Numbers and Operations - SSAT Middle Level Quantitative

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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

What is 220% of 0.00022?

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Answer

220% of a number is 2.2 multiplied by that number, so 220% of 0.00022 is equal to

$2.2 \times 0.00022 = 0.000484$ .

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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

The ratio of tea to milk in Kelsey’s favorite drink is 5:2. The total volume of the drink is 14 ounces. How many ounces of Kelsey’s drink are tea?

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Answer

Determine the total parts of tea and milk in the drink by adding them $(5+2=7\textsl{ total parts})$ .

Divide the total volume of the drink by the number of parts in the drink to determine how many ounces per part $(\frac{14\textsl{ ounces}}{7 parts}=\frac{2\textsl{ ounces}}{1 part})$

Finally, multiply the parts of tea (5) by the number of ounces/part. Therefore, $5\cdot2=10\textsl{ ounces of tea}$ .

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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

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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Question

Give the value of that makes this proportion statement correct:

$\frac{N}{80} = \frac{40}{30}$

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Answer

Multiply both sides by 80 and solve for :

$\frac{N}{80} = \frac{40}{30}$

$\frac{N}{80} \cdot80 = \frac{40}{30} \cdot80$

$N = \frac{40 \cdot 80}{30} = 106 \frac{2}{3}$

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Question

Give the value of that makes this proportion statement correct:

$\frac{N}{75} = \frac{40}{30}$

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Answer

Multiply both sides by 75 and solve for :

$\frac{N}{75} = \frac{40}{30}$

$\frac{N}{75} \cdot 75 = \frac{40}{30} \cdot 75$

$N = \frac{40 \cdot 75}{30} = 100$

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Question

Read this problem, but do not solve it.

4 out of every 5 dentists surveyed recommend Triton sugarless gum to patients who chew gum. If 2,100 dentists were surveyed, how many dentists recommended Triton?

If we let be the number of dentists who recommended Triton, what proportion statement could be used to solve this problem?

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Answer

The ratios that are set equal to each other in a proportion statement must compare the same quantities in the same order.

In each ratio, we can put number of dentists who recommended Triton in the numerator, and number of dentists who were surveyed in the denominator.

One ratio is 4 dentists recommending Triton to 5 dentists surveyed (the general ratio): this is $\frac{4}{5}$ .

The other ratio is dentists recommending Triton to 2,100 dentists surveyed (the actual number); this is $\frac{N}{2,100}$ .

The proportion statement sets these equal:

$\frac{N}{2,100} = \frac{4}{5}$

which is the correct choice.

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Question

Read this problem, but do not solve it: Two inches on a map represent twenty-five miles of actual distance. If Pierce Springs and Buchanan Falls are eight inches apart on the map, how far apart are they in actuality?

If we let be the actual distance between Pierce Springs and Buchanan Falls, which proportion could be used to solve this problem?

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Answer

The ratios that are set equal to each other in a proportion must compare the same quantities in the same order.

In each ratio, we can put number of map inches in the numerator and the number of actual miles in the denominator.

One ratio is two map inches to twenty-five actual miles (the map scale); this ratio is $\frac{2}{25}$ .

The other ratio is eight map inches to actual miles (the distance between Pierce Springs and Buchanan Falls); this ratio is $\frac{8}{N}$ .

The proportion statement that sets these equal to each other is $\frac{8}{N} = \frac{2}{25}$ , and is therefore the correct choice.

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