Ratios, Proportions, and Percents Grade 7 Pre-Algebra Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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’ Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

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. Copyright © Ed2Net Learning, Inc.

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. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Converting a rate Convert 10 mi/h to feet per minute 1 880 6 1 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Your Turn! 3.5 qt/min = __ gal/h Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Cross Products In a proportion, the cross products are equal. Copyright © Ed2Net Learning, Inc.

Multiplying to solve a proportion Solve x/9 = 4/6 Method 1: Multiplication Property of Equality Method 2: Cross Products Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Your Turn! Solve h/2 = 2/3 Copyright © Ed2Net Learning, Inc.

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. ? ? Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Your Turn! Tell whether the two ratios form a proportion. 6/9; 4/6 Copyright © Ed2Net Learning, Inc.

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. Copyright © Ed2Net Learning, Inc.

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 Copyright © Ed2Net Learning, Inc.

Similar Figures and Scale Drawings 16 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Your Turn! A 16 B Parallelogram ABCD ~ parallelogram KLMN. Find the value of y. 12 L K 21 D C Y M N Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

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 Copyright © Ed2Net Learning, Inc.

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 Copyright © Ed2Net Learning, Inc.

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% Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Your Turn! Write 58% as a fraction Write 16% as a decimal Write 0.4 as a percent Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Your Turn! 207 is 46% of what number? Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Break!!! Copyright © Ed2Net Learning, Inc.

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Copyright © Ed2Net Learning, Inc. 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 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 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? Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Good Job! Remember to do the practice worksheets!!! Copyright © Ed2Net Learning, Inc.