Unit 6 Review Lesson 1 Foundations

How is the mixed number below related to the improper fraction? 1 5 = 2 11 = 2

How to change an improper fraction to a mixed number Divide the numerator by the denominator. Put your remainder over the 5 = 2

How to change an improper fraction to a mixed number 2 r 1 ) 2 5 numerator denominator 5 = 2

How to change an improper fraction to a mixed number 1 2 denominator 2 ) 2 5 numerator Put your remainder over the Denominator. 5 = 2

How to change a mixed number to an improper fraction 1 7 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 4 = x 2 2

A ratio is a comparison of two numbers. What is a Ratio? A ratio is a comparison of two numbers. Ratios can be written in three different ways: a to b a:b Because a ratio is a fraction, b can not be zero Ratios are expressed in simplest form

The ratio of length and width of this rectangle is 4 to 1. How to Use Ratios? The ratio of boys and girls in the class is 12 to11. The ratio of length and width of this rectangle is 4 to 1. . 4cm 1cm The ratio of cats and dogs at my home is 2 to 1

= = How to simplify ratios? Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats and dogs to 2 to 1? = = Divide both numerator and denominator by their Greatest Common Factor 6.

How to simplify ratios? Let’s try cm first! A person’s arm is 80cm, he is 2m tall. Find the ratio of the length of his arm to his total height To compare them, we need to convert both numbers into the same unit …either cm or m. Let’s try cm first! Once we have the same units, we can simplify them.

More examples… Converting Percents to Decimals = = = = =

Converting Decimals to Percents In order to convert a decimal to a percent, either multiply the decimal by 100 and write the percent sign (%), or move the decimal point two places to the right and write the percent sign (%). Example 1: Convert 0.20 to a percent 0.20x 100= 20.00= 20% or 0.20= 0. 2 0= 20% Example 2: Convert 4.00 to a percent 4.00= 4.00x 100= 400.00= 400% or 4.00= 4. 0 0=400%

Converting Fractions to Percents To convert a fraction to a percent, change the fraction to a decimal ( by dividing the numerator by the denominator ). Then multiply the decimal by 100 and put a percent sign (%). Another way is to move the decimal point two places to the right and put a percent sign (%). Example 1: Convert 1/2 to a percent 1/2= 1÷ 2 = 0.50 0.50x 100= 50.00=50% or 0.50= 0. 5 0= 50% Example 2: Convert 1/3 to a percent 1/3= 1÷3= 0.333 0.333x 100= 33.300=33.3% or 0.333=0. 3 3 3=33.3%

Converting Percents to Fractions When converting percents to fractions, change the percent to a decimal ( divide the percent by 100 or move the decimal point two places to the left ). Then put the numbers behind the decimal point over the place that it is in ( tenths, hundredths, thousandths, etc.). Then simplify as necessary. Example 1: Convert 85% to a fraction 85% = 85÷ 100= 0.85= 85/100= 17/20 ( 85 is in the hundredths place. 17/20 is the simplified form of 85/100 ) Example 2: Convert 12.5% to a fraction 12.5%= 12.5÷ 100= 0.125= 125/1000=1/8 ( 125 is in the thousandths place. 1/8 is the simplified form of 125/1000 )

Word Problem Two out of every five movies rented from a store are action movies. Compare the number of action movies to the total number of movies rented.

How to Find the Percent of a Whole Number Step 1 - When you see a percent problem you know when you read “of” in the problem you multiply. x 25% of 200

How to Find the Percent of a Whole Number Step 2 – Change your percent to a decimal and then move it two places to the left. . . 25% x 200

How to Find the Percent of a Whole Number Step 3 – Multiply just like a regular decimal multiplication problem. 200 x . 25 1000 +400 5000

How to Find the Percent of a Whole Number Step 4 – Place the decimal point 2 places to the left in your answer. 200 x . 25 1000 +400 . 5000

Of a shipment of 450 flower pots and 8% arrived broken Of a shipment of 450 flower pots and 8% arrived broken. How many flower pots arrive broken?

How to find the Discount & Discounted Price Find out the % of the discount. Convert the % to a decimal. Multiply the decimal by the original price. Take the answer in step 2 and subtract it from the original price. Example Discount 20% = .20, $10 x .20 = $2.00 $10.00 - $2.00 = $8.00

Xbox 360 for $199.99 The Discount is 25% 9. What is the discount? $ 50.00 10. What is the price after the discount? $149.99 11. What is the price after the discount and after taxes? $162.36

Ipod Touch for $229.99 The tax rate is 4% 12. What is the tax? $ 9.20 13. What is the total price after taxes? $239.19

Interest paid by bank is unknown Principle (invested) 1. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $5,000 is invested at 4.5%, what is the total simple interest accumulated in the checking account after 2 years. I = PRT I= I=$450 Interest paid by bank is unknown Principle (invested) Rate changed to decimal Time is 2 years Multiply (.045) (2) (5,000)

Interest paid by bank is unknown Principle (invested) 2. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $7,000 is invested at 7.5%, what is the total simple interest accumulated in the checking account after 3 years. I = PRT I= I=$1575 Interest paid by bank is unknown Principle (invested) Rate changed to decimal Time is 3 years Multiply (7,000) (.075) (3)

Proportion is a statement that says two ratios are equal. In an election, Damon got three votes for each two votes that Shannon got. Damon got 72 votes. How many votes did Shannon get? Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x 24 48 n = 48, so Shannon got 48 votes.

Tires cost two for $75. How much will four tires cost? Proportion, continued Tires cost two for $75. How much will four tires cost? # of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150 n = 150, so four tires cost $150

Proportion, continued One more way to solve proportions: 2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24

Properties of a proportion? Reciprocal Property If Can you see it? If yes, can you think of why it works? Then

How about an example? 7(6) = 2x 42 = 2x 21 = x Solve for x: Cross Product Property

How about another example? Solve for x: 7x = 2(12) 7x = 24 x = Cross Product Property Can you solve it using Reciprocal Property? If yes, would it be easier?

How to find Scale Factor When a figure is dilated, its size is changed by multiplying the length of each side by a scale factor.  All angles remain the same and so the new shape (or image) is similar to the original. Can be found by dividing a new side length by the original side length.   When going from a small shape to a larger shape the scale factor is greater than 1. (Enlargement)   When going from a large shape to a smaller shape the scale factor is less than 1. (Reduction)   Determine the corresponding side lengths. Determine if you are making a larger shape or a smaller shape. Determine if the scale factor is greater than or less than 1. Write the correct ratio.

Scale Factor Scale factor = new measurement old measurement SF new old Old measurement x SF = new measurement Scale factor more than 1 => shape gets bigger (Enlargement) Scale factor less than 1 => shape gets smaller (Reduction) Congruent shapes are similar shapes with SF = 1

BAIP Instructional Support Version 2 7/5/2018 Write a Proportion Using a Scale Factor ¾ inch to 1 foot If the length in inches is 2 ¼ inch, what would the actual length be in feet ? (PowerPoint #5) Teacher Prompt: Write the following scale factor on the board. ¾ inch to 1 foot Teacher Prompt: Ask the students, “If the length in inches is 2 ¼ inch, what would the actual length be in feet using the scale factor written on the board?” Student Response: 3/4 inch = 1 foot 2 1/4 inch x 3/4 x = 2 1/4 Multiply 3/4 by its reciprocal of 4/3 to get 1x. Multiply the right side by the same reciprocal of 4/3. 1x = 9/4 ● 4/3 1x = 36/12 or 3 feet 1x = 3 feet Teacher prompt: Good job.