7 th Grade Pre-algebra Chapter 6 Notes

6.1 Ratios and Rates Vocabulary Ratio: a comparison of two numbers by division. Rate: a ratio of two measurements having different kinds of units. Unit Rate: when a rate is simplified so that it has a denominator of 1. Ex. mph

Writing Ratios as Fractions Express the ratio 9 goldfish out of 12 goldfish as a fraction in simplest form. Express the ratio of girls to boys in this class as a fraction in simplest form Express the ratio of boys to girls in this class as a fraction in simplest form.

Write Ratios as Fractions Units of measure must be the same in order to simplify!!! Express 3 feet to 16 inches as a fraction in simplest form.

Find Unit Rates Since we want the cost of 1 soda, put the soda on the bottom of our fraction Hint: Money will almost ALWAYS be the numerator of the fraction!!

Converting Rates To convert a rate such as miles per hour to feet per second, you can use dimensional analysis. Carry the units throughout the computation. A Grizzly bear can run 30 miles in 1 hour. How many feet is this per second? There are 5280 ft in a mile. 30 x 5280 = 158,400 There are 3600 second in an hour (60min x 60sec) Simplify to get 1 in the denominator by dividing both the numerator and denominator by 3600

You Try…

Problem Solving

6.2 Using Proportions Vocabulary Proportion: a statement of equality of two ratios Cross Products: when you multiply the numerator of the first ratio by the denominator of the second ratios and compare that product to the product of the denominator of the first ratios and the numerator of the second ratio.

Use Cross Products to identify Proportions Pairs of ratios are only proportional if their cross products are equal. 2x20 = 40 8x5 = 40 = equal 3x24 = 72 4x18 = 72 = equal 2.5x6 = x7.5 = 15.0 = equal

Solving Proportions We can solve for the unknown value in a proportion by using cross multiplication. 35x = 385

Solving Proportions 1m = 216 m = 216 2x = 135 x = 67.5

Problem Solving

6.3 Scale Drawings and Models Vocabulary Scale Drawing: a drawing used to represent an object that is too large or too small to be drawn at actual size. Scale Model: a model used to represent an object that is too large or too small to be built at actual size. Scale: gives the relationship between the measurements on the drawing or model and the measurements of the real object. Scale Factor: The ratio of a length on a scale drawing or model to the corresponding length on the real object.

Using Scales

.5/10=.45/x.5/10=1/x.5/10=.75/x

6.4 Fractions, Decimals, and Percents Vocabulary Percent: a ratio that compares a number to 100

Writing Percents as Decimals To write a percent as a decimal, divide by 100 and remove the percent symbol Divide by 100 Remove % sign

Writing Decimals as Percents To write a decimal as a percent, multiply by 100 and add the percent symbol multiply by 100 Add % sign

Writing Percents as Fractions To write a percent as a fraction, express the ratio as a fraction with a denominator of 100 Put % over 100 Simplify

Writing Fractions as percents Method #1 To write a Fraction as a percent, write an equivalent fraction with a denominator of 100. Write the new numerator as a percent multiply by 20 to get the denominator to be 100 Write the numerator as a percent

Writing Fractions as Percents Method #2 To write a fraction as a percent, first change the fraction to a decimal, then change the decimal to a percent change fractions to a decimal by dividing the numerator by the denominator Add % sign change decimal to a percent by multiplying by 100

Practice = 90% = 135% = 62%

Practice =50% =.50 =75% =.75 =125% =1.25

Problem Solving

6.5 Using the percent Proportion Vocabulary Percent Proportion: a proportion in which a ratio is being compared to a percent Part: the number being compared to the whole (always the numerator) Base: The whole quantity (the denominator)

Find the Percent Five is what percent of 8? Step 1: set up a proportion 5 is the part 8 is the base percent is the unknown always 100

Find the Percent Five is what percent of 8? Step 2: Find the cross products Step 3: Solve for the variable (p) 500 = 8p 62.5 = p Divide each side by 8 Add % sign since we were looking for the percent

Find the Part What number is 5.5% of 650? Step 1: set up a proportion the part is unknown 650 is the base 5.5 is the percent always 100

Find the Percent Five is what percent of 8? Step 2: Find the cross products Step 3: Solve for the variable (p) 100a = 3575 a = Divide each side by 100

Practice 1400 = 50x x = x = 3600 x = 36

Apply the Percent Proportion Since the jeans are 40% off, the remaining price is 60% of the original price