How to subtract fractions - ISEE Middle Level Math

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Question

Give the result in simplest form:

$\frac{7}{20} - \frac{11}{20} + \frac{9}{20}$

Answer

$\frac{7}{20} - \frac{11}{20} + \frac{9}{20}$

$=\frac{7-11+9}{20}$

$=\frac{-4+9}{20}$

$=\frac{5}{20} =\frac{5\div 5}{20\div 5} = \frac{1}{4}$

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Question

Evaluate:

Answer

Subtract vertically, appending the 9 with a decimal point and two placeholder zeroes first.

$\underline{6.36}$

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Question

Evaluate:

Answer

Rewrite this difference as a sum. The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the negative number here) affixed:

Subtract vertically by aligning the decimal points, making sure you append the 9 with a decimal point and two placeholder zeroes:

$\underline{6.54}$

Since the answer is negative, append a negative symbol in front. The answer is .

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Question

Evaluate:

Answer

By order of operations, subtractions are carried out in left-to-right order, so subtract 4.70 (adding the placeholder zero) from 7.82, aligning the decimal points:

$\underline{4.70}$

Now subtract 2.56 from this difference, again aligning vertically by decimal point:

$\underline{2.56}$

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Question

Subtract:

Answer

Since you are subtracting a larger number from a smaller, reverse them, and affix a negative symbol:

$0.005 - 0.15 = - \left (0.15 - 0.005 \right )$

Rewrite vertically, lining up the decimal digits. Subtract as you would two integers. (Note that you are appending a zero to the 0.15.)

$\begin{matrix} ; ; ; 0.150\ -\underline{0.005}\; ; ; 0.145\end{matrix}$

Affix the negative symbol to obtain the difference of .

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Question

Evaluate:

$6 \frac{9}{11} - 2 \frac{3}{11}+ 4 \frac{7}{11}$

Answer

Subtract the first two fractions first. This is best done by writing vertically, and subtracting integer and fraction parts.

$6 \frac{9}{11}$

$\underline{- 2 \frac{3}{11}}$

$4 \frac{6}{11}$

Now add this to the third fraction similarly, adjusting as shown for the improper fraction:

$4 \frac{6}{11}$

$\underline{+ 4 \frac{7}{11}}$

$8 \frac{13}{11} = 8 +1 + \frac{2}{11} = 9 \frac{2}{11}$

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Question

Solve:

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

Answer

The lowest common denominator of 2 and 7 is 14.

$\frac{1}{2}=\frac{7}{14}$

$\frac{3}{7}=\frac{6}{14}$

$\frac{7}{14}-\frac{6}{14}=\frac{1}{14}$

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Question

Subtract:

Answer

Subtract vertically, making sure the decimal points in all three numbers line up (note that a zero has been appended to the first number):

$\begin{matrix} ; ; ; 8.10\ \underline{-5.67}\ ; ; ;2.43 \end{matrix}$

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Question

Subtract: $8\frac{1}{4}-5\frac{7}{8}$

Answer

Rewrite the first fraction in eighths, as .

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

Now write vertically:

$8\frac{2}{8}$

$-\underline{5\frac{7}{8}}$

"Borrow" in the first expression, then subtract integer and fractional parts separately:

$7\frac{10}{8}$

$-\underline{5\frac{7}{8}}$

$2\frac{3}{8}$

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Question

$\frac{7}{15}-\frac{6}{15}=$

Answer

Subtract the numerators:

$\frac{7}{15}-\frac{6}{15}=\frac{1}{15}$

Answer: $\frac{1}{15}$

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Question

Which of the following expressions is equal to $15 - 7 \frac{3}{4}$ ?

Answer

Rewrite $7 \frac{3}{4}$ as a decimal:

$3 \div 4 = 0.75$ , so $7 \frac{3}{4} = 7.75$

Now subtract:

$\underline{-7.75}$

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Question

Which of the following is equal to ?

Answer

Subtract vertically, making sure the decimal points line up.

$\underline{-2.8}$

This is twelve tenths; write this as a fraction and simplify:

$\frac{12}{10} = \frac{12\div 2}{10\div 2} = \frac{6}{5}$

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Question

$\frac{12}{3}-\frac{8}{3}=$

Answer

In order to subtract fractions we need to have a common denominator (the number on the bottom of each fractions). In this case we do have common denominators.

We need to then subtract the numerators, in this case .

After subtracting the numerators we keep the denonimator the same.

$\frac{4}{3}$

This is known as an improper fraction because the numerator is greater than the denominator. So we need to rewrite into a mixed number. Fractions can also be read as division, meaning 4 divided by 3 is????

$1\frac{1}{3}$

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Question

Which of the following is equal to ?

Answer

$1.2 t \div 1.2 = 2.16\div 1.2$

Move the decimal point in each over one place:

$t= 21.6 \div 1 2 =1.8$

Rewrite as a fraction:

$t= 1.8 = \frac{18}{10} = \frac{9}{5}$

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Question

Solve:

$\frac{3}{7}-\frac{2}{9}=$

Answer

Find the least common denominator:

The least common denominator of $\small 7$ and $\small 9$ is $\small 63$ .

$\frac{3}{7}=\frac{27}{63}$

$\frac{2}{9}=\frac{14}{63}$

$\frac{27}{63}-\frac{14}{63}=\frac{13}{63}$

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Question

Find the difference:

$\frac{11}{50}-\frac{4}{50}=$

Answer

Since the denominators of the two fractions are the same, we can simply subtract one numerator from the other:

$\frac{11}{50}-\frac{4}{50}=\frac{7}{50}$

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Question

Find the difference:

$\frac{9}{17}-\frac{2}{17}=$

Answer

Since the denominators of the two fractions are the same, we can simply subtract one numerator from the other:

$\frac{9}{17}-\frac{2}{17}=\frac{7}{17}$

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Question

$\frac{17}{25}-\frac{11}{25}=$

Answer

Subtract the numerators and keep the denominator the same:

$\frac{17}{25}-\frac{11}{25}=\frac{6}{25}$

Answer:

$\frac{6}{25}$

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Question

$\frac{7}{14}-\frac{2}{14}=$

Answer

Subtract the numerators and keep the denominator the same:

$\frac{7}{14}-\frac{2}{14}=\frac{5}{14}$

Answer:

$\frac{5}{14}$

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Question

$\frac{15}{30}-\frac{4}{30}=$

Answer

Subtract the numerators and keep the denominator the same:

$\frac{15}{30}-\frac{4}{30}=\frac{11}{30}$

Answer:

$\frac{11}{30}$

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