7-1 RATIO AND PROPORTION

Answers to Warm Ups

1.

2.

3. 3:20

4. 2:15

5. 2 to 1

3

52

1

RATIO: A COMPARISON OF 2 NUMBERS

a:ba to b

Must be in same units12 in = 1 ft5280 ft = 1 mi100 cm = 1 m10 mm = 1 cm1000 mm = 1 m

a

b

EXAMPLE: SIMPLIFY THE RATIO 2 FT: 30 IN

Method 1* Feet

2 ft: 2.5 ft20 : 25

4 : 5

Method 2* Inches

24 in: 30 in4 : 5

TRY ON OWN

1) 1 m: 52 cm

2) 10 mm: 3.2 cm

3) 1.25 ft: 3 in

Answers:1) 25:132) 5:163) 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)

Answers:1)

2)

3)

y x

x

xy

y

2

1

x y

x y

1

2

2

1

3

2

EXAMPLE: SIMPLIFY26

12

x

xy

*Divide Whole Numbers

*Subtract Exponents

2

x

y

TRY ON OWN: SIMPLIFY

1)

2)

3)

Answers:1) In Simplest Form

2)

3)

y x

x

xy

y

2

1

x y

x y

1

x

1

xy

y

EXAMPLEThe 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 = 18015x = 180x = 12

4x = 4(12) = 484x = 4(12) = 487x = 7(12) = 84

TRY ON OWN

1) The ratio of the measures of 2 complementary angles is 1:2. Find the measure of each angle.

2) The measures of the angles of a pentagon are in the ratio 1:2:3:6:15. Find the measure of each angle.

Answers:1) 30,602) 20,40,60,120,300

HOMEWORK

Pg 243 #1-31