1. 9.1 & 9.2: Percentages, Fractions, and Decimals Essential Question: When and why do I use proportional comparisons?

2. Review Write each fraction as a decimal. 1. 2. Write each decimal as a fraction. 3. 0.3754. 0.05 3 4 __ 9 10 __

3. What is a percent?  A percent is a ratio that compares a number to 100. The symbol % is used to show a percent.

4. Think-Pair-Share  Is it possible to have a percent over 100?  Is it possible to have a decimal in a percentage?

5. Using a Grid to Model Percents  Model 17% on a 10 by 10 grid  Model 26% on a 10 by 10 grid

6. Percent  FractionFraction  Percent  Step 1: Write the percent as the numerator and 100 as the denominator  Step 2: If necessary, multiply the fraction to “get rid of” all decimals in the numerator.  Step 3: If necessary, simplify the fraction.  If the denominator is a factor of 100, multiply to find an equivalent fraction with a denominator of 100  If the denominator is NOT a factor of 100, divide the numerator by the denominator to change to a decimal. Then, multiply by 100.

7. Percent  DecimalDecimal  Percent  Step 1: Divide the percent by 100, which is the same as moving the decimal TWO places to the left  Step 1: Multiply the decimal by 100, which is the same as moving the decimal TWO places to the right.

8. Fraction  DecimalDecimal  Fraction  Step 1: Divide the numerator by the denominator.  Step 1: Read the decimal. The place value of the last decimal tells you the denominator of the fraction.

9. IS OVER OF = % OVER 100

10. Example Problems  Find 46% of 50 (Hint: You can rephrase the question as “What is 46% of 50?”)  Find 75% of 120 (Hint: You can rephrase the question as “What is 46% of 50?”)

11. Word Problems  A jacket is on sale for 25% off. The original price of the jacket was $45. How much would the jacket cost after the discount?  At a cat show, 60% of the cats had long hair. There were 168 cats in the show. How many cats had long hair?  The budget for a café includes $3,000 for new kitchen equipment. The chef spent 3% of that money for new aprons. How much money was spent on aprons?