Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #3071 : Algebra 1

Turn this fraction into a percent:

\displaystyle \frac{3}{25}

Possible Answers:

\displaystyle 12.8\%

\displaystyle 13\%

\displaystyle 12\%

\displaystyle 12.2\%

Correct answer:

\displaystyle 12\%

Explanation:

To change a fraction into a decimal, divide the numerator by the denominator. We do this by placing the numerator on the inside and doing long division. We can then change this decimal into a percent by moving the decimal place two places to the right, or multiplying the fraction by 100.

\displaystyle \frac{3}{25}=25\div3=0.12

\displaystyle 0.12*100=12\%

Example Question #3072 : Algebra 1

Turn this fraction into a percent:

\displaystyle \frac{4}{27}

Possible Answers:

\displaystyle 14.2\%

\displaystyle 14.8\%

\displaystyle 14\%

\displaystyle 14.6\%

Correct answer:

\displaystyle 14.8\%

Explanation:

To change a fraction into a decimal, divide the numerator by the denominator. We do this by placing the numerator on the inside and doing long division. We can then change this decimal into a percent by moving the decimal place two places to the right, or multiplying the fraction by 100.

\displaystyle \frac{4}{27}=27\div4=0.148

\displaystyle 0.148*100=14.8\%

Example Question #3073 : Algebra 1

Turn this fraction into a decimal:

\displaystyle \frac{5}{16}

Possible Answers:

\displaystyle 31.7\%

\displaystyle 31.8\%

\displaystyle 31\%

\displaystyle 31.3\%

Correct answer:

\displaystyle 31.3\%

Explanation:

To change a fraction into a decimal, divide the numerator by the denominator. We do this by placing the numerator on the inside and doing long division. We can then change this decimal into a percent by moving the decimal place two places to the right, or multiplying the fraction by 100.

\displaystyle \frac{5}{16}=16\div5=0.313

\displaystyle 0.313*100=31.3\%

Example Question #40 : Fractions And Percentage

Steven is the best penalty kick taker on his soccer team. Of every \displaystyle 15 shots he takes, he makes \displaystyle 9 of them. What is this relationship written as a percentage?

Possible Answers:

\displaystyle 40\%

\displaystyle 80\%

\displaystyle 60\%

\displaystyle 65\%

Correct answer:

\displaystyle 60\%

Explanation:

To figure out this you would divide to number made over the total number of shots. 

So,   \displaystyle \frac{9}{15}   which reduces to   \displaystyle \frac{3}{5}

To find the percent you need to get the top number to be out of \displaystyle 100, to do this you would multiply the top and bottom by \displaystyle 20.

So

 \displaystyle \frac{3 \cdot 20}{5 \cdot 20}=\frac{60}{100} 

which is equivalent to \displaystyle 60\%.

Example Question #41 : Fractions And Percentage

Which of the following is larger?

\displaystyle \frac{3}{5} ,  \displaystyle 61%  or, \displaystyle \frac{3}{10}

 

Possible Answers:

\displaystyle \frac{3}{5}

\displaystyle \frac{3}{10}

\displaystyle 61%

Correct answer:

\displaystyle 61%

Explanation:

To convert each fraction you must get them to be equivalent to something out of \displaystyle 100 since percents are based on this.

\displaystyle \frac{3}{5}=\frac{60}{100},  because you multiply the top and the bottom by \displaystyle 20

This makes,  \displaystyle \frac{3}{5}  equivalent to \displaystyle 60%.

 

Then do the same to the other fraction to get:

\displaystyle \frac{3}{10}=\frac{30}{100}, which is \displaystyle 30%

Example Question #31 : How To Find Percentage From A Fraction

What is the percent equivalent of \displaystyle \small \frac{2}{9}?  Round your answer to the nearest whole percent.

Possible Answers:

\displaystyle \small 44\%

\displaystyle \small 66\%

\displaystyle \small 11\%

\displaystyle \small 22\%

\displaystyle \small 33\%

Correct answer:

\displaystyle \small 22\%

Explanation:

To convert a fraction into a percentage, first convert the fraction into a decimal by dividing the numerator by the denomenator.  Then, to find the percentage equivalent of a decimal, simply move the decimal (if there is none, remember that there is always an implied decimal after the one's digit) to the right twice:

\displaystyle \small \frac{2}{9} = .2222 = 22\%

Example Question #32 : How To Find Percentage From A Fraction

What is the percent equivalent of \displaystyle \frac{1}{8}?  

