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SSAT Middle Level Math : How to subtract fractions

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

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Example Questions

Example Question #1 : How To Subtract Fractions

$7 \frac{1}{2}$ hours is how many more minutes than $3 \frac{3}{4}$ hours?

Possible Answers:

185

255

200

225

245

Correct answer:

225

Explanation:

This question requires you to subtract fractions as well as convert hours to minutes.

Subtracting $3\frac{3}{4}$ hours $\left ( \frac{15}{4} \right )$ from $7\frac{1}{2}$ hours $\left ( \frac{15}{2}\ or\ \frac{30}{4} \right )$

you get $3\frac{3}{4}$ hours $\left ( \frac{15}{4} \right )$ .

3 hours is 180 minutes $\left ( 3\cdot 60 \right )$

and $\frac{3}{4}$ of an hour is 45 minutes $\left ( \frac{3}{4}\cdot 60 \right )$ .

Thus the answer is

$180+45=225\ minutes$

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Example Question #1 : How To Subtract Fractions

Evaluate:

$9 - 5 \frac{3}{7}$

Possible Answers:

$4 \frac{4}{7}$

$3 \frac{4}{7}$

$4 \frac{3}{7}$

$3 \frac{3}{7}$

$4 \frac{2}{7}$

Correct answer:

$3 \frac{4}{7}$

Explanation:

"Borrow" 1 from the 9 to form $8 \frac{7}{7}$ . You can then subtract integers and fractions vertically:

$8 \frac{7}{7}$

$\underline{5 \frac{3}{7}}$

$3 \frac{4}{7}$

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Example Question #2 : How To Subtract Fractions

Evaluate:

$6 \frac{1}{5} - 4 \frac{1}{2}$

Possible Answers:

$2 \frac{3}{10}$

$1 \frac{7}{10}$

$1 \frac{3}{5}$

$2 \frac{1}{10}$

$1 \frac{9}{10}$

Correct answer:

$1 \frac{7}{10}$

Explanation:

Rewrite as the difference of improper fractions:

$6 \frac{1}{5} - 4 \frac{1}{2} = \frac{6 \times 5 + 1}{5} - \frac{4 \times 2 + 1}{2} = \frac{31}{5} - \frac{9}{2}$

Rewrite with a common denominator, then subtract numerators:

$\frac{31}{5} - \frac{9}{2} = \frac{2 \times 31}{2 \times 5} - \frac{9\times 5}{2\times 5} = \frac{62}{10} - \frac{45}{10} = \frac{17}{10}$

Rewrite as a mixed number:

$17 \div 10 = 1 \textrm{ R } 7$

$\frac{17}{10} = 1 \frac{7}{10}$

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Example Question #3 : How To Subtract Fractions

Evaluate:

$8 \frac{4}{5} - 4 \frac{1}{3}$

Possible Answers:

$4 \frac{8}{15 }$

$4 \frac{3}{5 }$

$4 \frac{7}{15 }$

$4 \frac{1}{2 }$

$4 \frac{1}{3 }$

Correct answer:

$4 \frac{7}{15 }$

Explanation:

Rewrite as the difference of improper fractions:

$8 \frac{4}{5} - 4 \frac{1}{3} = \frac{8 \times 5 + 4}{5} - \frac{4 \times 3 + 1}{3} = \frac{44}{5} - \frac{13}{3}$

Rewrite with a common denominator, then subtract numerators:

$\frac{44}{5} - \frac{13}{3} = \frac{44\times 3}{5 \times 3} - \frac{5 \times13}{5 \times3} = \frac{132}{15 } - \frac{65}{15 } = \frac{67}{15 }$

Rewrite as a mixed number:

$67\div 15 = 4 \textrm{ R } 7$

$\frac{67}{15 } = 4 \frac{7}{15 }$

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Example Question #4 : How To Subtract Fractions

Evaluate:

$5 - 1 \frac{4}{5}$

Possible Answers:

