4-4 Solving ProportionsNumber

Operations Which property is shown here: 777 + 0 = 777?

Algebra An art teacher had a total of t markers. He gave an equal number of markers to each of 18 students and had 16 markers left over. Which equation should be used to find n, the number of markers each student received?A. t = 18n B. t = 34n C. t =18n + 16 D. t = 16n + 18

Geometry & Measurement

If the diameter of a circle is 25 inches, what is the radius of that circle?

Data, Statistics & Probability

A group of pet owners at a dog show were asked to name their favorite pet. Explain why this sample could be biased.

Potpourri List at least 5 different ways to represent the number 35.

BELLRINGER (DAY 79)

4-4 Solving ProportionsWorkbook page 105-106

1. x = 18

2. B = 11

3. P = 2

4. R = 15

5. Y = 5

6. C = 27

7. Z = 2

8. A = 36

9. Q = 2

10.S = 1

11. W = 1412. D = 513. 3/2 = c/18; c = 2714. 9/2 = x/16; x = 7215. 6/20 = 54/b; b = 18016. m/18 = 5/90; m = 117. 100/75 = 4/r; r = 318. 29/7 = x/28; x = 116 hrs19. 150/27 = 120/x; x = 21.6 lbs20. 2/8 = 5/x; x = 20 pints21. 512/4 = 7680/x; x = 60sec

4-4 Solving Proportions

Warm UpDetermine whether the ratios are proportional.

1. 58

, 1524

2. 1215

, 1625

3. 1510

, 2016

4. 1418

, 4254

yes

no

yes

no

4-4 Solving Proportions

Review how to solve proportions by using cross products.

4-4 Solving Proportions

For two ratios, the product of the numerator in one ratio and the denominator in the other is a cross product. If the cross products of the ratios are equal, then the ratios form a proportion.

5 · 6 = 30

2 · 15 = 30=2

56

15

4-4 Solving Proportions

Use cross products to solve the proportion.

Additional Example 1: Solving Proportions Using Cross Products

15 · m = 9 · 5

15m = 45

15m15

= 4515

m = 3

The cross products are equal.

Multiply.

Divide each side by 15 to isolate the variable.

= m5

915

4-4 Solving Proportions

Check It Out: Example 1

Use cross products to solve the proportion.

7 · m = 6 · 14

7m = 84

7m7

= 847

m = 12

The cross products are equal.

Multiply.

Divide each side by 7 to isolate the variable.

67

= m14

4-4 Solving Proportions

It is important to set up proportions correctly. Each ratio must compare corresponding quantities in the same order.

Suppose a boat travels 16 miles in 4 hours and 8 miles in x hours at the same speed. Either of these proportions could represent this situation.

16 mi4 hr

= 8 mix hr

16 mi8 mi

= 4 hrx hr

4-4 Solving Proportions

Check It Out: Example 2John filled his new radiator with 6 pints of coolant, which is the 10 inch mark. How many pints of coolant would be needed to fill the radiator to the 25 inch level?

11 Understand the Problem

Rewrite the question as a statement.• Find the number of pints of coolant required

to raise the level to the 25 inch level.

List the important information:• 6 pints is the 10 inch mark.

4-4 Solving Proportions

22 Make a Plan

Set up a proportion using the given information. Let p represent the pints of coolant.

6 pints10 inches

= p25 inches

pints inches

Check It Out: Example 2 Continued

4-4 Solving Proportions

Solve33

610

= p25

10 · p = 6 · 25

10p = 150

10p10

= 15010

p = 15

15 pints of coolant will fill the radiator to the 25 inch level.

Write the proportion.

The cross products are equal.

Multiply.

Divide each side by 10 to isolate the variable.

Check It Out: Example 2 Continued

4-4 Solving Proportions

Look Back44

610

= 1525

10 · 15 = 150

6 · 25 = 150

The cross products are equal, so 15 is the answer.

Check It Out: Example 2 Continued

4-4 Solving Proportions

1. Use cross products to solve the proportion.

=

A. t = 16

B. t = 24

C. t = 32

D. t = 36

Lesson Quiz for Student Response Systems

24 16

48 t

4-4 Solving Proportions

2. Use cross products to solve the proportion.

=

A. r = 20

B. r = 15

C. r = 10

D. r = 5

Lesson Quiz for Student Response Systems

4 5

r 25

4-4 Solving Proportions

Closure

What do you know about the cross-products of a proportion?