1. Ratios, Proportions, and Percents
Grade 7 Pre-Algebra
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Writing Ratios
A ratio is a comparison of two quantities by division.
10 to 15
10:15
a to b
a:b
Regardless of how you write the ratio, you read as “ten to fifteen’
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Writing Ratios
A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form.
Students with jobs to students without jobs
= 40/60 = 2/3
Students without jobs to all students surveyed
=60/100 = 3/5
Response
Number
Have a job 40
Don’t have a job 60
Total
100
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Your Turn!
Use the table above to write each ratio in the simplest form.
Students with jobs to all students surveyed.
Students without jobs to students with jobs
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5. Finding rates and Unit Rates
A rate is a ratio that compares quantities in different units.
A unit rate is a rate that has a denominator of 1.
Examples : unit cost, gas mileage, speed etc.
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6. Finding rates and Unit Rates
The table shows prices for different sizes of the same dish detergent. Which size has the lowest unit cost?
Trial: price/volume=$.78/6 fl oz = $.13/fl oz
Regular: price/volume= $1.20/12 fl oz = $.10/fl oz
Family: price/volume= $2.24/28 fl oz = $.08/fl oz
Economy: price/volume = $3.60/40 fl oz = $.09/fl oz
Size
Volume (fl oz)
Price
Trial 6
$.78
Regular 12
$1.20
Family 28
$2.24
Economy 40
$3.60
The family size has the lowest unit cost.
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Your Turn!
Find each unit rate.
Two liters of spring water cost $1.98
A car goes 425 mi on 12.5 gal of gas
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Converting a rate
Convert 10 mi/h to feet per minute 1
880 6 1
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Your Turn!
3.5 qt/min = __ gal/h
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Solving Proportions
A proportion is an equality of two ratios
6/9 = 8/12 If
The products ad and bc are called the cross products of the proportion a/b = c/d
Multiplication Property of Equality
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Cross Products
In a proportion, the cross products are equal.
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12. Multiplying to solve a proportion
Solve x/9 = 4/6
Method 1: Multiplication Property of Equality
Method 2: Cross Products
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Your Turn!
Solve h/2 = 2/3
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14. Testing for a Proportion
In a proportion, the cross products are always equal. If they are not equal, the ratios do not form a proportion.
Do the ratios 4/6 and 10/14 form a proportion? Explain. ? ?
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Your Turn!
Tell whether the two ratios form a proportion.
6/9; 4/6
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16. Similar Figures and Scale Drawings
Similar figures have the same shape, but not necessarily the same size.
They have corresponding angles and corresponding sides.
The symbol ~ means is similar to.
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17. Similar Figures and Scale Drawings
Corresponding angles
Similar figures have two properties:
The corresponding angles have equal measures.
The lengths of corresponding sides are in proportion.
8.3
64° B
61°
10.0
55° X C
9.1
64°
12.4
15.0 Y
61°
Corresponding sides
55°
13.6 Z
∆ABC ~ ∆XYZ
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18. Similar Figures and Scale Drawings16 B
Parallelogram ABCD ~ parallelogram EFGH. Find the value of x.
Write a proportion to the corresponding sides.
Side DA corresponds to side HE and Side AB corresponds to side EF. X F E 24 D C 18 G H
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Your Turn! A 16 B
Parallelogram ABCD ~ parallelogram KLMN. Find the value of y. 12 L K 21 D C Y M N
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Indirect Measurement
A tree casts a shadow 10ft long. A 5ft woman casts a shadow 4 ft long. The triangle shown for the woman and her shadow is similar to the triangle shown for the tree and its shadow. How tall is the tree?
10 ft
5 ft
4 ft
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Your Turn!
A building 70ft high casts a 150-ft shadow. A nearby flagpole casts a 60-ft shadow. Draw a diagram. Use similar triangles to find the height of the flagpole.
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Scale Drawing
A scale drawing is an enlarged or reduced drawing that is similar to an actual object or place.
The ratio of a distance in the drawing to the corresponding actual distance is the scale of the drawing.
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Scale Drawing
The scale of the map is 1 in.: 40 mi. About how far from Atlanta is Charlotte?
Map distance = 1 ½ in. or 1.5 in.
Map/actual : 1/40 = 1.5/d
1 x d = 40 x 1.5
d = 60
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24. Fractions, Decimals, and Percents
A percent is a ratio that compares a number to 100.
You can write is a fraction with denominator of 100.
5% = 5/100 = 1/20
125% = 125/100 = 5/4 = 1 ¼
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25. Fractions, Decimals, and Percents
To write a percent as a decimal, write the percent as a fraction with a denominator of 100.
Then divide to convert the fraction to a decimal.
9.7% = 9.7/100 = 0.097
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26. Fractions, Decimals, and Percents
To write a decimal as a percent, rewrite the decimal as a fraction with a denominator of 100. Then write the fraction as a percent.
Another way is to move the decimal point two places to the right and add a percent sign.
0.333 = 333/1000=33.3/100 = 33.3%
0.333 = 33.3%
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Your Turn!
Write 58% as a fraction
Write 16% as a decimal
Write 0.4 as a percent
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Finding Part of a Whole
Find 75% of 40.
75/100 = n/40
75 x 40 = 100n
75 x 40/100 = 100n/100
30 = n
75% of 40 is 30
75% 30
part
100% 40
whole
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Your Turn!
207 is 46% of what number?
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Break!!!
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Assessment
Write 9:24 as a fraction in simplest form.
Write 150 mi in 3 h as a unit rate.
Solve 5/6 = n/42.
The figures are similar. Find x. 20 30 30 x
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Assessment
A map has a scale of 1 cm : 75 km. What is the distance on the map for an actual distance of 37.5 km?
Write 24% as a fraction in simplest form and as a decimal.
Write 0.3 as a percent.
Find 15% of 48.
20% of x is 30. What is x?
Do a% of b and b% of a represent the same amount?
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Good Job!
Remember to do the practice worksheets!!!
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