Round your answer to the nearest whole percent.

Possible Answers:

\displaystyle 1.2\%

\displaystyle 12\%

\displaystyle 13\%

\displaystyle 1.25\%

\displaystyle 12.5\%

Correct answer:

\displaystyle 13\%

Explanation:

To convert a fraction into a percentage, first convert the fraction into a decimal by dividing the numerator by the denomenator.  Then, to find the percentage equivalent of a decimal, simply move the decimal (if there is none, remember that there is always an implied decimal after the one's digit) to the right twice:

\displaystyle \frac{1}{8} = .125 = 12.5\%

Round up to 

\displaystyle 13\%

Example Question #33 : How To Find Percentage From A Fraction

What is the percent equivalent of \displaystyle \frac{27}{81}?  Round your answer to the nearest whole percent.

Possible Answers:

\displaystyle 33\%

\displaystyle 50\%

\displaystyle 66\%

\displaystyle 43\%

\displaystyle 33.33\%

Correct answer:

\displaystyle 33\%

Explanation:

To convert a fraction into a percentage, first convert the fraction into a decimal by dividing the numerator by the denominator.  Then, to find the percentage equivalent of a decimal, simply move the decimal (if there is none, remember that there is always an implied decimal after the one's digit) to the right twice.  Don't forget to round your answer.  The best answer is:

\displaystyle 33\%

Example Question #33 : How To Find Percentage From A Fraction

If \displaystyle \frac{11}{16} of a pizza remains after a party, what percent of the pizza was eaten?

Possible Answers:

68%

31%

42%

27%

0.33%

Correct answer:

31%

Explanation:

This problem is merely asking us to convert the eaten fraction of the pizza into a percent. This can be easily solved for by thinking of a whole pizza as being 1. This would mean a whole pizza could be represented by the fraction \displaystyle \frac{16}{16}. Because \displaystyle \frac{11}{16} of the pizza remians, if we subtract this from \displaystyle \frac{16}{16}, we should be able to solve for the fraction of the pizza that was consumed. 

\displaystyle \frac{16}{16}-\frac{11}{16}=\frac{5}{16}

Therefore, \displaystyle \frac{5}{16} of the pizza was eaten. This is the fraction we must convert into a percent. In order to do so, we must first convert this into a decimal. As a decimal we can multiply by \displaystyle 100, which will yield our percent value. 

\displaystyle \frac{5}{16}=0.3125

\displaystyle 0.3125 \cdot 100 = 31.25 percent \approx {\color{Blue}31 percent }

Therefore, 31% of the pizza was eaten. 

Example Question #34 : How To Find Percentage From A Fraction

If \displaystyle \frac{3}{7} of pie has been eaten, what percent of the pie remains?

Possible Answers:

43%

Not enough information

63%

57%

52%

Correct answer:

57%

Explanation:

This problem is merely asking us to convert the remaining fraction of the pie into a percent. This can be easily solved for by thinking of a whole pie as being 1. This would mean a whole pie could be represented by the fraction \displaystyle \frac{7}{7}. Because \displaystyle \frac{3}{7} of the pie has been consumed, if we subtract this from \displaystyle \frac{7}{7}, we should be able to solve for the fraction of the pie that is left over. 

\displaystyle \frac{7}{7}-\frac{3}{7}=\frac{4}{7}

Therefore, \displaystyle \frac{4}{7} of the pie remains. This is the fraction we must convert into a percent. In order to do so, we must first convert this into a decimal. As a decimal we can multiply by \displaystyle 100, which will yield our percent value. 

\displaystyle \frac{4}{7}=0.571

\displaystyle 0.571 \cdot 100 = 57.1 percent \approx {\color{Blue} 57 percent }

Therefore, 57% of the pie remains. 

Learning Tools by Varsity Tutors