6.1 Percents Percent: a ratio whose denominator is 100 (x/100) What percent is each color?

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Presentation transcript:

6.1 Percents Percent: a ratio whose denominator is 100 (x/100) What percent is each color?

6.1 Percents Write the percent as a fraction in simplest form: 42%, 60%, 107% 42%: 42/100 ÷ 2/2 = 21/ 50 60%: 107%: Write the percent as a decimal: 42%, 60%, 107% 42%: 42/100 → 0.42 (drop % and move decimal left two places) 60%: 107%:

6.2 Fractions, Decimals, and Percents Remember that fractions are part of a proportion. We can rewrite a fraction as decimal-type fraction (x/100, x/1,000, x/10,000): 2/5 = 4/10 = 40/100 We can rewrite the decimal-type fraction as a decimal number: 2/5 = 4/10 = 0.4; 3 ¼ = 3 25/100 = 3.25 Ordering Rational Numbers 1.Write all the number in decimal with same number of places. 2.Plot the points on a number line. 3.Compare the decimal numbers.

6.3 Estimating with Percents Estimate with fractions/Use simple percents/round numbers Common percent – fraction equivalents: 1/5 =20%= 0.2 ¼=25%=0.25 1/3=33 1/3 %=0.333… 2/5=40%=0.4 ½=50%=0.5 3/5= 60%=0.6 2/3=66 2/3 %=0.666… ¾= 75%=0.75 4/5=80%=0.8 2/2 = 1=100%=1.0

6.3 Estimating with Percents Use simple percents/round numbers What is a 15% tip of a $91 dinner bill. –10% of $90 is $9 –5% is half of 10%, so 5% of $90 is $4.50 –$9 + $4.50 is about $13.50

6.4 Percent of a Number Proportion Percent is part of a hundred – a fraction. Think of fractions as parts of wholes Part/whole= 67/100 = n/90 Do cross product of equivalent ratios 67 × 90 = ÷ 100 = 60.3 Decimal Equivalents Convert percent to decimal equivalent and multiply. 15% of a class of 20 students like lima beans × 20 = 3

6.5 Solving Percent Problems Solve as a proportion part/whole: x/100 = a/b Solve as an equation What x% of b is a? → x% × b = a Sloth example on p 352: Sloths sleep 16.5 hours a day. What percent of 24 hours is this? x/100 = 16.5/24 → 1650 ÷ 24 = = 68.75% What n% of 24 is 16.5?→n × 24 = 16.5→n = 16.5/24 =.6875 = 68.75% Clues: “Percent of” means “% ×”ex: 5% of 50 →.05 × 50 = 2.5 “is % of” means “= % ×”ex: 10 is 20% of → 10 =.2 × n = 10/.2 = 50

6.5 Solving Percent Problems What is the sales tax rate if you pay $18 tax on a $225 DVD player? 18/225 = x/ × 100 = 225 × x 1800 = 225x 1800 ÷ 225 = 8 = 8%