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```7-1 RATIO AND PROPORTION
1. 3
5
2. 2
1
3. 3:20
4. 2:15
5. 2 to 1
RATIO: A COMPARISON OF 2 NUMBERS
a
b
a:b
a to b
Must be in same units
12 in = 1 ft
5280 ft = 1 mi
100 cm = 1 m
10 mm = 1 cm
1000 mm = 1 m
EXAMPLE:
SIMPLIFY THE RATIO 2 FT: 30 IN
Method 1
* Feet
2 ft: 2.5 ft
20 : 25
4:5
Method 2
* Inches
24 in: 30 in
4:5
TRY ON OWN
1)
1 m: 52 cm
2)
10 mm: 3.2 cm
3)
1.25 ft: 3 in
1) 25:13
2) 5:16
3) 5:1
EXAMPLE: LET X = 2 AND Y = 3
6x2 to 12xy
6(2)2 to 12(2)3
6(4) to 12(6)
24 to 72
4 to 12
1 to 3
TRY ON OWN: X = 2 AND Y = 3
1)
2)
3)
yx
x
xy
y
x2 y
x  y  1
1)
1
2
2) 2
1
3) 3
2
EXAMPLE: SIMPLIFY
2
6x
12 xy
*Divide Whole Numbers
*Subtract Exponents
x
2y
TRY ON OWN: SIMPLIFY
1)
2)
3)
yx
x
xy
y
x2 y
x  y  1
1) In Simplest Form
2)
3)
x
1
xy
y 1
EXAMPLE
The ratio of the angles of a triangle are 4:4:7.
Find the measure of each angle.
*Usually we reduce by dividing. Now we will
work backwards by multiplying
4x + 4x + 7x = 180
15x = 180
x = 12
4x = 4(12) = 48
4x = 4(12) = 48
7x = 7(12) = 84
TRY ON OWN
1)
2)
The ratio of the measures of 2 complementary
angles is 1:2. Find the measure of each angle.
The measures of the angles of a pentagon are in
the ratio 1:2:3:6:15. Find the measure of each
angle.