Numbers and Operations - SSAT Middle Level Quantitative

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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

What is the value of in the proportion?

$\frac{24}{64} = \frac{x}{8}$

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Answer

Simplify $\frac{24}{64}$ by dividing both the numerator and denominator by 8 so that it simplifies to $\frac{3}{8}$ . Now it should be obvious that in order for both sides of the equation to be equal.

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Question

Phil earns $\$10.00$ for each hour he works. For every hour he works, he then gives $\$2.00$ to his sister Lola. How much money will Lola have if Phil works hours?

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Answer

To Solve:

Multiply the $\$2.00$ Lola receives by the hours Phil worked:

$\small $2.00 \cdot 13.5=27$

Phil will give Lola $\$27.00$ if he works hours.

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Question

For every $3 I earn at work, I donate $1 to charity. How much money will I donate if I make $27.00/week.

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Answer

To find the amount of the donation, divide 27 by 3.

$27\div 3=9$

The answer is 9.

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Question

Give the value of that makes this proportion statement correct:

$\frac{100}{N} = \frac{70}{30}$

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Answer

Cross-multiply, then solve for :

$\frac{100}{N} = \frac{70}{30}$

$70 N = 100 \cdot 30$

$70 N \div 70= 3,000\div 70$

$N = 42 \frac{6}{7}$

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Question

Give the value of that makes this proportion statement correct:

$\frac{100}{N} = \frac{40}{30}$

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Answer

Cross-multiply, then solve for :

$\frac{100}{N} = \frac{40}{30}$

$40 N = 100 \cdot 30$

$40 N \div 40= 3,000\div 40$

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