Fractions

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HSPT Math › Fractions

Questions 1 - 10

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Explanation

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

Solve:

$\frac{1}{2}-\frac{3}{7}$

$\frac{1}{14}$

$\frac{3}{5}$

$-\frac{3}{5}$

$-\frac{1}{14}$

$\frac{1}{7}$

Explanation

The lowest common denominator of 2 and 7 is 14.

$\frac{1}{2}=\frac{7}{14}$

$\frac{3}{7}=\frac{6}{14}$

$\frac{7}{14}-\frac{6}{14}=\frac{1}{14}$

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

$\frac{8}{15}$

$\frac{6}{8}$

$\frac{6}{15}$

$\frac{8}{8}$

Explanation

Multiply the numerators then denominators:

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

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

Multiply:

$0.58 \times 8.3$

Explanation

First, multiply the numbers, ignoring the decimal points:

$58 \times 83 = 4814$

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

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

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

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

demonstrates this property, so it is the correct choice.

The gas tank in Renee's mustang is filled to capacity at $13\frac{1}{2}$ gallons. She used $\frac{2}{3}$ of a tank of gas to take a drive to the shore. How much gas did it take to drive to the shore?

gallons

$8 \frac{1}{2}$ gallons

$9 \frac{1}{2}$ gallons

Explanation

To solve this word problem, multiply the fractions. First convert any mixed number to an improper fraction:

$13\frac{1}{2} = \frac{(2\times13 )+1}{2} = \frac{27}{2}$

Next, multiply the numerators and the denominators of both improper fractions.

$\frac{27}{2} \times\frac{2}{3} = \frac{54}{6} = 9$

gallons of gas was consumed on Renee's trip to the shore.

The gas tank in Renee's mustang is filled to capacity at $13\frac{1}{2}$ gallons. She used $\frac{2}{3}$ of a tank of gas to take a drive to the shore. How much gas did it take to drive to the shore?

gallons

$8 \frac{1}{2}$ gallons

$9 \frac{1}{2}$ gallons

Explanation

To solve this word problem, multiply the fractions. First convert any mixed number to an improper fraction:

$13\frac{1}{2} = \frac{(2\times13 )+1}{2} = \frac{27}{2}$

Next, multiply the numerators and the denominators of both improper fractions.

$\frac{27}{2} \times\frac{2}{3} = \frac{54}{6} = 9$

gallons of gas was consumed on Renee's trip to the shore.

$-\frac{5}{6 }\times \frac{3}{5}$

$-\frac{1}{2}$

$-\frac{1}{6}$

$\frac{7}{11}$

$-\frac{5}{6}$

Explanation

The formula for multiplication of fractions is:

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

Where and It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

$-\frac{5}{6\ }\times \frac{3}{5} =\frac{-5\times 3}{6\times 5}$

$\frac{-5\times 3}{6\times 5} = -\frac{15}{30}$ A negative times a positive is a negative.

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 15.

$-\frac{15\div 15}{30\div 15} =-\frac{1}{2}$

$-\frac{5}{6 }\times \frac{3}{5}$

$-\frac{1}{2}$

$-\frac{1}{6}$

$\frac{7}{11}$

$-\frac{5}{6}$

Explanation

The formula for multiplication of fractions is:

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

Where and It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

$-\frac{5}{6\ }\times \frac{3}{5} =\frac{-5\times 3}{6\times 5}$

$\frac{-5\times 3}{6\times 5} = -\frac{15}{30}$ A negative times a positive is a negative.

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 15.

$-\frac{15\div 15}{30\div 15} =-\frac{1}{2}$

Simplify the expression.

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

$\frac{3}{16}$

$\frac{1}{8}$

$\frac{5}{12}$

$\frac{5}{16}$

Explanation

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

Start with the terms in parentheses, using the order of operations. Find the least common denominator.

$\left ( {\frac{1* 2}{2* 2} + \frac{1}{4}}\right ) *\left ({\frac{1* 2}{2*2} - \frac{1}{4}}\right )$

$\left ( {\frac{2}{4} + \frac{1}{4}}\right ) * \left ({\frac{ 2}{4} - \frac{1}{4}}\right )$

Add the fractions in parentheses.

$\left ( {\frac{2+1}{4} } \right ) * \left ({\frac{2-1}{4} } \right )$

Multiply the fractions and simplify.

${\frac{3}{4} } *{\frac{1}{4} } = \frac{3 * 1}{4 * 4} = \frac{3}{16}$

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