Transcript Chapter 7 - Mrs. Van Boening

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 ratio.
Ex: 6 = 3
10 5
6 x 5 = 3 x 10 so the ratios 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 percent
Ex: 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 35
2*35 = 100x
70 = 100x; x = 0.7
 62 is 90.5% of what number?
90.5 = 62
100
x
90.5x = 100*62
90.5x = 6200; x = 6200/90.5
= 68.5