ISEE Middle Level Math : How to subtract fractions

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

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Example Questions

Example Question #31 : How To Subtract Fractions

What is the solution to the expression below?

\(\displaystyle \frac{3}{4}-\frac{7}{9}\)

Possible Answers:

\(\displaystyle \frac{1}{36}\)

\(\displaystyle 36\)

\(\displaystyle -36\)

\(\displaystyle -\frac{1}{36}\)

Correct answer:

\(\displaystyle -\frac{1}{36}\)

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:

\(\displaystyle \frac{3}{4}-\frac{7}{9}\)

\(\displaystyle \frac{27}{36}-\frac{28}{36}\)

\(\displaystyle -\frac{1}{36}\)

Example Question #32 : How To Subtract Fractions

\(\displaystyle \frac{20}{21}-\frac{14}{21}=\)

Possible Answers:

\(\displaystyle \frac{6}{21}\)

\(\displaystyle \frac{10}{21}\)

\(\displaystyle \frac{3}{21}\)

 

\(\displaystyle \frac{20}{21}\)

Correct answer:

\(\displaystyle \frac{6}{21}\)

Explanation:

Subtract the numerators and keep the denominator as is:

\(\displaystyle \frac{20}{21}-\frac{14}{21}=\frac{6}{21}\)

Answer: \(\displaystyle \frac{6}{21}\)

Example Question #281 : Fractions

Evaluate:

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

Possible Answers:

\(\displaystyle -1.3\)

\(\displaystyle 36.3\)

\(\displaystyle - 3.7\)

\(\displaystyle 22.5\)

\(\displaystyle 6.5\)

Correct answer:

\(\displaystyle -1.3\)

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:

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

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

\(\displaystyle = 20 - 21.3\)

\(\displaystyle = -1.3\)

Example Question #33 : How To Subtract Fractions

Subtract:

\(\displaystyle \frac{17}{63}-\frac{11}{63}=\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle \frac{6}{63}\)

\(\displaystyle \frac{63}{6}\)

\(\displaystyle \frac{28}{63}\)

Correct answer:

\(\displaystyle \frac{6}{63}\)

Explanation:

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

\(\displaystyle \frac{17}{63}-\frac{11}{63}=\frac{6}{63}\)

Answer: \(\displaystyle \frac{6}{63}\)

Example Question #34 : How To Subtract Fractions

Subtract:

\(\displaystyle \frac{25}{88}-\frac{16}{88}=\)

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle \frac{41}{88}\)

\(\displaystyle \frac{34}{88}\)

\(\displaystyle \frac{9}{88}\)

Correct answer:

\(\displaystyle \frac{9}{88}\)

Explanation:

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

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

Answer: \(\displaystyle \frac{9}{88}\)

Example Question #35 : How To Subtract Fractions

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

Possible Answers:

\(\displaystyle 0.01\)

\(\displaystyle 1\)

\(\displaystyle 0.81\)

\(\displaystyle 0.881\)

\(\displaystyle 0.71\)

Correct answer:

\(\displaystyle 0.881\)

Explanation:

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

     \(\displaystyle 0.900\)

\(\displaystyle \underline{- \; 0.019}\)

     \(\displaystyle 0.881\)

Example Question #36 : How To Subtract Fractions

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

Possible Answers:

\(\displaystyle \frac {3}{5}\)

\(\displaystyle \frac{7}{10}\)

\(\displaystyle \frac{7}{15 }\)

\(\displaystyle \frac{13}{15}\)

\(\displaystyle \frac{2}{15}\)

Correct answer:

\(\displaystyle \frac{7}{15 }\)

Explanation:

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

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

Example Question #37 : How To Subtract Fractions

Subtract:

\(\displaystyle \frac{9}{9}-\frac{5}{9}=\)

Possible Answers:

\(\displaystyle 1\frac{3}{9}\)

\(\displaystyle \frac{4}{9}\)

\(\displaystyle 4\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle \frac{4}{9}\)

Explanation:

Subtract the numerators and leave the denominators the same:

\(\displaystyle \frac{9}{9}-\frac{5}{9}=\frac{4}{9}\)

Answer: \(\displaystyle \frac{4}{9}\)

Example Question #38 : How To Subtract Fractions

Subtract:

\(\displaystyle \frac{90}{91}-\frac{47}{91}=\)

Possible Answers:

\(\displaystyle \frac{34}{91}\)

\(\displaystyle 43\)

\(\displaystyle \frac{43}{91}\)

\(\displaystyle \frac{47}{91}\)

Correct answer:

\(\displaystyle \frac{43}{91}\)

Explanation:

Subtract the numerators and leave the denominators the same:

\(\displaystyle \frac{90}{91}-\frac{47}{91}=\frac{43}{91}\)

Answer: \(\displaystyle \frac{43}{91}\)

Example Question #288 : Fractions

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

Possible Answers:

\(\displaystyle 10:41 \textrm{ PM}\)

\(\displaystyle 10:31 \textrm{ PM}\)

\(\displaystyle 9:41 \textrm{ PM}\)

\(\displaystyle 9:21 \textrm{ PM}\)

\(\displaystyle 9:31 \textrm{ PM}\)

Correct answer:

\(\displaystyle 9:41 \textrm{ PM}\)

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:

\(\displaystyle 14 \times 60 + 17 = 840 + 17 = 857\) minutes

4 hours 36 minutes:

\(\displaystyle 4 \times 60 + 36 = 240 + 36 = 276\) minutes

Subtract these quantities:

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

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

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