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ISEE Middle Level Math : How to subtract fractions

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Example Questions

Example Question #31 : How To Subtract Fractions

What is the solution to the expression below?

$\frac{3}{4}-\frac{7}{9}$ $\displaystyle \frac{3}{4}-\frac{7}{9}$

Possible Answers:

$\frac{1}{36}$ $\displaystyle \frac{1}{36}$

$\displaystyle 36$

$\displaystyle -36$

$-\frac{1}{36}$ $\displaystyle -\frac{1}{36}$

Correct answer:

$-\frac{1}{36}$ $\displaystyle -\frac{1}{36}$

Explanation:

In order to subtract fractions, the least common denominator must be found for the denominator. The least common denominator of 4 and 9 is 36. Therefore, the fractions should be converted accordingly:

$\frac{3}{4}-\frac{7}{9}$ $\displaystyle \frac{3}{4}-\frac{7}{9}$

$\frac{27}{36}-\frac{28}{36}$ $\displaystyle \frac{27}{36}-\frac{28}{36}$

$-\frac{1}{36}$ $\displaystyle -\frac{1}{36}$

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Example Question #32 : How To Subtract Fractions

$\frac{20}{21}-\frac{14}{21}=$ $\displaystyle \frac{20}{21}-\frac{14}{21}=$

Possible Answers:

$\frac{6}{21}$ $\displaystyle \frac{6}{21}$

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

$\frac{3}{21}$ $\displaystyle \frac{3}{21}$

$\frac{20}{21}$ $\displaystyle \frac{20}{21}$

Correct answer:

$\frac{6}{21}$ $\displaystyle \frac{6}{21}$

Explanation:

Subtract the numerators and keep the denominator as is:

$\frac{20}{21}-\frac{14}{21}=\frac{6}{21}$ $\displaystyle \frac{20}{21}-\frac{14}{21}=\frac{6}{21}$

Answer: $\frac{6}{21}$ $\displaystyle \frac{6}{21}$

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Example Question #281 : Fractions

Evaluate:

$20 - \left ( 7.5 \times 3 - 1.2 \right )$ $\displaystyle 20 - \left ( 7.5 \times 3 - 1.2 \right )$

Possible Answers:

-1.3 $\displaystyle -1.3$

36.3 $\displaystyle 36.3$

- 3.7 $\displaystyle - 3.7$

22.5 $\displaystyle 22.5$

6.5 $\displaystyle 6.5$

Correct answer:

-1.3 $\displaystyle -1.3$

Explanation:

By the order of operations, carry out the operations in parentheses first; since there is a multiplication and a subtraction present, carry them out in that order. Finally, carry out the remaining subtraction:

$20 - \left ( 7.5 \times 3 - 1.2 \right )$ $\displaystyle 20 - \left ( 7.5 \times 3 - 1.2 \right )$

$= 20 - \left ( 22.5 - 1.2 \right )$ $\displaystyle = 20 - \left ( 22.5 - 1.2 \right )$

$\displaystyle = 20 - 21.3$

= -1.3 $\displaystyle = -1.3$

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Example Question #33 : How To Subtract Fractions

Subtract:

$\frac{17}{63}-\frac{11}{63}=$ $\displaystyle \frac{17}{63}-\frac{11}{63}=$

Possible Answers:

$\displaystyle 6$

$\frac{6}{63}$ $\displaystyle \frac{6}{63}$

$\frac{63}{6}$ $\displaystyle \frac{63}{6}$

$\frac{28}{63}$ $\displaystyle \frac{28}{63}$

Correct answer:

$\frac{6}{63}$ $\displaystyle \frac{6}{63}$

Explanation:

To solve, subtract the numerators and leave the denominators the same:

$\frac{17}{63}-\frac{11}{63}=\frac{6}{63}$ $\displaystyle \frac{17}{63}-\frac{11}{63}=\frac{6}{63}$

Answer: $\frac{6}{63}$ $\displaystyle \frac{6}{63}$

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Example Question #34 : How To Subtract Fractions

Subtract:

$\frac{25}{88}-\frac{16}{88}=$ $\displaystyle \frac{25}{88}-\frac{16}{88}=$

Possible Answers:

$\displaystyle 9$

$\frac{41}{88}$ $\displaystyle \frac{41}{88}$

$\frac{34}{88}$ $\displaystyle \frac{34}{88}$

$\frac{9}{88}$ $\displaystyle \frac{9}{88}$

Correct answer:

$\frac{9}{88}$ $\displaystyle \frac{9}{88}$

Explanation:

To solve, subtract the numerators and leave the denominators the same:

$\frac{25}{63}-\frac{16}{88}=\frac{9}{88}$ $\displaystyle \frac{25}{63}-\frac{16}{88}=\frac{9}{88}$

Answer: $\frac{9}{88}$ $\displaystyle \frac{9}{88}$

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Example Question #35 : How To Subtract Fractions

Which of the following is the difference of nine tenths and nineteen thousandths?

Possible Answers:

0.01 $\displaystyle 0.01$

$\displaystyle 1$

0.81 $\displaystyle 0.81$

0.881 $\displaystyle 0.881$

0.71 $\displaystyle 0.71$

Correct answer:

0.881 $\displaystyle 0.881$

Explanation:

Nine tenths is equal to 0.9; nineteen thousandths is equal to 0.019. Subtract them, rewriting 0.9 as 0.900:

0.900 $\displaystyle 0.900$

$\underline{- \; 0.019}$ $\displaystyle \underline{- \; 0.019}$

0.881 $\displaystyle 0.881$

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Example Question #36 : How To Subtract Fractions

Which of the following is the difference of two-thirds and one-fifth?

