Monday October 18,2010Monday October 18,2010

Review for Benchmark Assessment on Rates, Ratios and Proportions

Vocabulary ReviewVocabulary ReviewRate

◦Are ratios that compare 2 different kinds of quantities. Ex: miles per hour, distance over time

Ex: If I can run 5 miles in 3 hours how many hours will it take me to run 15 miles?

Vocabulary cont’dVocabulary cont’dUnit Rate:

◦Rate for a single unit of measure◦Ex: If Joe gets paid $400 in 2 weeks

how much does he get paid per week?

◦Per week tells for 1 week

12

400 x

Vocabulary cont’dVocabulary cont’dRatio

◦Ratio compares 2 quantities using division.

◦Ex: A garden has 23 flowers with 17 roses and 6 tulips. What is the ratio if tulips to Roses?

◦ Tulips to roses : 6 to 17◦ Tulips to roses 6:17◦ Tulips to roses

17

6

Vocabulary Cont’dVocabulary Cont’dVariable : a lower case letter used

to represent an unknown valueProportion

◦A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal• What is an equivalent ratio?• You can find equivalent ratios by multiplying

or dividing both sides by the same number.This is similar to finding equivalent fractions.

Vocabulary cont’dVocabulary cont’dA ratio is in its simplest form

when both sides are whole numbers and there is no whole number which both sides can be divided by.

RatiosRatios3 ways to write

ratios 5 to 65 : 6

6

5

Ratios cont’dRatios cont’dEquivalent

Ratios:Multiply or divide

both sides by the same number ( any number but 0 and 1)

When a 2 equivalent ratios are given but one value is missing how do we solve?◦ Find the

relationship and do whatever you do to the numerator to the denominator.

RatesRatesA rate is a ratio that expresses how

long it takes to do something, such as traveling a certain distance.

To walk 3 kilometers in one hour is to walk at the rate of 3 km/h. The fraction expressing a rate has units of distance in the numerator and units of time in the denominator.

set two ratios equal to each other and solving for an unknown quantity (variable), that is, solving a proportion.

RatesRates cont’dcont’dExample:Juan runs 4 km in 30 minutes. At

that rate, how far could he run in 45 minutes?

ProportionsProportionsStep 1: set the 2 ratios equal to

eachotherStep 2: Cross multiply the means

( denominator 1 times numerator 2) and the extremes ( numerator 1 times denominator 2). Make sure the products are equal.

Step 3: divide both sides by the term in front of the variable.

Review SheetReview SheetHandout will be given for review

Homework : STUDY STUDY STUDY!!!!!!!!!!!