How to subtract fractions - SSAT Middle Level Quantitative

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Question

Tim mowed $\frac{1}{7}$ of the yard and Tom mowed $\frac{1}{3}$ . How much more of the yard did Tom mow?

Answer

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

In order to solve this problem, we first need to make common denominators.

$\frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$

$\frac{1}{3}\times \frac{7}{7}=\frac{7}{21}$

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{7}{21}-\frac{3}{21}=\frac{4}{21}$

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Question

Select the fraction model that shows the difference of $\frac{4}{4}-\frac{1}{4}$

Answer

$\frac{4}{4}-\frac{1}{4}=\frac{3}{4}$

The fraction model is broken up into four pieces and three of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

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Question

Select the fraction model that shows the difference of $\frac{5}{6}-\frac{3}{6}$

Answer

$\frac{5}{6}-\frac{3}{6}=\frac{2}{6}$

The fraction model is broken up into six pieces and two of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

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Question

Select the fraction model that shows the difference of $\frac{5}{6}-\frac{2}{6}$

Answer

$\frac{5}{6}-\frac{2}{6}=\frac{3}{6}$

The fraction model is broken up into six pieces and three of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

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Question

Select the fraction model that shows the difference of $\frac{5}{6}-\frac{1}{6}$

Answer

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

The fraction model is broken up into six pieces and four of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

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Question

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

Answer

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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Question

Evaluate:

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

Answer

"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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Question

Evaluate:

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

Answer

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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Question

Evaluate:

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

Answer

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:

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

so

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

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Question

Evaluate:

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

Answer

"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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Question

Give the result in simplest form:

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

Answer

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

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

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

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

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Question

Evaluate:

Answer

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

$\underline{3.27}$

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Question

Evaluate:

Answer

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:

$\underline{1.73}$

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

$\underline{2.50}$

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Question

Subtract:

Answer

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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Question

Subtract

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

Answer

Rewrite the first fraction in eighths, as :

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

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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Question

Which of the following expressions is equal to $20 - 7 \frac{4}{5}$ ?

Answer

Rewrite $7 \frac{4}{5}$ as a decimal:

$4 \div 5 = 0.8$ , so

$7 \frac{4}{5} = 7.8$

Now subtract:

$\underline{-7.8}$

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Question

Find $\frac{3}{5}-\frac{2}{15}$ .

Answer

When substracting one fraction from another, first find the common denominator, then subtract one numerator from another.

$\frac{3}{5}-\frac{2}{15}=\frac{9}{15}-\frac{2}{15}$

$\frac{9}{15}-\frac{2}{15}=\frac{7}{15}$

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Question

Which of the following is the difference of seven tenths and seventeen hundredths?

Answer

Seven tenths is equal to 0.7; seventeen hundredths is equal to 0.17. Subtract them, rewriting 0.7 as 0.70;

$\underline{- ; 0.17 }$

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Question

The time is now 1:32 PM. What time was it three hours and seventeen minutes ago?

Answer

One hour and thirty-two minutes have elapsed since midnight. Since three hours and seventeen minutes make a greater quantity, we need to look at this as thirteen hours and thirty-two minutes having elapsed since noon.

We can subtract hours, then subtract minutes:

$13\textrm{ hr }32\textrm{ min}$

$\underline{- 3\textrm{ hr }17\textrm{ min}}$

$10 \textrm{ hr }15 \textrm{ min}$

The time was 10:15 AM.

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Question

Evaluate:

$-20 - 7.5 \times 3 - 1.2$

Answer

By the order of operations, carry out the multiplication first, then the leftmost subtraction, then the rightmost subtraction:

$-20 - 7.5 \times 3 - 1.2$

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