 4 hours. At that rate, how long would it take Chris to drive 340mi?
200 4
340 h
=
hours = 6.8
4 • 340 = 200h
1360 200h
1360200
200h200
=
=
Writing Proportions:
