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HSPT Math : Problem Solving

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Example Questions

Example Question #51 : Hspt Mathematics

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?

Possible Answers:

gallons

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

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

Correct answer:

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.

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Example Question #51 : Problem Solving

The height or h of a triangle is $\frac{2}{3}$ inches. The base or b = $1\frac{1}{8}$ inches. What is the area of the triangle?

Possible Answers:

$A =\frac{2}{3}in^{2}$

$A =\frac{1}{2}in^{2}$

$A=\frac{5}{8}in^{2}$

$A =\frac{3}{8} in^{2}$

Correct answer:

$A =\frac{3}{8} in^{2}$

Explanation:

The formula for the Area of a triangle is:

$A= \frac{1}{2}(b\times h)$ where b represents the base and h represents height.

Convert any mixed numbers to improper fractions.

$1\frac{1}{8} = \frac{(8\times 1)+1}{8} = \frac{9}{8}$

Plug in the values for the base and the height into the formula; multiply.

$A = \frac{1}{2} (\frac{2}{3} \times \frac{9}{8})$

$A = \frac{(1\times 2\times 9)}{(2\times 3\times 8}) = \frac{18}{48}$

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor (GCF) of 18 and 48, which is 6.

$18\div6 =3$

$48\div6 = 8$

Because a triangle is two-dimensional, the answer must be represented in square units.

$A = \frac{3}{8} in^{2}$

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Example Question #52 : Problem Solving

A rectangular prism has a length of $2\frac{1}{2}$ cm, a width of $1\frac{1}{3}$ cm, and a height of $\frac{3}{4}$ cm. What is the volume of this rectangular prism?

Possible Answers:

$2\frac{3}{4}cm^{3}$

$3cm^{3}$

$2\frac{1}{2}cm^{3}$

$2\frac{1}{4}cm^{3}$

Correct answer:

$2\frac{1}{2}cm^{3}$

Explanation:

The formula for the Volume of a rectangular prism is: $V = l\times w \times h$ , where

l= length , w = width and h = height.

$V = 2\frac{1}{2} \times 1\frac{1}{3} \times \frac{3}{4}$

Convert mixed numbers (whole number and fraction) to improper fractions.

$2\frac{1}{2}= \frac{(2 \times 2)+1}{2} = \frac{5}{2}$

$1\frac{1}{3} = \frac{(3\times 1)+1}{3} = \frac{4}{3}$

$V = \frac{5}{2} \times \frac{4}{3}\times\frac{3}{4}$

$V = \frac{60}{24} cm^{3}$

$V = 2\frac{12}{24}cm^{3}$

Reduce to simplest form by dividing the numerator and the denominator of the fraction by the Greatest Common Factor of 12 and 24, which is 12.

A rectangular prism is a 3-dimensional shape, therefore the measurement must be expressed in cubic units.

$V = 2\frac{1}{2}cm^{3}$

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Example Question #12 : How To Multiply And Divide Fractions

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

Possible Answers:

$-\frac{5}{6}$

$-\frac{1}{2}$

$\frac{7}{11}$

$-\frac{1}{6}$

Correct answer:

$-\frac{1}{2}$

Explanation:

The formula for multiplication of fractions is:

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

Where $b\neq 0$ and $d\neq 0.$ 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.

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

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Example Question #51 : Hspt Mathematics

Evaluate $a\times b\times c$ , if $a=\frac{4}{5}$ , $b=-\frac{1}{3}$ , and $c = \frac{3}{4}$ .

Possible Answers:

$-\frac{2}{3}$

$-\frac{1}{5}$

$\frac{2}{3}$

$\frac{1}{5}$

Correct answer:

$-\frac{1}{5}$

Explanation:

Evaluate $a\times b\times c$ , if $a=\frac{4}{5}$ , $b=-\frac{1}{3}$ , and $c = \frac{3}{4}$

$\frac{4}{5} \times -\frac{1}{3}\times\frac{3}{4} = \frac{-12}{60}$ (A positive times a negative is negative, and a negative times a positive is negative.)

Simplify by dividing the numerator and the denominator by the GCF or the Greatest Common Factor, which is 12.

$-12\div12 = -1$

$60 \div 12 = 5$

$\frac{-12}{60} = -\frac{1}{5}$

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Example Question #21 : How To Multiply And Divide Fractions

What is the product of $-2\times 3\frac{1}{4} \times - \frac{5}{6}$ ?

Possible Answers:

$-6\frac{1}{2}$

$-6\frac{1}{4}$

$5\frac{5}{12}$

$6\frac{1}{2}$

Correct answer:

$5\frac{5}{12}$

Explanation:

$-2\times 3\frac{1}{4} \times - \frac{5}{6} =$

To begin solving, convert any mixed numbers to improper fractions, and if there is a whole number, place a one underneath that number to make it an improper fraction.

