CHAPTER 7: RELATING FRACTIONS, DECIMALS, AND PERCENTS 7. CONVERTING FRACTIONS TO DECIMALS P. -3 7. CONVERTING DECIMALS TO FRACTIONS P. 4-5 7.3 CONVERTING DECIMALS AND PERCENTS P. 6-7 7.4 CONVERSIONS REVIEW P. 8-9 7.5 THE PERCENT CIRCLE P. 0-7.6 FINDING THE PART P. -3 7.7 FINDING THE WHOLE P. 4-5 7.8 FINDING THE PERCENT P. 6-7 ANSWER KEY P. 8-9
7. CONVERTING FRACTIONS TO DECIMALS Key Vocabulary 7. Repeating decimals: Rational numbers: Think 7. Divide the numerator by the denominator. a ba b Add a decimal after the dividend and at least one zero. ba.0 Add at least additional zeros to dividend until it divides evenly or until you get a repeating pattern. 0.4 5.0 5 0 0 0.5 4.00 4 8 0 0 0 0.33 or 0.33 3 3.00 3 9 0 9 0 Try It 7. Divide to convert the fractions to decimals ) 3 4 ) 8 3) 3 5 4) 3 5) 3 0 6) 7 8
7. Practice Exercises Divide to convert the fractions to decimals. ) 4 ) 3 8 3) 7 0 4) 5 6 5) 6) 3 9 7) 6 8) 3 5 Tanner spent ⅓ of his time at work stocking shelves and ⅔ of the time with customers. 9) Write the amount of time Tanner spent stocking shelves as a decimal: 0) Write the amount of time Tanner spent with customers as a decimal:
7. Converting Decimals to Fractions Think 7. To convert decimals to fractions, you need to write the decimal in fraction form. Simplify the fraction by reducing to lowest terms. 6 3 0.6 0 5 5 5 0.5 00 5 4 75 5 0.75,000 5 40 For repeating fraction decimals, exclude the decimal and use just the fraction. 0.33 or 3 3 3 3 Try It 7. Write each decimal as a fraction simplify by reducing the fraction to lowest terms. ) 0.4 = ) 0.8 = 3) 0.45 = 4) 0.55 = 5) 0.5 = 6) 0.075 =
7. Practice Exercises Write each decimal as a fraction simplify by reducing the fraction to lowest terms. Decimal Form Fraction Form Simplify Fraction ) 0.5 = ) 0. = 3) 0.5 = 4) 0.35 = 5) 0.70 = 6) 0.075 = 7) 0.0 = 8) 0.375 = 9) 0.005 = 0) Phillip walked 0.35 miles on Monday and 0.5 miles on Tuesday. Write the total distance he walked as a fraction.
7.3 CONVERTING DECIMALS AND PERCENTS Key Vocabulary 7.3 Percent: Think 7.3 To convert a decimal to a percent, multiply the decimal by 00. Move the decimal places right. Be sure to add zero placeholders as needed. Drop the decimal, & add a percent sign. ( added zero) (0.5) 0. 5 x00 5% (0.5) 0.50 x00 50% (0.33 ) 0.33 x00 33 % (.5).5 x00 5% 3 3 3 To convert a percent to a decimal, divide the number by 00 (move the decimal places to the left. Add zeros as needed, drop the percent sign and add a decimal. (5%) 5% 00 0.5 (50%) 50% 00 0.5 Try It 7.3 Convert the percent to decimal. ) 35% = ) 8 % = (33 %) 33 % 00.33 (5%) 05% 00 0.05 3 3 3 ( added zero) 3) 66 % 3 = 4) 8% = 5) 80% = 6) 0%
7.3 Practice Exercises Convert each decimal to a percent. ) 0.3 = % ) 0.05 = % 3) 0.45 = % 4) 0.05 = % 5).45 = % Convert each percent to a decimal. 6) 3% = 7) 5% = 8) 90% = 9) 60% = 0) Jake ate 30% of his pizza for lunch. Write the amount he ate as a decimal.
