Table Of Contents. Ratio. Tape/Bar Diagrams. Ratio Table. Double Line Diagram. Rates and Unit Rates. Proportions. Finding Equivalent Rates.

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1 RP Notes.

2 Table Of Contents Ratio Tape/Bar Diagrams 3 4 Ratio Table 5 d Double Line Diagram 6 Rates and Unit Rates Proportions Finding Equivalent Rates Percent Discount Tips and Tax Percent Conversion

3 Ratio- a comparison of two things. Ratios are always written in the order they are appear. 3 Ways to Write Ratios Fraction form, colon form, to form Example: In a class there are 6 girls and 5 boys. What is the ratio of boys to girls. Fraction form Colon form to form 5 6 5:6 5 to 6 You may simplify the ratios, however NEVER make the fraction form a mixed number. When reading fraction form you would read it as seven to three NOT seven thirds.

4 Tape Diagrams Tape diagrams are visual models that use rectangles to represent the parts of a ratio. David and Jason have marbles in a ratio of 2:3. Together, they have a total of 35 marbles. How many marbles does each boy have? David Jason This ratio is modeled here by drawing 2 rectangles to represent David s portion, and 3 rectangles to represent Jason s portion. The rectangles are uniform in size and lined up. Each box has the same value Since together they have 35 marbles, divide this by the number of boxes to find the value of each box 35 5 = 7 ***each box has a value of 7 David 7 7 Jason David 7 x 2 = 14 marbles

5 Ratio Tables A ratio table organizes data into columns that are filled with pairs of numbers that have the same ratio, or are equivalent. Equivalent ratios express the same relationship between two quantities. A recipe for 1 apple pie calls for 6 cups of sliced apples. How many cups of sliced apples are needed to make 4 apple pies? Refer to the original ratio pies 1 4 Cups of 6? apples Multiplying or dividing two related quantities by the same number is called scaling. You may sometimes need to scale back and then scale forward or vice versa to find an equivalent ratio. A department store has socks on sale for 4 pairs for $10. Use the ratio table at the right to find the cost of 6 pairs of socks. 2 x 3 Pairs of Socks 4 2 Cost in $ ? There is no whole number by which you can multiply 4 to get 6. Instead, scale back to 2 and then forward to 6. So, the cost of 6 pairs of socks would be $15

6 Double Line Diagrams Double number line diagrams are best used when the quantities have different units. Double number line diagrams can help make visible that there are many, even infinitely many, pairs of numbers in the same ratio It took Megan 2 hours to complete 3 pages of math homework. Assuming she works at a constant rate, if she works for 8 hours, how many pages of math homework will she complete? What is the average rate at which she works? 0 3 Pages 0 2 Hours Pages Hours

7 Rates and Unit Rates A rate is a ratio that compares two quantities with different kind of units. Units must be included when writing or solving rates. A unit rate is a rate that has a denominator of 1 unit. Danny typed a 15-letter text message in 3 seconds. 1. Write the Rate: 15 characters 3 seconds 2. Set up to find unit rate, how many per second 15 characters 3 second = 1 second 3. Compute the Unit Rate by dividing top and bottom by the same number characters 3 second = 5 characters 1 second 3 5 Characters per second

8 Is It Proportional (Equivalent Rates)? A proportion is a name we give to a statement that two ratios are equivalent. When two ratios are equal, then the cross products of the ratios are equal. a b = c d a d = c b 5 15 = = = 150 Multiply the diagonals and determine if the statement is true. If the statements is true, then the ratios are equivalent or proportional.

9 Finding Equivalent Rates Method 1 Unit Rates If 5 pairs of socks cost $15, how much does 11 pairs of socks cost? Step 1 Write Equivalent Rates $15 5 = m 11 Step 2: Find the unit rate of the given rate. $15 5 = m 11 $5 1 = m 11 Step 3: Multiply top and bottom by same number x 11 $5 1 = m 11 x 11 $55 for 11 pairs of socks Method 2 Multiply or Divide Top and Bottom Eli is making guacamole. He uses 2 tablespoons of cilantro for every 3 avocados. At this rate how many tablespoons of cilantro are needed for 9 avocados? Step 1- Write Equivalent Rates 2 3 = t 9 Step 2: multiply or divide top and bottom by same number x = t 9 x3 T = 6 tablespoons Method 3 Cross Products Eli is making guacamole. He uses 2 tablespoons of cilantro for every 3 avocados. At this rate how many tablespoons of cilantro are needed for 9 avocados? Step 1- Write Equivalent Rates 2 3 = t 9 Step 2- Cross multiply 2 9 = = 6 tablespoons

10 Percent Percent means parts per 100 The symbol is % Example: 25% means 25 per 100 (25% of this box is green) Solve for the Percent Solve for the Part Solve for the Whole Shane got 30 out of 50 problems on a quiz correct. What percent did he get correct? What percent of 50 is 30? = % 100 Cross multiply and show steps = % Tommy got an 80% on a 60 question test. How many questions did he get correct? 80% of 60 is what number? x 60 = Cross multiply to show all steps = = x 48 questions correct Maria got 90% of her test correct. If she got 45 problems correct, how many problems were on the test? 90% of what number is 45? 45 x = Cross multiply to show all steps = = x problems on the test

11 Discount is the percentage you save on an item that is on sale. It is not what you are paying for the item. Example: I have a 20% off coupon. If the item I am buying costs $50, how much will I be saving? Your original price is the whole and the discount is the part. x = 20% You will save $10. Sale Price is how much you are paying for an item on sale. It is the original price minus the discount. Example: In the above example what is the sale price? = $40 Tax is a percentage of a bill or item that is added to the price. The tax amount is the part. Example: Alexandra bought a pair of jeans that cost $ There is an 8% sales tax on clothing. How much tax will she pay? The price is the whole and the tax amount is the part. $49.99 = 8% 100 $5.00 tax Final price = $54.99 Tip is the percentage of a bill that is left for the server based on their service. It is customary to leave 10%- 20%. The tip is the part. Victoria went out to lunch and the bill came to $ She want to leave the waitress a 20% tip. How much tip will she leave? The cost of the bill is the whole and the tip is the part. = 20% $5.00 tip

12 Percent Conversions Converting Decimal to Percent Example: Write.63 as a percent. To write a decimal as a percent, move the decimal point two places to the right ( multiply by 100).63 = 63% Converting Percent to Decimal Example: Write 7.2% as a decimal. To write a percent as a decimal, move the decimal point two places to the left (divide by 100) 7.2 % =.072 Converting Percent to Fraction Example: Write 25% as a fraction Place the percent number over 100 and reduce = 1 4 Converting Fraction to Percent Example: Write 3 as a percent 4 Method 1: Change the fraction to a decimal: numerator divided by denominator. Then convert decimal to percent. Method 2: Set up an equivalent ratio 3 4 = 3 4 =.75 = 75% 3 = % Then cross multiply: 3 x = 75 and add percent sign, 75% 4 100