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1. write 51 out of 100 as a percent. 2. write 97% as a fraction. 3. cha…

Question

  1. write 51 out of 100 as a percent.
  2. write 97% as a fraction.
  3. change \\( \frac { 4 } { 5 } \\) into a percent.
  4. write 1% as a decimal.
  5. change.42 into a percent.
  6. what is 100% of $300?
  7. what percent of 180 is 108?
  8. what is 32% of 75?
  9. 250 is 8% of what number?
  10. in each question below, you are given two facts. the third fact is missing. for each question, circle the word that tells which fact is missing. part whole percent a. 20 is what percent of 100? part whole percent b. what is 5% of 100? part whole percent c. 20 is 5% of what number? part whole percent
  11. what is 110% of $26.70?
  12. what is \\( 7 \frac { 1 } { 2 } \\% \\) of $810?
  13. the price went from $2.00 to $2.18. what is the percent of increase?
  14. what is 295 decreased by 97%?
  15. the current price is $33.75. this is 12.5% more than last years price. what was last years price?

Explanation:

1. Write 51 out of 100 as a percent.

Step1: Use the formula for percentage

The formula to convert a fraction \(\frac{a}{b}\) to a percentage is \(\frac{a}{b}\times100\%\). Here \(a = 51\) and \(b=100\).

$$ \frac{51}{100}\times100\% $$

Step2: Simplify the expression

\(\frac{51\times100\%}{100}=51\%\)

2. Write \(97\%\) as a fraction.

Step1: Recall the definition of percentage

\(x\%=\frac{x}{100}\). For \(x = 97\), we have \(\frac{97}{100}\). Since \(97\) is a prime number and \(97\) and \(100\) have no common factors other than \(1\), the fraction is in its simplest form.

3. Change \(\frac{4}{5}\) into a percent.

Step1: Use the percentage formula

\(\frac{4}{5}\times100\%=\frac{4\times100\%}{5}\)

Step2: Simplify the expression

\(\frac{400\%}{5}=80\%\)

4. Write \(1\%\) as a decimal.

Step1: Recall the conversion formula

\(x\%=\frac{x}{100}\). For \(x = 1\), \(\frac{1}{100}=0.01\)

5. Change \(0.42\) into a percent.

Step1: Use the conversion formula

To convert a decimal \(d\) to a percentage, we use \(d\times100\%\). For \(d = 0.42\), \(0.42\times100\% = 42\%\)

6. What is \(100\%\) of \(\$300\)?

Step1: Use the percentage - of formula

\(x\%\) of a number \(N\) is \(\frac{x}{100}\times N\). For \(x = 100\) and \(N=300\), \(\frac{100}{100}\times300=300\)

7. What percent of \(180\) is \(108\)?

Step1: Set up the equation

Let \(p\) be the percentage. Then \(\frac{p}{100}\times180 = 108\)

Step2: Solve for \(p\)

$$ p=\frac{108\times100}{180}=\frac{10800}{180}=60 $$

So \(p = 60\%\)

8. What is \(32\%\) of \(75\)?

Step1: Use the percentage - of formula

\(\frac{32}{100}\times75=\frac{32\times75}{100}\)

Step2: Simplify the expression

\(32\times75 = 2400\), and \(\frac{2400}{100}=24\)

9. \(250\) is \(8\%\) of what number?

Step1: Set up the equation

Let the number be \(n\). Then \(\frac{8}{100}\times n=250\)

Step2: Solve for \(n\)

$$ n=\frac{250\times100}{8}=\frac{25000}{8}=3125 $$

10.

  • a. In the question “\(20\) is what percent of \(100\)?”:
  • We know the part (\(20\)) and the whole (\(100\)), and we are looking for the percent. So we circle “percent”.
  • b. In the question “What is \(5\%\) of \(100\)?”:
  • We know the percent (\(5\%\)) and the whole (\(100\)), and we are looking for the part. So we circle “part”.
  • c. In the question “\(20\) is \(5\%\) of what number?”:
  • We know the part (\(20\)) and the percent (\(5\%\)), and we are looking for the whole. So we circle “whole”.

11. What is \(110\%\) of \(\$26.70\)?

Step1: Use the percentage - of formula

\(\frac{110}{100}\times26.70=\frac{110\times26.70}{100}\)

Step2: Simplify the expression

\(110\times26.70=2937\), and \(\frac{2937}{100}=29.37\)

12. What is \(7\frac{1}{2}\%\) of \(\$810\)?

Step1: Convert the mixed - number percentage to a fraction

\(7\frac{1}{2}\%=\frac{15}{2}\%=\frac{15}{2\times100}=\frac{3}{40}\)

Step2: Use the percentage - of formula

\(\frac{3}{40}\times810=\frac{3\times810}{40}=\frac{2430}{40}=60.75\)

13. The price went from \(\$2.00\) to \(\$2.18\). What is the percent of increase?

Step1: Find the amount of increase

\(A=2.18 - 2.00=0.18\)

Step2: Use the percent - increase formula

Percent increase \(=\frac{A}{Original}\times100\%=\frac{0.18}{2.00}\times100\% = 9\%\)

14. What is \(295\) decreased by \(97\%\)?

Step1: Find the amount of decrease

The amount of decrease is \(97\%\) of \(295\), \(\frac{97}{100}\times295=\frac{97\times295}{100}=286.15\)

Step2: Find the new value

\(295-286.15 = 8.85\)

15. The current price is \(\$33.75\). This is \(12.5\%\) more than last year…

Answer:

s:

  1. \(51\%\)
  2. \(\frac{97}{100}\)
  3. \(80\%\)
  4. \(0.01\)
  5. \(42\%\)
  6. \(\$300\)
  7. \(60\%\)
  8. \(24\)
  9. \(3125\)

10.

  • a. percent
  • b. part
  • c. whole
  1. \(\$29.37\)
  2. \(\$60.75\)
  3. \(9\%\)
  4. \(8.85\)
  5. \(\$30\)