7.4 CONVERTING FRACTIONS, DECIMALS, AND PERCENTS Think 7.4 Fraction Decimal Percent (Simplify the fraction first as needed.) 0 50 0.4 5.0 0.4 x 00 40% 5 Percent Decimal Fraction (Simplify fraction as needed.) 35 5 7 3 5% 0 00 5 0 Try It 7.4 Convert the numbers and simplify. Fraction Decimal Percent (Simplify the fraction first as needed.) 4 ) ) 3) 0 Percent Decimal Fraction (Simplify fraction as needed.) 4)60% 5) 6)
7.4 Practice Exercises Fill in the chart by converting the fractions, decimals, and percents. Percent Decimal Fraction () (5) 8 () 0.0 (8) 5% (6) (9) (3) (7) 4 5 (4) 0.66 3 (0)
7.5 THE PERCENT CIRCLE Key Vocabulary 7.5 percent circle: part: whole: percent: Think 7.5 Using the percent circle as a guide, you can solve percent exercises with either multiplication or division. Part Percent (as decimal) P % W Whole Means Divide Means Multiply Part Percent (as decimal) Whole 36 is 0% (0.) of 360. Percent (as decimal) Part Whole 30% (0.3) of 60 is 00 Try It 7.5 Find what is missing: Part (P) Percent (%) Whole (W) Circle One ) What is 75% of 300? P % W ) 30 is what percent of 90? P % W 3) 60% of 800 is what number? P % W 4) 0 is what percent of 00? P % W 5) What percent of 300 is 90? P % W 6) What is 40% of 0? P % W
7.5 Practice Exercises What s missing? Part (P) Percent (%) Whole (W) Circle One ) What is 40% of 80? P % W ) 6 is what percent of 8? P % W 3) 75% of what number is 5?? P % W 4) 30% of 300 is what number?? P % W 5) What percent of 60 is 0?? P % W Draw lines and fill in the percent circles below. 6) 30% of 90 is 7. 7) 7 is 35% of 8. 8) 6 is 0% of 80. 9) 8 ½ % of $40 is $34. (0) A shirt that normally sells for $40 is 5% off. The sale price is $30. Identify. Part % Whole
7.6 FINDING THE PART Think 7.6 FORMULA: Part (P) = Percent (%) multplied by the Whole ( P % x W)? Percent (as decimal) % W Whole Means Multiply 60% 0f 80 is what number? First change the percent to a decimal. 60% 00 = 0.06 Then multiply. Part = (0.06) (80) Answer: 08 8 % of $40 is what amount? First change the percent to a decimal. 8 % 8.5% 00 0.85 Then multiply. Part = (0.085) (40) Answer: $3.40 8 % 8.5% 00 0.85 You can also change the percent to a fraction. 33 % 3 3 33 % 0f 90 is what number? 3 Multiply the fraction by the whole number to find the part. Try It 7.6 3 x 30 90 30 30 Multiply the decimal or the fraction by the whole number to find the part. ) 5% of 68 is ) 5% of 300 is 3) 66 3 of 39 is 4) 8 % of 80 is 5) 50% of 50 is 6) 6% of 80 is
7.6 Practice Exercises Use the percent to decimal method to find the part. ) 5% of 40 is ) 60% of 40 is 3) 7 % of $4 is 4) 5% of 60 is 5) 5% of $60 is Use the percent to fraction method to find the part. 6) 7) 33 % 3 of 54 is 66 % 3 of 60 is 8) Carlos was charged 6% sales tax on a shirt that cost $40. How much was the tax? 9) Lydia bought a dress on sale for a 0% discount. The dress was originally $50. How much was the discount? 0) What was the sale price for Lydia s dress?
