Percent Power! Fractions, Decimals Percents Grade 6 Math Lesson 2-3 I Can... I can relate fractions, decimals, and percents using place value. I can explain that a percent is a ratio that compares a number to 100. I can write any
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I Can... I can relate fractions, decimals, and percents using place value.
I can explain that a percent is a ratio that compares a number to 100.
I can write any percent as a fraction and a decimal, and go back again. 2<br>
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Warm-Up: Soccer Survey Who chose soccer?
Group A: 3 out of 20
Group B: 3 out of 25
Group C: 1 out of 20
Group D: 9 out of 100
Which group is easiest to compare? Why? 9 out of 100 squares Group D: 9 out of 100 = 9% 3<br>
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What Is a Percent? A percent is a ratio that compares a number to 100.
35% means 35 : 100
As a fraction: 35/100 = thirty-five hundredths 35 out of 100 squares 4<br>
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35% as a Fraction 35% = 35/100 (definition of percent)
= 7/20 (divide both 35 and 100 by 5) As a fraction, 35% = 35/100 or 7/20 5<br>
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35% as a Decimal 35% = 35/100 (definition of percent)
= 0.35 (35/100 means thirty-five hundredths) As a decimal, 35% = 0.35 6<br>
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Real Life #1: Smartphones (Part A) About 95% of smartphone users claimed to send text messages.
What fraction is this? What decimal?
95% = 95/100 (definition of percent)
= 19/20 (divide both 95 and 100 by 5) 7<br>
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Real Life #1: Smartphones (Part B) 95% = 95/100
= 0.95 (95/100 means ninety-five hundredths) About 19/20 or 0.95 of smartphone users claimed to send text messages. 8<br>
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Check: E-mail Spam 22% of e-mail users claimed to spend less time using e-mail because of spam.
What fraction of e-mail users is this?
What decimal is this?
Show your work! Answer: 22/100 = 11/50 and 0.22 9<br>
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Fraction to Percent: 3/20 3/20 = 15/100 (× 5 on top and bottom, because 20 × 5 = 100)
= 15% (definition of percent) As a percent, 3/20 = 15% 10<br>
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3/20 as a Decimal 3/20 = 15/100 (× 5 on top and bottom)
= 0.15 (fifteen hundredths) As a decimal, 3/20 = 0.15 11<br>
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What About 9/15? No whole number times 15 gives 100. Simplify first!
9/15 = 3/5 (÷ 3 on top and bottom)
3/5 = 60/100 (× 20 on top and bottom)
= 60% As a percent, 9/15 = 60% 12<br>
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Example 2: 6/8 as a Percent Write 6/8 as a percent and as a decimal.
6/8 = 3/4 (÷ 2 on top and bottom)
3/4 = 75/100 (× 25 on top and bottom)
= 75% 75 out of 100 squares 13<br>
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Example 2: 6/8 as a Decimal 75% = 0.75 (75/100 means seventy-five hundredths)
CHECK: Write 4/16 as a percent and as a decimal. 6/8 = 75% = 0.75 | Check: 4/16 = 25% = 0.25 14<br>
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Real Life #2: Cheetah vs. Falcon (Step 1) The falcon's top speed is 2 9/10 times as fast as a cheetah's. What percent?
Step 1: Write the mixed number as an improper fraction.
2 9/10 = 2 + 9/10
= 10/10 + 10/10 + 9/10
= 29/10 15<br>
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Real Life #2: Cheetah vs. Falcon (Step 2) Step 2: Find an equivalent ratio with 100 as the denominator.
29/10 = 290/100 (× 10 on top and bottom)
= 290% (definition of percent) The falcon's top speed is 290% that of a cheetah's. 16<br>
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Real Life #3: Blue Whale (Check) Blue whales can take in 1 1/25 times their body weight in food and water in one gulp.
What percent of their body weight is this?
Show your work! Answer: 1 1/25 = 26/25 = 104/100 = 104% 17<br>
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Decimals to Percents and Fractions 0.7 = 7/10 = 70/100 = 70%
0.34 = 34/100 = 17/50, and 34%
0.125 = 125/1,000 = 1/8, and 12.5/100 = 12.5% 18<br>
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Example 4: Write 0.025 0.025 = 25/1,000 (twenty-five thousandths)
= 2.5/100 = 2.5% (percent)
= 1/40 (simplify 25/1,000)
CHECK: Write 1.4 as a percent and as a mixed number. 0.025 = 2.5% = 1/40 | Check: 1.4 = 140% = 1 2/5 19<br>
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Practice Time! 1. 22% of e-mail users: fraction and decimal?
2. Write 4/16 as a percent and a decimal.
3. Blue whales take in 1 1/25 times their body weight. What percent?
4. Write 1.4 as a percent and as a mixed number. 20<br>
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Practice Answer Key 1. 22/100 = 11/50 and 0.22
2. 4/16 = 1/4 = 25% and 0.25
3. 1 1/25 = 26/25 = 104%
4. 1.4 = 140% and 1 2/5 21<br>
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Summary Percent = a ratio out of 100.
Fraction to percent: make the denominator 100 (simplify first if needed).
Percent to fraction/decimal: write over 100, then simplify.
Mixed number: write as an improper fraction first. 22<br>
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Exit Ticket 1) Write 40% as a fraction and a decimal.
2) Write 3/5 as a percent.
3) Why does a percent compare a number to 100? Answers: 1) 2/5 and 0.4 2) 60% 3) Percent means per hundred 23<br>
