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TACHS Math : Operations

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Example Questions

Example Question #1 : Mixed Numbers

Which of the following is the most reduced form of 2.4 ?

Possible Answers:

$2 \frac{4}{10}$

$2 \frac{2}{5}$

$\frac{24}{10}$

$\frac{22}{5}$

Correct answer:

$2 \frac{2}{5}$

Explanation:

Start by converting 2.4 into a fraction.

$\frac{2.4}{1} \times \frac{10}{10}=\frac{24}{10}$

We multiply both numerator and denominator by to get rid of the decimal.

Now, convert $\frac{24}{10}$ into a mixed number.

$\frac{24}{10}=2\frac{4}{10}=2\frac{2}{5}$

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Example Question #1 : Order Of Operations

Evaluate:

$15 \times 8 - 12 + 25$

Possible Answers:

157

107

133

Correct answer:

133

Explanation:

In the order of operations, in the absence of grouping symbols, multiplication takes precedence over addition and subtraction. Multiply 15 by 8 first:

$15 \times 8 - 12 + 25$

=120 - 12 + 25

Addition and subtraction have equal precedence and are worked in left-to-right order. Subtract 120 and 12 next:

=108 + 25

Now add:

= 133

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Example Question #2 : Order Of Operations

What is the value of $(3+1)^2\times 2-(2\times2)+15$ ?

Possible Answers:

Correct answer:

Explanation:

Make sure to follow the order of operations.

Start by simplifying what is found in the parentheses.

$(3+1)^2\times 2-(2\times2)+15=4^2\times 2-4+15$

Next, simplify any exponents.

$4^2\times 2-4+15=16 \times 2-4+15$

Next, simplify any multiplication and division.

$16 \times 2-4+15=32-4+15$

Finally, simplify any addition and subtraction.

32-4+15=43

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Example Question #1 : Order Of Operations

What is the value of $3+(7\times 4)\times (2+1)-10$ ?

Possible Answers:

Correct answer:

Explanation:

Make sure you follow the order of operations (PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction—from the left to the right).

Start by simplifying what's found within the parentheses:

$3+(7\times 4)\times (2+1)-10=3+28 \times 3-10$

Next, simplify any multiplication and division.

$3+28 \times 3-10=3+84-10$

Finally, simplify any addition and subtraction.

3+84-10=77

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TACHS Math : Operations

Study concepts, example questions & explanations for TACHS Math

All TACHS Math Resources

Example Questions

Example Question #1 : Mixed Numbers

Example Question #1 : Order Of Operations

Example Question #2 : Order Of Operations

Example Question #1 : Order Of Operations

All TACHS Math Resources

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