Fractions - SSAT Middle Level Quantitative

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Question

Add: $\frac{1}{12}+\frac{6}{12}=$

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Answer

Add the numerators and leave the denominators the same:

$\frac{1}{12}+\frac{6}{12}=\frac{7}{12}$

Answer: $\frac{7}{12}$

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Question

Add:

$\frac{2}{15}+\frac{5}{15}=$

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Answer

Add the numerators and leave the denominators the same:

$\frac{2}{15}+\frac{5}{15}=\frac{7}{15}$

Answer: $\frac{7}{15}$

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Question

Add:

$\frac{3}{12}+\frac{4}{12}=$

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Answer

Add the numerators and leave the denominators the same:

$\frac{3}{12}+\frac{4}{12}=\frac{7}{12}$

Answer: $\frac{7}{12}$

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Question

Solve:

$\frac{11}{13}+\frac{1}{13}=$

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Answer

Add the numerators and leave the denominators the same:

$\frac{11}{13}+\frac{1}{13}=\frac{12}{13}$

Answer: $\frac{12}{13}$

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Question

Solve:

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

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Answer

Add the numerators and leave the denominators the same:

$\frac{6}{14}+\frac{3}{14}=\frac{9}{14}$

Answer: $\frac{9}{14}$

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Question

Solve:

$\frac{10}{22}+\frac{9}{22}=$

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Answer

Add the numerators and leave the denominators the same:

$\frac{10}{22}+\frac{9}{22}=\frac{19}{22}$

Answer: $\frac{19}{22}$

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Question

Solve the expression.

$24(\frac{1}{12}+\frac{5}{6})$

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Answer

Start by solving for the term in parenthesis. We will need to find the least common denominator in order to add the fractions. Since 6 can be multiplied by 2 to get 12, 12 must be the least common denominator.

Convert the fractions so that they share a denominator of 12.

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

$24(\frac{1}{12}+\frac{5}{6})=24(\frac{1}{12}+\frac{10}{12})$

Add the fractions in parenthesis.

$24(\frac{1+10}{12})=24(\frac{11}{12})$

Multiply.

$24(\frac{11}{12})=\frac{24}{1}\times\frac{11}{12}=\frac{24\times11}{1\times12}=\frac{264}{12}$

You can then simplify the fraction be removing 12 from both the numerator and denominator.

$\frac{264}{12}=\frac{264\div12}{12\div12}=\frac{22}{1}=22$

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Question

Add:

$\frac{3}{23}+\frac{3}{23}=$

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Answer

Add the numerators and leave the denominators alone:

$\frac{3}{23}+\frac{3}{23}=\frac{6}{23}$

Answer: $\frac{6}{23}$

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Question

Subtract:

$\frac{4}{23}-\frac{1}{23}=$

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Answer

Subtract the numerators and leave the denominators alone:

$\frac{4}{23}-\frac{1}{23}=\frac{3}{23}$

Answer: $\frac{3}{23}$

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Question

Add:

$\frac{5}{21}+\frac{15}{21}=$

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Answer

Because the two fractions have the same denominator, simply add the numerators and leave the denominator as is:

$\frac{5}{21}+\frac{15}{21}=\frac{20}{21}$

Answer: $\frac{20}{21}$

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Question

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

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Answer

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

$\underline{+ ; 0.17 }$

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Question

Which of the following is the sum of five-sevenths and one-half?

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Answer

Since , express each fraction as its equivalent in fourteenths, and add the numerators, as follows:

$\frac{5}{7} + \frac{1}{2} = \frac{5 \times 2}{7 \times 2} + \frac{7 \times 1}{7 \times 2} = \frac{10}{14} + \frac{7 }{14} = \frac{10+7}{14} = \frac{17}{14}$

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Question

Which of the following is the sum of sixty-seven tenths, sixty-seven hundredths, and sixty-seven ten-thousandths?

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Answer

Sixty-seven tenths, sixty-seven hundredths, and sixty-seven ten-thousandths can be rewritten as 6.7, 0.67, and 0.0067, respectively. Add, appending zeroes at the end of each number as needed:

$\begin{matrix} &6.7000 \ & 0.6700\ +&\underline{0.0067} \ & 7.3767 \end{matrix}$

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Question

Tim has $\frac{1}{3}lb$ of peanuts that he wants to divide evenly into bags. How much will each bag of peanuts weigh?

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Answer

We are splitting $\frac{1}{3}$ into equal groups, so we are dividing $\frac{1}{3}$ by .

To solve $\frac{1}{3}\div8$ we multiply by the reciprocal.

$\frac{1}{3}\times\frac{1}{8}=\frac{1}{24}$

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Question

Drew has $\frac{1}{3}lb$ of peanuts that he wants to divide evenly into bags. How much will each bag of peanuts weigh?

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Answer

We are splitting $\frac{1}{3}$ into equal groups, so we are dividing $\frac{1}{3}$ by .

To solve $\frac{1}{3}\div9$ we multiply by the reciprocal.

$\frac{1}{3}\times\frac{1}{9}=\frac{1}{27}$

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Question

Tim has $\frac{1}{3}lb$ of peanuts that he wants to divide evenly into bags. How much will each bag of peanuts weigh?

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Answer

We are splitting $\frac{1}{3}$ into equal groups, so we are dividing $\frac{1}{3}$ by .

To solve $\frac{1}{3}\div10$ we multiply by the reciprocal.

$\frac{1}{3}\times\frac{1}{10}=\frac{1}{30}$

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Question

Tim has $\frac{1}{3}lb$ of peanuts that he wants to divide evenly into bags. How much will each bag of peanuts weigh?

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Answer

We are splitting $\frac{1}{3}$ into equal groups, so we are dividing $\frac{1}{3}$ by .

To solve $\frac{1}{3}\div11$ we multiply by the reciprocal.

$\frac{1}{3}\times\frac{1}{11}=\frac{1}{33}$

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Question

$1 \frac{1}{2} + 2 \frac{3}{4} =$

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Answer

I think the easiest way to do this problem is to make a common denominator. 4 is the smallest common denominator.

$2 \frac{3}{4}$ is equivalent to $\frac{11}{4}$ .

When you add $\frac{6}{4}$ and $\frac{11}{4}$ you get $\frac{17}{4}$ .

$\frac{17}{4}$ reduces to $4 \frac{1}{4}}$ and is equivalent to .

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Question

Add the fractions below.

$\frac{4}{5} + \frac{7}{10}$

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Answer

First, we need to find a common denominator. In this case, we can convert both denominators to .

$\frac{4}{5} + \frac{7}{10} = (\frac{4 }{5 }*\frac{2}{2}) + \frac{7}{10} = \frac{8}{10} + \frac{7}{10}$

Now we can add the numerators.

$\frac{8}{10}+\frac{7}{10}=\frac{15}{10}$

Both the numerator and denominator are divisible by , so we can simplify.

$\frac{15}{10}= \frac{15\div 5}{10\div 5}= \frac{3}{2}$

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Question

Find the sum: $4\tfrac{2}{3}+ 5 \tfrac{1}{2}$

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Answer

Add the fractions by writing each with the lowest common denominator, which is .

$\frac{2}{3} + \frac{1}{2} = \frac{2 \cdot 2}{3\cdot 2} + \frac{1\cdot 3}{2\cdot 3} = \frac{4}{6} + \frac{3}{6}= \frac{7}{6}=1 \frac{1}{6 }$

Add the integers:

Now add the two sums: $9 + 1\tfrac{1}{6} =10 \tfrac{1}{6}$

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