Possible Answers:

$\frac {3}{5}$ $\displaystyle \frac {3}{5}$

$\frac{7}{10}$ $\displaystyle \frac{7}{10}$

$\frac{7}{15 }$ $\displaystyle \frac{7}{15 }$

$\frac{13}{15}$ $\displaystyle \frac{13}{15}$

$\frac{2}{15}$ $\displaystyle \frac{2}{15}$

Correct answer:

$\frac{7}{15 }$ $\displaystyle \frac{7}{15 }$

Explanation:

Since $\displaystyle GCF (3,5)= 15$, express each fraction as its equivalent in fifteenths, and subtract the numerators, as follows:

$\frac{2}{3 } - \frac{1}{5} = \frac{2 \times 5}{3 \times 5 } - \frac{3 \times 1}{3 \times 5} = \frac{10}{15 } - \frac{3 }{15} = \frac{10-3}{15 } = \frac{7}{15 }$ $\displaystyle \frac{2}{3 } - \frac{1}{5} = \frac{2 \times 5}{3 \times 5 } - \frac{3 \times 1}{3 \times 5} = \frac{10}{15 } - \frac{3 }{15} = \frac{10-3}{15 } = \frac{7}{15 }$

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Example Question #37 : How To Subtract Fractions

Subtract:

$\frac{9}{9}-\frac{5}{9}=$ $\displaystyle \frac{9}{9}-\frac{5}{9}=$

Possible Answers:

$1\frac{3}{9}$ $\displaystyle 1\frac{3}{9}$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$\displaystyle 4$

$\displaystyle 9$

Correct answer:

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Explanation:

Subtract the numerators and leave the denominators the same:

$\frac{9}{9}-\frac{5}{9}=\frac{4}{9}$ $\displaystyle \frac{9}{9}-\frac{5}{9}=\frac{4}{9}$

Answer: $\frac{4}{9}$ $\displaystyle \frac{4}{9}$

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Example Question #38 : How To Subtract Fractions

Subtract:

$\frac{90}{91}-\frac{47}{91}=$ $\displaystyle \frac{90}{91}-\frac{47}{91}=$

Possible Answers:

$\frac{34}{91}$ $\displaystyle \frac{34}{91}$

$\displaystyle 43$

$\frac{43}{91}$ $\displaystyle \frac{43}{91}$

$\frac{47}{91}$ $\displaystyle \frac{47}{91}$

Correct answer:

$\frac{43}{91}$ $\displaystyle \frac{43}{91}$

Explanation:

Subtract the numerators and leave the denominators the same:

$\frac{90}{91}-\frac{47}{91}=\frac{43}{91}$ $\displaystyle \frac{90}{91}-\frac{47}{91}=\frac{43}{91}$

Answer: $\frac{43}{91}$ $\displaystyle \frac{43}{91}$

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Example Question #288 : Fractions

The time is now 2:17 AM. What time was it four hours and thirty-six minutes ago?

Possible Answers:

$10:41 \textrm{ PM}$ $\displaystyle 10:41 \textrm{ PM}$

$10:31 \textrm{ PM}$ $\displaystyle 10:31 \textrm{ PM}$

$9:41 \textrm{ PM}$ $\displaystyle 9:41 \textrm{ PM}$

$9:21 \textrm{ PM}$ $\displaystyle 9:21 \textrm{ PM}$

$9:31 \textrm{ PM}$ $\displaystyle 9:31 \textrm{ PM}$

Correct answer:

$9:41 \textrm{ PM}$ $\displaystyle 9:41 \textrm{ PM}$

Explanation:

Two hours and seventeen minutes have elapsed since midnight. Since four hours and thirty-six minutes make a greater quantity, we need to look at this as fourteen hours and seventeen minutes having elapsed since noon.

Change both to minutes as follows:

14 hours 17 minutes:

$14 \times 60 + 17 = 840 + 17 = 857$ $\displaystyle 14 \times 60 + 17 = 840 + 17 = 857$ minutes

4 hours 36 minutes:

$4 \times 60 + 36 = 240 + 36 = 276$ $\displaystyle 4 \times 60 + 36 = 240 + 36 = 276$ minutes

Subtract these quantities:

$\displaystyle 857 - 276 = 5 81$ minutes have elapsed since noon. 581 minutes is equal to

$581 \div 60 = 9 \frac{41}{60 }$ $\displaystyle 581 \div 60 = 9 \frac{41}{60 }$ hours, or 9 hours 41 minutes after noon, so the time was 9:41 PM.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to subtract fractions

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #31 : How To Subtract Fractions

Example Question #32 : How To Subtract Fractions

Example Question #281 : Fractions

Example Question #33 : How To Subtract Fractions

Example Question #34 : How To Subtract Fractions

Example Question #35 : How To Subtract Fractions

Example Question #36 : How To Subtract Fractions

Example Question #37 : How To Subtract Fractions

Example Question #38 : How To Subtract Fractions

Example Question #288 : Fractions

All ISEE Middle Level Math Resources

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