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 Numbers1. 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% = 0.2¼ = 25% = 0.251/3 = 33 1/3 % = 0.333…2/5 = 40% = 0.4½ = 50% = 0.53/5 = 60% = 0.62/3 = 66 2/3 % = 0.666…¾ = 75% = 0.754/5 = 80% = 0.82/2 = 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 = 6030• 6030 ÷ 100 = 60.3

Decimal Equivalents• Convert percent to decimal equivalent and multiply.• 15% of a class of 20 students like lima beans.• 0.15 × 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 = 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

18 × 100 = 225 × x

1800 = 225x

1800 ÷ 225 = 8 = 8%