Fractions - HSPT Math

Card 1 of 1100

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

$3\frac{1}{2 }\times 2\frac{2}{3}$

Tap to reveal answer

Answer

The formula for multiplication of fractions is:

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

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

Convert each mixed number to an improper fraction; then multiply.

$3\frac{1}{2} = \frac{(2\times 3)+1}{2} = \frac{7}{2}$

$2\frac{2}{3} = \frac{(3\times 2) +2}{3} = \frac{8}{3}$

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

$\frac{7}{2} \times \frac{8}{3} = \frac{7\times 8}{2\times 3} = \frac{56}{6}$

Convert the improper fraction back to a mixed number by dividing the numerator by the denominator.

$56\div6 = 9\frac{2}{6}$

Simplify by dividing the numerator and denominator of the fraction part of the mixed number by the GCF or Greatest Common Factor which is 2.

$\frac{2\div 2}{6\div2 } = \frac{1}{3}$

$9 \frac{2}{6}$ reduced to simplest form is $9\frac{1}{3}.$

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

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

← Didn't Know|Knew It →

Question

$6 \frac{8}{9}\times\frac{3}{8}$

Tap to reveal answer

Answer

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.

Convert any mixed number (whole number and fraction) to an improper fraction:

$6\frac{8}{9} = \frac{(9\times6)+8}{9} = \frac{62}{9}$

$\frac{62}{9 }\times \frac{3}{8} = \frac{62\times 3}{9\times 8}$

$\frac{186}{72} = 2\frac{42}{72}$

To simplify, divide the numerator and the denominator by the GCF, or the greatest common factor, which is 6.

$2\frac{42}{72} = 2\frac{42\div 6}{72\div 6} =$

$2\frac{7}{12}$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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.

$-12\div12 = -1$

$60 \div 12 = 5$

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

← Didn't Know|Knew It →

Question

What is the area of a rectangle with $l =3\frac{5}{9}$ cm and a $w = 2 \frac{1}{4}$ cm?

Tap to reveal answer

Answer

The formula for Area of a rectangle is $A = l\times w$ , where and

To solve $3\frac{5}{9} \times 2\frac{1}{4}$ , first convert both mixed numbers to improper fractions.

$3\frac{5}{9} = \frac{(9 \times 3)+5}{9} = \frac{32}{9}$

$2\frac{1}{4} = \frac{(4\times 2) +1}{2} = \frac{9}{2}$

Then multiply the numerators and the denominators. Simplify.

$\frac{32}{9} \times \frac{9}{4} =\frac{32\times 9}{9\times 4}$

Because there is a 9 in the numerator and a 9 in the denominator the nines cancel each other out, and you are left with:

$\frac{32}{4} = 8$

Area is 2-dimensional: it has a length and a width. Area is measured in square units.

The area of the rectangle is $8cm^{2}$ .

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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.

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

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

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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.

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

← Didn't Know|Knew It →

Question

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

Let,

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

Tap to reveal answer

Answer

The formula for the circumference of a circle is:

$C = \pi d$

The diameter is found by multiplying the radius by 2.

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

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

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

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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

, and

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

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.

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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 in the numerator of the first fraction and in the denominator of the second fraction, they will cancel out. What is left is:

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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 $4x^{2}$ .

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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 .

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

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

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

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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 and , which is .

$18xz \div2x = 9z$

$16xy\div 2 = 8y$

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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)

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

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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,

and

.

So the answer is

$\frac{16}{81}$ .

← Didn't Know|Knew It →

Question

Simplify the expression.

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

Tap to reveal answer

Answer

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

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

$\left ( {\frac{1* 2}{2* 2} + \frac{1}{4}}\right ) \left ({\frac{1 2}{22} - \frac{1}{4}}\right )$

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

Add the fractions in parentheses.

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

Multiply the fractions and simplify.

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

← Didn't Know|Knew It →

Question

Which of these expressions is the greatest?

Tap to reveal answer

Answer

The easiest way to see that all four are equivalent is to convert each to a decimal product, noting that twenty percent and one-fifth are equal to , and twenty-five percent and one fourth are equal to .

One fourth of 0.2: $\frac{1}{4}0.2=\frac{1}{4}\frac{2}{10}=\frac{2}{40}=\frac{1}{20}$

One fifth of 0.25: $\frac{1}{5}0.25=\frac{1}{5}\frac{25}{100}=\frac{25}{500}=\frac{5}{100}=\frac{1}{20}$

Twenty-five percent of one fifth: $\frac{1}{5}=\frac{25}{100}\frac{1}{5}=\frac{25}{500}=\frac{1}{20}$

Twenty percent of one fourth: $\frac{1}{4}=\frac{20}{100}\frac{1}{4}=\frac{20}{400}=\frac{1}{20}$

← Didn't Know|Knew It →

Question

Express the product in simplest form:

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

Tap to reveal answer

Answer

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

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

← Didn't Know|Knew It →

Question

What is $\frac{3}{5}$ divided by $\frac{3}{25}$ ?

Tap to reveal answer

Answer

$\frac{3}{5}\div\frac{3}{25}=\frac{3}{5}\cdo*\frac{25}{3}=5$

← Didn't Know|Knew It →

Question

Express the product in simplest form:

$\frac{5}{7} \cdot 1 \frac{1}{7} \cdot 2 \frac{4}{5}$

Tap to reveal answer

Answer

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

$\frac{5}{7} \cdot 1 \frac{1}{7} \cdot 2 \frac{4}{5} = \frac{5}{7} \cdot \frac{8}{7} \cdot \frac{14}{5}= \frac{1}{1} \cdot \frac{8}{7} \cdot \frac{2}{1}= \frac{16}{7}= 2\frac{2}{7}$

← Didn't Know|Knew It →

0

Knew It