7.7 FINDING THE WHOLE Think 7.7 P FORMULA: Whole (W) = Part (P) divided by the Percent (as decimal). ( W ) % P Percent (as decimal) %? Whole Means Divide First convert the percent to a decimal, or a fractions (See 7.6) Then divide the part by the decimal 0% of what number is 60? (0% = 0.) 60 300 ( answer) Whole 0. 600 600 0. 5 is 33 % of what number?( 33 % = 3 3 3 ) 5 3 75 Whole 5 x 75( answer) 3 Try It 7.7 Find the whole. ) 30% of what number is 7? ) 36 is 40% of what number? 3) 0% of what number is? 4) 7 is 60% of what number? 5) $5.5 is 7 % of what number? 6) of what number is 56?
7.7 Practice Exercises Find the whole. ) 8 is 30% of what number? ) 0% of what number is 50? 3) 5% of what number is 7? 4) 6 is 5% of what number? 5) 6) 7) 7 % of what number is $5? 33 % 3 of what number is 40? % 4 of what number is 5? 8) 5 is 5% of what number? 9) Brittany paid 7 % for state taxes on a car she purchased for $,000. How much did she pay for taxes? 0) Alex earned 3 % interest on a deposit of $00. How much money did he earn in interest on his deposit?
7.8 FINDING THE PERCENT Think 7.8 P FORMULA: Percent (%) = Part (P) divided by the Whole (W) (% ) W P Percent (as decimal)? W Whole Means Divide Write the part divided by the whole as a fraction. Simplify the fraction by reducing to lowest term Convert the fraction to a decimal (See 7.) Multiply the resulting decimal by 00, add zero as place holders, drop the decimal and add the % sign. What percent of 40 is 8? P 8 8 Percent W 40 8 5 0. x 00 0%( answer) 0. 5.0 Try It 7.8 Find the percent. ) What percent of 6 is? ) 5 is what percent of 5? 3) inches is what percent of yard? (Hint: yard = 36 inches) 4) 48 is what percent of 64? 5) $5 is what percent of $60? 6) 33 is what percent of 99?
7.8 Practice Exercises ) What percent of 4 is 8? ) 8 inches is what percent of 3 inches? 3) What percent of $90 is $36? 4) 8 is what percent of 60? 5).7 is what percent of 36? 6) What percent of 0 is 40? 7) 4 is what percent of 36? 8) $35 is what percent of $80? 9) Victor deposited $300 in his savings account. He earned $3.75 on his deposit. What is the percent he earned on his deposit? 0) Marcella bought a text book for $78 and had to pay an additional $5.85 for the tax what percent of $78 is the $5.85 tax?
Chapter 7 Answer Key 7. 7.3 7. ) 0.5 ) 0.375 3) 0.7 4) 0.83 or 5) 0.5 0.8 3 6) 0.3 or 0.3 3 7) 0.6 or 0.6 3 8) 0.6 9) 0.3 or 0.33 3 0) 0.6 or ) ) 5 3) 3 0 4) 7 0 5) 7 0 6) 3 40 7) 50 8) 3 8 9) 400 0.66 3 7.4 ) 30% ) 5% 3) 45% 4).5% 5) 45% 6) 0.03 7) 0.5 8) 0.9 9).6 0) 0.3 ).5% ) 0% 3) 80% 4) 66 % 3 5) 0.5 6) 0.5 7) 0.8 8) 5 9) 4 0) 3 5 0) 3
7.5 7.7.7.7 7.6 ) P ) % 3) W 4) P 5) % 6) P=7 W= 90 %=30 7) P=7 W= 8 %=5 8) P=6 W= 80 %=0 9) P=34 W= 40 %=8 / 0) P = 30 % = 5 W = 40 ) 0 ) 44 3) $3.5 4) 3 5) 9 6) 8 7) 40 8) $.40 9) $0.00 0) $40.00 7.8 ) 60 ) 50 3) 80 4) 04 5) $00 6) 0 7) 400 8) 00 9) $50 0) $7.00 7.8 ) 75% ) 5% 3) 40% 4) 30% 5) 6) 7) 7 % 33 % 3 66 % 3 8) 75% 9).5% 0) 7 %