 9-1: Relating Fractions, Decimals, and Percents

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9-1: Relating Fractions, Decimals, and Percents
IWBAT convert a percent to a fraction or decimal and convert a fraction or decimal to a percent.

Vocabulary Percent – A special ratio that compares a number with 100
Percent means “per hundred”

Fraction to Decimal and Percent
Fraction to Percent Divide the numerator by the denominator Put the whole number in front of decimal, if needed Convert the fraction to a decimal Move the decimal to the right twice Add the % sign

Examples 1) 2) 3 5 3)

Percent to Decimal and Fraction
Percent to Fraction Remove the % sign Move the decimal left twice Remove % sign Put number over 100 Simplify

Examples 1) 15% 2) 3) 120%

Decimal to Fraction and Percent
Decimal to Percent Look at the place value of the fraction Place decimal over corresponding place value Simplify Put whole number in front if there is one Move decimal right twice Add the % sign

Examples 1) 2) 3)

9-2: Estimating Percent IWBAT estimate percents of numbers between 0% and 100% using multiples of 10% or fractions

Estimating Using Rounding
Round the percent to the nearest 10% Round the number to the nearest 10s If the number is less than 10, do not round it Change the percent to a decimal Multiply

Examples 1) Estimate 28% of 71 2) Estimate 9% of \$19.99

Estimating Using Fractions
Memorize the following common percent to fraction conversions: Round the whole number to the nearest 10s Choose the corresponding fraction Multiply 10% 20% 25% 33% or 34% 50% 66% or 67% 75% 90% 1 10 1 5 1 4 1 3 1 2 2 3 3 4 9 10

Examples 1) 75% of 200 2) 39% of 600 3) 21% of 400 4) 26% of 19

9-3: Finding a Percent of a Number
IWBAT use a proportion to set up percent problems and solve using cross products.

Percent Proportion Formula
% 100 = 𝑝𝑎𝑟𝑡(𝑖𝑠) 𝑤ℎ𝑜𝑙𝑒 (𝑜𝑓) Think of problems as asking, “What is ?”

9-4: Is an Estimate Enough?
IWBAT determine whether an estimate is a sufficient solution or whether an exact amount is needed.

9-5: Mental Math: Finding a Percent of a Number
IWBAT use mental math to calculate percents of numbers

Use the same rules as estimating percent

9-6: Solving Percent Problems Using Equations
IWBAT write and solve percent equations.

Use the Percent Proportion Formula
% 100 = 𝑝𝑎𝑟𝑡 (𝑖𝑠) 𝑤ℎ𝑜𝑙𝑒 (𝑜𝑓) Break up the problem and substitute into proper place in proportion formula

Write a proportion and solve.
What number is 25% of 62? 1) Break into sections. What number is 25% Of 62 = 𝑛 62 2) Substitute into formula 3) Simplify, if possible 4) Cross-Multiply

Examples 1) 15 is what percent of 75? 2) What number is 40% of 88?
3) What percent of 90 is 27? 4) What is 120% of 360? 5) 16 is what percent of 40? 6) The 6th grade class is having a book sale. Their order included 300 novels. So far, 180 novels have been sold. What percent of the novels have been sold?

IWBAT writ and solve one-step linear equation involving percent
9-7: Write an Equation IWBAT writ and solve one-step linear equation involving percent

IWBAT find sales tax and total cost.
9-8: Finding Sales Tax IWBAT find sales tax and total cost.

Vocabulary Tip – A percentage of the total of your bill that you give for a service Tax – A percentage of the total of your bill that you pay to the government

Finding Sales Tax and Total Cost
You buy a soccer ball priced at \$ If the rate of the sales tax is 6.5%, what is the total cost of the ball? 1) Convert the percent to a decimal 6.5% = 0.065 2) Multiply the decimal by the price. This is the sales tax. 14.69 ∙ 0.065 3) Round UP to the nearest cent ≈ 0.96 4) Add to the price to find the total cost \$ \$15.65

Examples Find the sales tax and the total cost. Round the sales tax up to the nearest cent. Cost: \$19 Rate of sales tax: 8% 2) Cost: \$412 Rate of sales tax: 6% 3) Cost: \$62.50 Rate of sales tax: 5.5% 4) A basketball costs \$30. The rate of sales tax was 5%. Find the total cost of the basketball.

IWBAT find discount and sales price.
9-9: Computing Discount IWBAT find discount and sales price.

Finding the Discount and the Sale Price
The Nature Shop had a 25% sale on kaleidoscopes. Michael bought one originally priced at \$ How much did he pay on sale? 1) Convert the percent to a decimal 25% = 0.25 2) Multiply the decimal by the original cost. This is the discount. 15.99 ∙ 0.25 3.9975 3) Round the discount DOWN to the nearest cent. ≈ 3.99 4) Subtract the discount from the original price to find the sale price. \$15.99 – 3.99 \$12.00

Examples 1) Regular price: \$200 Rate of discount: 10%
4) Tommy bought two kaleidoscopes on sale for 20% off. If each kaleidoscope cost \$29 before the sale, what did Tommy pay for both on sale?

9-10: Using the Interest Formula
IWBAT use the simple interest formula to calculate interest and find the total amount earned or charged.

Vocabulary Interest – the amount of money paid for the use of money
Investments, loans, savings Interest Formula: I = prt I is interest p is principal (original amount deposited or borrowed) r is the rate of interest (the percent earned or charged) t is the time the money is in the account or is borrowed (measured in years)

Find the interest and total with interest
You put \$200 in a savings account earning 5.5% simple interest per year. What is the total you will have in your account after one year? 1) Identify each variable I = ? p = \$200 r = 5.5% = 0.055 t = 1 2) Rewrite the interest formula I = prt 3) Substitute. Solve the equation to find interest. I = prt I = 200(0.055)(1) I = \$11 4) Add the interest to the principal \$ = \$211

Find the interest and the total with interest.
Examples Find the interest and the total with interest. Principal: \$6,000 Rate: 5% Time: 5 months 2) Principal: \$4,500 Rate: 18% Time: 6 months 3) Principal: \$500 Rate: 7.5% Time: 1 year 4) You want to borrow \$500,000 for 6 months at 12% interest. How much money will you owe the bank?