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SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

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All SSAT Middle Level Math Resources

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Example Questions

Example Question #1 : How To Add Fractions

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

Possible Answers:

4.5

4.7

3.75

3.25

4.25

Correct answer:

4.25

Explanation:

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 4.25 .

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Example Question #4 : Negative Numbers

Evaluate:

-3.2+7.17

Possible Answers:

-10.37

-3.97

-7.49

6.85

3.97

Correct answer:

3.97

Explanation:

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

-3.2+7.17 = +(7.17 - 3.2) = 7.17 - 3.2

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

7.12

$\underline{3.20}$

3.97

This is the correct choice.

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Example Question #2 : How To Add Fractions

Evaluate:

$6 \frac{3}{7}- 4 \frac{1}{7} + 1 \frac{6}{7}$

Possible Answers:

$4 \frac{1}{7}$

$12\frac{3}{7}$

$8 \frac{5}{7}$

$\frac{3}{7}$

$5 \frac{2}{7}$

Correct answer:

$4 \frac{1}{7}$

Explanation:

Rewrite these numbers as improper fractions.

$6 \frac{3}{7}= \frac{6 \cdot 7 + 3}{7}= \frac{45}{7}$

$4 \frac{1}{7}=\frac{4 \cdot 7+ 1}{7} = \frac{29}{7}$

$1 \frac{6}{7} = \frac{1 \cdot 7 + 6}{7} = \frac{13}{7}$

Now evaluate:

$6 \frac{3}{7}- 4 \frac{1}{7} + 1 \frac{6}{7}$

$= \frac{45}{7}- \frac{29}{7}+ \frac{13}{7}$

$= \frac{45-29+13}{7}$

$= \frac{16+13}{7}$

$= \frac{29}{7}$

$29 \div 7 = 4 \textrm{ R }1$ , so

$\frac{29}{7} = 4 \frac{1}{7}$

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Example Question #183 : Fractions

Add:

$\frac{1}{12}+\frac{4}{3}$

Possible Answers:

$\frac{5}{3}$

$\frac{19}{12}$

$\frac{17}{12}$

$\frac{1}{3}$

$\frac{17}{3}$

Correct answer:

$\frac{17}{12}$

Explanation:

Rewrite using the lowest comon denominator. Since LCM (12, 3) = 12 :

$\frac{1}{12}+\frac{4}{3}$

$= \frac{1}{12}+\frac{4 \times 4}{3 \times 4}$

$= \frac{1}{12}+\frac{16}{12}$

$= \frac{16+1}{12}$

$= \frac{17}{12}$

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Example Question #483 : Arithmetic

$\frac{2}{3} + \frac{1}{6}$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{5}{6}$

$\frac{3}{9}$

$\frac{1}{2}$

Correct answer:

$\frac{5}{6}$

Explanation:

When adding fractions, both denominators must be the same. A quick and easy way to do this is to multiply the numerator and the denominator of each fraction by the other fraction's denominator:

$\frac{2}{3} \times \frac{6}{6} = \frac{12}{18}$ and $\frac{1}{6} \times \frac{3}{3} = \frac{3}{18}$

The $\tfrac{2}{3}$ is multiplied by 6 on both ends because the denominator of $\tfrac{1}{6}$ is 6. Likewise, $\tfrac{1}{6}$ is multiplied by 3 on both ends because the denominator of $\tfrac{2}{3}$ is 3. The problem should now look like this:

$\frac{12}{18} + \frac{3}{18} = \frac{15}{18}$

Remember to reduce. 15 and 18 are both divisible by 3.

$\frac{15}{18} = \frac{5}{6}$

Your answer is $\frac{5}{6}$ .

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Example Question #483 : Concepts

Add the following fractions and simplify, if possible.

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

Possible Answers:

$\frac{1}{2}$

$\frac{5}{4}$

$\frac{2}{3}$

$\frac{1}{3}$

Correct answer:

$\frac{5}{4}$

Explanation:

In order to add fractions with different denominators, first find a common denominator of the fractions by finding the least common multiple. The least common multiple of these denominators is:

4*1=4 and 2 * 2 = 4 .

Because $\frac{3}{4}$ already has the required denominator, nothing needs to be done to $\frac{3}{4}$ .

Since the in $\frac{1}{2}$ needs to be multiplied by in order to get as the deonominator, multiply the numberator of $\frac{1}{2}$ by .

The "new" addition problem is now: $\frac{3}{4}+\frac{2}{4}$ .

The answer to this question is therefore $\frac{5}{4}$ .

Because and do not have a common factor, the answer cannot be simplified.

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Example Question #5 : How To Add Fractions

$\frac{7}{12}+\frac{5}{4}=$

Possible Answers:

$\frac{13}{12}$

$\frac{11}{6}$

$\frac{1}{2}$

$\frac{11}{5}$

$\frac{3}{4}$

Correct answer:

$\frac{11}{6}$

Explanation:

To add two fractions, first find the common denominator. We can convert $\frac{5}{4}$ to $\frac{15}{12}$ . $\frac{7}{12}+\frac{15}{12}= \frac{22}{12}$ , which reduces to $\frac{11}{6}$ .

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Example Question #485 : Arithmetic

Find $\frac{7}{8}+\frac{3}{2}$ .

Possible Answers:

$\tiny {}\frac{19}{8}$

$\large 11$

$\small \frac{8}{19}$

$\tiny 1$

$\large \frac{9}{1}$

Correct answer:

$\tiny {}\frac{19}{8}$

Explanation:

To add two fractions, first find the common denominator, then add the two numerators.

$\frac{7}{8}+\frac{3}{2}=\frac{7}{8} + \frac{12}{8}$

$\frac{7}{8}+\frac{12}{8} = \frac{19}{8}$

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Example Question #2 : Commutative Property Of Addition

Which of the following statements demonstrates the commutative property of addition?

Possible Answers:

None of the examples in the other responses demonstrates the commutative property of addition.

$\frac{3}{4} +\left ( \frac{7}{8} + \frac{1}{6} \right )= \left (\frac{3}{4} + \frac{7}{8} \right ) + \frac{1}{6}$

$\frac{3}{4} +0 = \frac{3}{4}$

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

$\frac{7}{8} + \left (- \frac{7}{8} \right ) = 0$

Correct answer:

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

Explanation:

The commutative property of addition states that two numbers can be added in either order to obtain the same sum. Of the given responses, only

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

demonstrates this property, so it is the correct choice.

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Example Question #4 : Associative Property Of Addition

Which of the following statements demonstrates the associative property of addition?

Possible Answers:

2.5+5= 5+2.5

None of the examples in the other responses demonstrates the associative property of addition.

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

2.5+ (-2.5) = 0

2.5 + 0 = 2.5

Correct answer:

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

Explanation:

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

demonstrates this property, so it is the correct choice.

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SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : How To Add Fractions

Example Question #4 : Negative Numbers

Example Question #2 : How To Add Fractions

Example Question #183 : Fractions

Example Question #483 : Arithmetic

Example Question #483 : Concepts

Example Question #5 : How To Add Fractions

Example Question #485 : Arithmetic

Example Question #2 : Commutative Property Of Addition

Example Question #4 : Associative Property Of Addition

All SSAT Middle Level Math Resources

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