Chapter 7

RATIOS AND PROPORTIONS

Lesson 1 Ratios

Equivalent ratios – two ratios that have the same value.

You can simplify ratios just as you simplify fractions (do not write ratios as mixed numbers, leave them as improper fractions if necessary).

You can cancel units that are the same in the numerator and in the denominator.

Lesson 7-1 (cont.)

You can use ratios to compare units of measure.

Example: Write the ratio 2 feet to 10 inches as a fraction in simplest form.

2 feet = 24 inches

10 inches 10 inches (Convert 2 feet to in.)

= 12 inches = 12

5 inches 5

Lesson 7-2 Rates

Rate – A ratio that compares two quantities with different kinds of units.

Unit Rate – A rate that is simplified so that it has a denominator of 1.

(To find the unit rate, divide the numerator by the denominator. Be sure to write the units in your answer)

Ex: 24 miles in 3 hours = 8 miles/1 hour = 8 miles/hr

Lesson 7-3 Solving Proportions

Proportion – two ratios that are equivalent.Cross product – the product of the

numerator of one ratio and the denominator of the other ration.

Ex: 6 = 3

10 5

6 x 5 = 3 x 10 so the rations form a proportion.

7-4 Scale Drawings

Scale drawing – a drawing that represents something too larg or too smal to be drawn actual size.

Scale – the relationship between the distance on the map and the actual distance.

Scale factor – a scale written as a ratio in simplest form.

Scale model – can be used to represent something too large or too small to for an actual size model.

Lesson 7-4 (cont.)

Be sure to include the correct units when writing ratios.

The scale is the ratio of the drawing measure to the actual measure.

To find the scale factor:

½ in = ½ in (Convert 3 feet to inches)

3 ft 36 in (Simplify)

½ ÷ 36 = ½ x 1/36

= 1/72 ← scale factor

7-5 Fractions, Decimals, and Percents

Percent – a ratio that compares a number to 100.

Percents, fractions, and decimals are all different names that represent the same number.

To write a percent as a fraction, write it as a fraction with a denominator of 100. Divide or simplify.

7-5 (cont.)

Ex: 13.5% = 13.5 x 10 = 135 = 27

100 10 1000 200

Ex: 66 2/3% = 66 2/3 = 200/3

100 100

= 200/3 x 1/100

= 2/3

7-5 (cont.)

To write a fraction as a percent you may:Write an equivalent fraction with a denominator of 100 4/25

= 16/100 = 16%Write a proportion and cross multiply – 5/8 = x/100 → 5 x 100 = 8x 500/8 = x x = 62.5%Write fraction as a decimal and multiply by 100 5/6 = 0.83333…. (Multiply by 100) ~ 83.33%

7-6 Percents Greater Than 100% and Less Than 1%

Percents greater than 100% or less than 1% can be written as decimals by dividing by 100 (or moving the decimal point two places to the left).

Decimals less than 0.01 and greater than one can be written as percents by multiplying by 100 (or moving the decimal point two places to the right).

Some percents are written as whole numbers.

Ex: 300% = 3; 500% = 5

7-7 Percent of a Number

A proportion can be used to find a percentEx: What number is 120% of 24? 120 = x Part 100 24 Whole 120 * 24 = 100x Cross Multiply x = 28.8 You can multiply to find a percent What number is 120% of 24?120% of 24 = 120% x 24 (of means multiply)

= 1.2 x 24 = 28.8

Lesson 7-8 The Percent Proportions

Percent Proportion – compares a part of a quantity to the whole quantity (the base).

Part = Percent tip: is = %

Whole 100 of 100

Ex: What percent of 50 is 18?

x = 18 (Solve by cross multiplying)

100 50

50x = 1800; x = 36% (Your answer is a %)

Lesson 7-8 (cont)

What number is 2% of 35? 2 = x 100 352*35 = 100x70 = 100x; x = 0.7 62 is 90.5% of what number? 90.5 = 62 100 x90.5x = 100*6290.5x = 6200; x = 6200/90.5 = 68.5