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HSPT Math : Arithmetic

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Example Questions

Example Question #291 : Arithmetic

Express the product in simplest form:

$\frac{3}{5} \cdot 2 \frac{1}{7} \cdot 1 \frac{2}{5}$

Possible Answers:

$2 \frac{1}{5}$

$1 \frac{6}{7}$

$1 \frac{11}{15}$

$1 \frac{9}{10}$

$1 \frac{4}{5}$

Correct answer:

$1 \frac{4}{5}$

Explanation:

Rewrite the mixed fractions as improper fractions, cross-cancel, and multiply across:

$\frac{3}{5} \cdot 2 \frac{1}{7} \cdot 1 \frac{2}{5} = \frac{3}{5} \cdot \frac{15}{7} \cdot \frac{7}{5} = \frac{3}{1} \cdot \frac{3}{1} \cdot \frac{1}{5} = \frac{9}{5} = 1 \frac{4}{5}$

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Example Question #292 : Arithmetic

Evaluate:

$-3.6 \cdot (-0.07)$

Possible Answers:

2.52

-0.0252

0.252

0.0252

- 0.252

Correct answer:

0.252

Explanation:

The product of two negative numbers is the (positive) product of theie absolute values.

$-3.6 \cdot (-0.07) = +(3.6 \cdot 0.07) = 3.6 \cdot 0.07$

There are a total of three digits to the right of the two decimal points. Therefore, the product can be calculated by multiplying 36 by 7, then placing the decimal point so that there are three digits at right.

$36 \cdot 7 = 252 \Rightarrow 3.6 \cdot 0.07 = 0.252$

This is the correct choice.

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Example Question #293 : Arithmetic

Solve:

$\frac{2}{5}\times\frac{7}{8}=$

Possible Answers:

$\frac{7}{20}$

$\frac{7}{4}$

$\frac{9}{13}$

$\frac{16}{35}$

Correct answer:

$\frac{7}{20}$

Explanation:

$\frac{2}{5}\times\frac{7}{8}=\frac{2\times7}{5\times8}=\frac{14}{40}=\frac{7}{20}$

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Example Question #4 : Fractions

Multiply:

$4.3 \times 3.7$

Possible Answers:

15.91

1.3201

14.911

1.591

13.201

Correct answer:

15.91

Explanation:

First, multiply the numbers, ignoring the decimal points:

$43 \times 37 = 1591$

Since the two factors in the original product have two digits to the right of the decimal points between them, position the decimal point in the product such that two digits are at its right. The result, therefore, is

15.91

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Example Question #294 : Arithmetic

$\frac{2}{5}*\frac{2}{5}=$

Possible Answers:

$\frac{4}{25}$

$\frac{4}{10}$

$\frac{2}{5}$

Correct answer:

$\frac{4}{25}$

Explanation:

Multiply the numerators and then denominators:

$\frac{2}{5}* \frac{2}{5}=\frac{4}{25}$

Answer:

$\frac{4}{25}$

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Example Question #295 : Arithmetic

$\frac{4}{5}*\frac{2}{3}=$

Possible Answers:

$\frac{8}{8}$

$\frac{6}{8}$

$\frac{6}{15}$

$\frac{8}{15}$

Correct answer:

$\frac{8}{15}$

Explanation:

Multiply the numerators then denominators:

$\frac{4}{5}* \frac{2}{3}=\frac{8}{15}$

Answer: $\frac{8}{15}$

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Example Question #296 : Arithmetic

$\frac{1}{6}* \frac{1}{6}=$

Possible Answers:

$\frac{1}{12}$

$\frac{2}{12}$

$\frac{1}{36}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{36}$

Explanation:

Multiply the numerators and the denominators:

$\frac{1}{6}*\frac{1}{6}=\frac{1}{36}$

Answer: $\frac{1}{36}$

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Example Question #4 : Fractions

What is the simplest form of the result:

$\frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}$

Possible Answers:

$\frac{2}{x}$

Correct answer:

Explanation:

In order to multiply fractions, we can simply multiply straight across:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

So we can write:

$\frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}=\frac{1\times 3x\times 4x^4}{x^3\times 2x^2\times 3}$

$\frac{12x^5}{6x^5}=\frac{12}{6}=2$

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Example Question #9 : Fractions

Simplify

$\frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}$

Possible Answers:

$\frac{24}{35}$

$\frac{6}{35}$

$\frac{1}{12}$

$\frac{4}{35}$

$\frac{3}{35}$

Correct answer:

$\frac{3}{35}$

Explanation:

In order to multiply fractions, we can simply multiply straight across:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

So we can write:

$\frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}=\frac{3\times 2\times 3}{5\times 6\times 7}$

$=\frac{18}{210}$

Divide it by the least common factor (i.e. 6) to simplify:

$\frac{18}{210}=\frac{3}{35}$

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Example Question #5 : Fractions

$\frac{1}{4}\times \frac{2}{6}-\frac{1}{8}=?$

Possible Answers:

$\frac{45}{24}$

$\frac{1}{4}$

$-\frac{1}{24}$

$\frac{1}{24}$

$\frac{2}{17}$

Correct answer:

$-\frac{1}{24}$

Explanation:

In this problem we need to follow our order of operations; in this case we need to multiply before we subtract fractions.

To multiply fractions we just need to multiply the numerator by the numerator and the denominator by the denominator. In this case $1\times 2$ (the numerators of the fractions being multiplied) and $4\times 6$ (the denominators) giving us

$\frac{2}{24}$

We then rewrite our equation.

$\frac{2}{24}-\frac{1}{8}=?$

In order to subtract fractions, we must have a common denominator. To do this we need to find a common multiple of 24 and 8. In this case, the 8 nicely goes into 24 three times, so we will only need to multiply one of our fractions to have common denominators.

To do this we must multiply one-eighth three times like this...

$\frac{3}{3}\left(-\frac{1}{8}\right)=-\frac{3}{24}$

Remember that if you are multiplying a fraction, you must multiply both the numerator and the denominator in order to obtain a multiple of your original factor.

Lastly subtract.

$\frac{2}{24}-\frac{3}{24}=-\frac{1}{24}$

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #291 : Arithmetic

Example Question #292 : Arithmetic

Example Question #293 : Arithmetic

Example Question #4 : Fractions

Example Question #294 : Arithmetic

Example Question #295 : Arithmetic

Example Question #296 : Arithmetic

Example Question #4 : Fractions

Example Question #9 : Fractions

Example Question #5 : Fractions

All HSPT Math Resources

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