$3\frac{1}{4} = \frac{(4\times 3)+1}{4} = \frac{13}{4}$

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

$-\frac{2}{1\ }\times \frac{13}{4} \times -\frac{5}{6} =$

Then multiply the numerators and then multiply the denominators. Remember, a negative times a positive is a negative.

$-\frac{2}{1} \times \frac{13}{4} = -\frac{26}{4}$

And a negative times a negative is positive.

$-\frac{26}{4\ }\times -\frac{5}{6} = \frac{130}{24}$

$\frac{130}{24} = 5 \frac{5}{12}$

Reduce the fraction part of the mixed number to simplest form by dividing both the numerator and the denominator by the GCF or the Greatest Common Factor which is 5.

$\frac{130}{24}=\frac{24\times 5}{24}+\frac{10}{24}$

$5\frac{10}{24}=5\frac{2\times 5}{2\times 12}=5\frac{5}{12}$

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Example Question #31 : Fractions

A wheel has a radius of inches. What is the circumference of the wheel?

Let,

$\pi =\frac{22}{7}$ .

Possible Answers:

88 inches

60 inches

28 inches

44inches

Correct answer:

88 inches

Explanation:

The formula for the circumference of a circle is:

$C = \pi d$

The diameter is found by multiplying the radius by 2.

$C = \frac{22}{7} \times (\frac{2}{1}\times \frac{14}{1})$

$C = \frac{(14\times 2\times 22)}{7}$

$C = \frac{616}{7}$

C = 88 inches

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Example Question #51 : Arithmetic

$\frac{4 (x-3)}{x+5} \div \frac{x-3}{12}$

Possible Answers:

$\frac{48}{x-5}$

$\frac{x-5}{48}$

$\frac{x-3}{48}$

$\frac{48}{x-3}$

Correct answer:

$\frac{48}{x-5}$

Explanation:

$\frac{4 (x-3)}{x+5} \div \frac{x-3}{12}$

To divide algebraic fractions, change the fraction that comes after the division sign to its multiplicative inverse or reciprocal. Then change the division sign to a multiplication sign and multiply.

The multiplicative inverse for

$\frac{x-3}{12} = \frac{12}{x-3}$

$\frac{4(x-3)}{x+5} \times\frac{12}{x-3}$

Because there is x -3 in the numerator of the first fraction and x-3 in the denominator of the second fraction, they will cancel out. What is left is:

$\frac{4\times 12}{x+5} = \frac{48}{x+5}$

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Example Question #31 : Fractions

$\frac{4}{x^{2}}\div\frac{12}{x^{3}}$

Possible Answers:

$\frac{48}{x^{5}}$

$\frac{x^{5}}{48}$

$\frac{x}{3}$

$\frac{3}{x}$

Correct answer:

$\frac{x}{3}$

Explanation:

To divide algebraic fractions, change the fraction that comes after the division sign to its multiplicative inverse or reciprocal. Then change the division sign to a multiplication sign and multiply.

The multiplicative inverse for

$\frac{12}{x^{3}} = \frac{x^{3}}{12}$

$\frac{4}{x^{2}}\times\frac{x^{3}}{12} = \frac{4x^{3}}{12x^{2}}$

Reduce this to simplest form by dividing both the numerator and the denominator by the Greatest Common Factor of $4x^{3}$ and $12x^{2}$ , which is $4x^{2}$ .

$\frac{4x^{3}\div 4x^{2}}{12x^{2}\div 4x^{2}} = \frac{x}{3}$

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Example Question #31 : Fractions

$\frac{4x-8}{6}\div \frac{x-2}{3}$

Possible Answers:

Correct answer:

Explanation:

$\frac{4x-8}{6}\div \frac{x-2}{3}$

To divide algebraic fractions, change the fraction that comes after the division sign to its multiplicative inverse or reciprocal. Then change the division sign to a multiplication sign and multiply.

The multiplicative inverse for $\frac{x-2}{3} = \frac{3}{x-2}$ .

Factor the 4 x-8 .

4x-8 = 4(x-2)

$\frac{4(x-2)}{6} \times\frac{3}{x-2}$

Because x-2 is in the numerator of the first fraction and the denominator of the second fraction, it cancels out. What is left is:

$\frac{4}{6} \times \frac{3}{1} = \frac{12}{6}$

$\frac{12}{6} = 2$

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HSPT Math : Problem Solving

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #51 : Hspt Mathematics

Example Question #51 : Problem Solving

Example Question #52 : Problem Solving

Example Question #12 : How To Multiply And Divide Fractions

Example Question #51 : Hspt Mathematics

Example Question #21 : How To Multiply And Divide Fractions

Example Question #31 : Fractions

Example Question #51 : Arithmetic

Example Question #31 : Fractions

Example Question #31 : Fractions

All HSPT Math Resources

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