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HSPT Math : How to multiply and divide fractions

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Example Questions

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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Example Question #26 : How To Multiply And Divide Fractions

$\frac{3x}{2y} \times \frac{6z}{8x}$

Possible Answers:

$\frac{9y}{8z}$

$\frac{8y}{9z}$

$\frac{9z}{8y}$

$\frac{8z}{9y}$

Correct answer:

$\frac{9z}{8y}$

Explanation:

Multiplying an algebraic fraction is the same as multiplying fractions. Just multiply the numerators and the denominators and simplify.

$\frac{3x}{2y} \times \frac{6z}{8x} = \frac{18xz}{16xy}$

To simply, divide the numerator and the denominator by the greatest common factor of 18xyz and 16xy , which is .

$18xz \div2x = 9z$

$16xy\div 2 = 8y$

$\frac{9z}{8y}$

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Example Question #21 : How To Multiply And Divide Fractions

$\frac{3x^{2}}{5y^{2}} \times \frac{5y^{5}}{15x^{3}}$

Possible Answers:

$\frac{5x}{y^{3}}$

$\frac{y^{2}}{5x}$

$\frac{y^{3}}{5x}$

$\frac{5x}{y^{2}}$

Correct answer:

$\frac{y^{3}}{5x}$

Explanation:

$\frac{3x^{2}}{5y^{2}} \times \frac{5y^{5}}{15x^{3}} = \frac{15x^{2}y^{5}}{75x^{3}y^{2}}$

To simplify divide the numerator and the denominator by the Greatest Common Factor, which is $15x^{2}y^{2}$ .

$15x^{2}y^{5} \div 15x^{2}y^{2} = y^{3}$ (when you are dividing, subtract the exponents)

$75x^{3}y^{2} \div 15x^{2}y^{2} = 5x$

$\frac{y^{3}}{5x}$

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Example Question #41 : Fractions

$\frac{8}{9} \div\frac{9}{2}=?$

Possible Answers:

$\frac{72}{11}$

$\frac{16}{81}$

$\frac{10}{81}$

Correct answer:

$\frac{16}{81}$

Explanation:

To divide fractions, you multiply by the reciprocal (flip the denominator and multiply instead. \

So the problem now looks like

$\frac{8}{9}*\frac{2}{9}$ .

Then you multiply across,

8*2=16

and

9*9=81 .

So the answer is

$\frac{16}{81}$ .

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HSPT Math : How to multiply and divide fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

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

Example Question #26 : How To Multiply And Divide Fractions

Example Question #21 : How To Multiply And Divide Fractions

Example Question #41 : Fractions

All HSPT Math Resources

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