$4 \frac{4}{5}$

$4 \frac{1}{5}$

$3 \frac{4}{5}$

$3 \frac{3}{5}$

$3 \frac{1}{5}$

Correct answer:

$3 \frac{1}{5}$

Explanation:

"Borrow" 1 from the 5 to form $4 \frac{5}{5}$ . You can then subtract integers and fractions vertically:

$4 \frac{5}{5}$

$\underline{1 \frac{4}{5}}$

$3 \frac{1}{5}$

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Example Question #5 : How To Subtract Fractions

Give the result in simplest form:

$\frac{17}{40} - \frac{1}{40} + \frac{19}{40}$

Possible Answers:

$\frac{7}{24}$

$\frac{3}{40}$

$\frac{7}{8}$

$\frac{37}{40}$

$-\frac{3}{40}$

Correct answer:

$\frac{7}{8}$

Explanation:

$\frac{17}{40} - \frac{1}{40} + \frac{19}{40}$

$=\frac{17-1+19}{40}$

$=\frac{16+19}{40}$

$=\frac{35}{40} = \frac{35\div 5}{40\div 5} = \frac{7}{8}$

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Example Question #6 : How To Subtract Fractions

Evaluate:

7.89 - 1.73 + 2.5

Possible Answers:

5.91

3.66

6.41

8.66

7.12

Correct answer:

8.66

Explanation:

By order of operations, subtractions and additions are carried out in left-to-right order, so subtract 1.73 from 7.89 first. This is best done vertically, aligning decimal points:

7.89

$\underline{1.73}$

6.16

Now add 2.50 to the difference (note that a zero has been added to the end), again aligning vertically by decimal point:

6.16

$\underline{2.50}$

8.66

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Example Question #3 : How To Subtract Fractions

Evaluate:

8-3.27

Possible Answers:

3.73

5.27

5.73

4.27

4.73

Correct answer:

4.73

Explanation:

Subtract vertically by aligning the decimal points, making sure you append the 8 with a decimal point and two placeholder zeroes:

8.00

$\underline{3.27}$

4.73

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Example Question #4 : How To Subtract Fractions

Subtract:

19 - 0.006

Possible Answers:

-0.00013

18.9994

-0.0013

18.0994

18.994

Correct answer:

18.994

Explanation:

Rewrite vertically, lining up the decimal digits. Subtract as you would two integers. (Note that you are appending zeroes to the 19.)

$\begin{matrix} 19.000 \\ - \underline{0.006}\\ 18.994 \end{matrix}$

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Example Question #7 : How To Subtract Fractions

Subtract

$7\frac{1}{2}-3\frac{7}{8}$

Possible Answers:

$4\frac{3}{8}$

$3\frac{7}{8}$

$4\frac{5}{8}$

$3\frac{5}{8}$

$3\frac{3}{8}$

Correct answer:

$3\frac{5}{8}$

Explanation:

Rewrite the first fraction in eighths, as LCD (2,8) = 8 :

$7\frac{1}{2} = 7\frac{1 \times 4}{2 \times 4} = 7\frac{4}{8}$

Write vertically:

$7\frac{4}{8}$

$-\underline{3\frac{7}{8}}$

Now "borrow" one from 7 and add it to the $\frac{4}{8}$ , then subtract integer and fractional parts separately:

$6\frac{12}{8}$

$-\underline{3\frac{7}{8}}$

$3\frac{5}{8}$

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SSAT Middle Level Math : How to subtract fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : How To Subtract Fractions

Example Question #1 : How To Subtract Fractions

Example Question #2 : How To Subtract Fractions

Example Question #3 : How To Subtract Fractions

Example Question #4 : How To Subtract Fractions

Example Question #5 : How To Subtract Fractions

Example Question #6 : How To Subtract Fractions

Example Question #3 : How To Subtract Fractions

Example Question #4 : How To Subtract Fractions

Example Question #7 : How To Subtract Fractions

All SSAT Middle Level Math Resources

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