Applying percents Understanding Cross multiplying Proportions are equal

Applying percents

Understanding Cross multiplying Proportions are equal, what do we notice about the cross products

Percent Review Percent means parts per 100. The symbol is % Example: 25% means 25 per 100 0 10 20 30 40 50 60 60 80 90 100

Percent Proportion Compares part of a quantity to the whole quantity, called the base, using a percent. The percent proportion is: part whole = percent 100 a b = p 100

Percent Proportion. 15 15 0 10 15 20 15 15 30 150 40 15 50 15 60 60 What number is 30% of 150? a 150 = 30 Cross multiply. 80 100 15 90 100 Each box represents How much of 150? 100 a = 4500 15 15 a = 45 So 45 is 30% of 150.

Proportions for Percent Problems Percent 100 Part (is) Whole (of) The variable can be placed in the Part, Whole, or Percent.

Proportions for Percent Problems Louis got 40 out of 50 correct on his test. What is his percent correct? Percent 100 x 100 Part Whole 40 50 50 x = 40 100 50 x = 4000 50 50 x = 80 Louis got 80% right.

Proportions for Percent Problems Susan answered 90% of the questions from an online survey. If she has answered 18 questions, how many questions were on the survey? Percent 100 90 100 Part Whole 18 x x = 20 The survey had 20 questions.

Proportions for Percent Problems Five hundred students applied to Jordan’s IB magnet. How many will get accepted if Jordan IB only accepts 40% ? Percent 100 40 100 Part Whole x 500 x = 200 students will be accepted into Jordan’s IB magnet.

Discounts Caleb bought a suit that is 40% off. The original price of the suit is $360. How much did he pay for the suit? • What is the discount? • What is the sale price? Understanding the problem Price you pay is what percent? Discount is what percent? Discount

Price you pay 40 60 100 Discount 360 100 360

Steve bought a jacket that was priced at $80. Find the sales price and discount if the jacket was 20% off Price you pay Discount

Discounts (proportions) Sheila bought a dress that is 30% off. The original price of the dress is $150. • What is the discount? • What is the sale price? Price you pay Discount

Commission Phillip makes 8% commission at AA Appliance store. His sales last month were $15, 000. What was his commission last month? Percent 100 Part Whole Phillip made $1200 in commission!

Sales Tax Example 5% sales tax on a $55 dress What is it? A percent of the total price How do you determine the amount you pay? Full price + t ax How can you write this as a decimal? Now multiply by the price

Sales Tax (proportion) Steve bought a jacket that was priced at $80. Find the sales tax and price including tax if the sales tax is 6%. Step 1: Calculate the sales tax Step 2: Add the sales tax to the price The sales tax is $4. 80 $80. 00 pirce + 4. 80 sales tax $84. 80 price after tax

Sales Tax (equation) Felicia is buying a pair of steel toe work boots for $80. Find the sales tax and price including tax if the sales tax is 9%. Step 1: Calculate sales tax Whole • Percent = Part Step 2: Add the Sales tax to the original price The sales tax is $7. 20 $80. 00 original price + 7. 20 sales tax $87. 20 Total price Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6 -5 Applying % increase and decrease

Total Price (multi- step problem) Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii? Step 1: Find the price you pay

Total Price (cont. ) Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii? Sales price = $187 Step 2 Find the sales tax Step 3 Sales price + tax = Total price Find the total price 187 + 16. 83 = 203. 83 The total price of the Wii is $203. 83

Profit Marilee's Travel Agency makes 20% profit on all tickets sold. Last month Marilee’s Travel Agency made $60, 000 in profit, what were the total sales last month? Whole • Percent = Part s • 20% = 60, 000 s • 0. 20 = 60, 000 0. 20 s = 300, 000 Marilee’s total sales were $300, 000.

Simple Interest = Principal rate time I=P r t Interest: the amount of money paid to you on savings, or paid by you on money borrowed Principal: the initial amount of money rate: the percent charged or paid (must be changed to a decimal or fraction) time: measured in years Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6 -7 Applying Simple and Compound Interest

Simple Interest You have $5000 in a savings account earning 3% interest. How much interest will you earn in 2 years? Step 4 Your savings account will have earned $300 in interest in 2 years.

Percent of Increase At Julio’s Computers they buy computers for $500 and sell them for $650. What is the percent of increase? 1. Find the amount of change between the old price and new price 650 — 500 = 150 2. Use The percent of increase is 30%. Amount of Change Original Set up a proportion or Change to decimal 0 Change to percent

Percent of Increase At Kat’s Computers they buy computers for $250 and sell them for $400. What is the percent of increase? The percent of increase is 60%. 1. Find the amount of change between the old price and new price 400 – 250 = 150 Amount of Change Original p = 0. 6 Change to percent p = 60%

Percent of Decrease Kat’s Computers is having a sale. They are advertising a $1000 computer for $600. What is the percent of decrease? 1. Find the amount of change between old price and new price 1000― 600 = 400 The percent of decrease is 40%. p = 0. 4 Change to percent p = 40%