Multiply and Divide Mixed Fractions 1

Question 1 of 4

Multiply the following:

2 \frac{1}{4} \times 3 \frac{1}{3}

$2 1/4xx3 1/3$

1. $7 \frac{1}{2}$ $7 1/2$
2. $5 \frac{5}{12}$ $5 5/12$
3. $8 \frac{5}{6}$ $8 5/6$
4. $6 \frac{1}{2}$ $6 1/2$

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Transforming a Fraction from Mixed to Improper

=

$=$

\frac{(c \times A) + b}{c}

$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$

First, convert the mixed numbers into improper form

Multiply the denominator by the whole number and then add it to the numerator

		$\color{#00880A}{2}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{4}}\times\color{#00880A}{3}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}$

	$=$ $=$	$\frac{(\color{#9a00c7}{4}\times\color{#00880A}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{4}} \times \frac{(\color{#9a00c7}{3}\times\color{#00880A}{3})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}$

	$=$ $=$	$\frac{8 + 1}{4} \times \frac{9 + 1}{3}$ $(8+1)/4 xx (9+1)/3$

	$=$ $=$	$\frac{9}{4} \times \frac{10}{3}$ $9/4 xx 10/3$

Proceed with multiplying the fractions and then simplify.

	$\frac{9}{4} \times \frac{10}{3}$ $9/4 xx 10/3$

$=$ $=$	$\frac{90}{12}$ $90/12$

$=$ $=$	$\frac{90\color{#CC0000}{\div6}}{12\color{#CC0000}{\div6}}$	Reduce to lowest terms

$=$ $=$	$\frac{15}{2}$ $15/2$

$=$ $=$	$\frac{14 + 1}{2}$ $(14+1)/2$	Transform the fraction back to a mixed number
$=$ $=$	$7 \frac{1}{2}$ $7 1/2$

7 \frac{1}{2}

$7 1/2$

Question 2 of 4

Multiply the following:

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

$4 1/2xx2 2/3$

(12)

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Mute

Transforming a Fraction from Mixed to Improper

=

$=$

\frac{(c \times A) + b}{c}

$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$

First, convert the mixed numbers into improper form

Multiply the denominator by the whole number and then add it to the numerator

		$\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}\times\color{#00880A}{2}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$

	$=$ $=$	$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{4})+\color{#007DDC}{1}}{\color{#9a00c7}{2}} \times \frac{(\color{#9a00c7}{3}\times\color{#00880A}{2})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$

	$=$ $=$	$\frac{8 + 1}{2} \times \frac{6 + 2}{3}$ $(8+1)/2 xx (6+2)/3$

	$=$ $=$	$\frac{9}{2} \times \frac{8}{3}$ $9/2 xx 8/3$

Proceed with multiplying the fractions and then simplify.

	$\frac{9}{2} \times \frac{8}{3}$ $9/2 xx 8/3$

$=$ $=$	$\frac{72}{6}$ $72/6$

$=$ $=$	$72 \div 6$ $72-:6$	Reduce to lowest terms

$=$ $=$	$12$ $12$

12

$12$

Question 3 of 4

Multiply the following:

3 \frac{3}{4} \times 1 \frac{4}{5}

$3 3/4xx1 4/5$

1. $6 \frac{3}{4}$ $6 3/4$
2. $5 \frac{3}{5}$ $5 3/5$
3. $3 \frac{2}{3}$ $3 2/3$
4. $4 \frac{1}{2}$ $4 1/2$

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Transforming a Fraction from Mixed to Improper

=

$=$

\frac{(c \times A) + b}{c}

$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$

Transforming an Improper to Mixed Fraction

\frac{b}{c} = Q \frac{R}{c}

$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}=\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$

(

$($ $b$ $b$

\div

$-:$ $c$ $c$

) =

$)=$ $Q$ $Q$ and $R$ $R$ is the remainder

First, convert the mixed number into improper form

Multiply the denominator by the whole number and then add it to the numerator

		$\color{#00880A}{3}\frac{\color{#007DDC}{3}}{\color{#9a00c7}{4}}\times\color{#00880A}{1}\frac{\color{#007DDC}{4}}{\color{#9a00c7}{5}}$

	$=$ $=$	$\frac{(\color{#9a00c7}{4}\times\color{#00880A}{3})+\color{#007DDC}{3}}{\color{#9a00c7}{4}}\times\frac{(\color{#9a00c7}{5}\times\color{#00880A}{1})+\color{#007DDC}{4}}{\color{#9a00c7}{5}}$

	$=$ $=$	$\frac{12 + 3}{4} \times \frac{5 + 4}{5}$ $(12+3)/4xx(5+4)/5$

	$=$ $=$	$\frac{15}{4} \times \frac{9}{5}$ $15/4 xx 9/5$

Proceed with multiplying the fractions and then simplify.

	$\frac{15}{4} \times \frac{9}{5}$ $15/4 xx 9/5$

$=$ $=$	$\frac{15\div\color{#CC0000}{5}}{4} \times \frac{9}{5\div\color{#CC0000}{5}}$	$15$ $15$ and $5$ $5$ are multiples of $5$ $5$

$=$ $=$	$\frac{3}{4} \times \frac{9}{1}$ $3/4xx9/1$

$=$ $=$	$\frac{27}{4}$ $27/4$

Convert the fraction from improper to mixed

Start by dividing the numerator by the denominator

Arrange the numbers for long division

4

$4$ goes into

27

$27$ six times. So write

6

$6$ above the line.

Multiply

6

$6$ to

4

$4$ and write the answer below

27

$27$

Subtract

24

$24$ from

27

$27$ and write the answer one line below

Since

4

$4$ cannot go into

3

$3$ anymore, $3$ $3$ is left as the Remainder and $6$ $6$ is the Quotient

Substitute values into the given formula

$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$	$=$ $=$	$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$

$\frac{\color{#007DDC}{27}}{\color{#9a00c7}{4}}$	$=$ $=$	$\color{#00880A}{6}\frac{\color{#e65021}{3}}{\color{#9a00c7}{4}}$

6 \frac{3}{4}

$6 3/4$

Question 4 of 4

Multiply the following:

5 \frac{1}{3} \times 4 \frac{1}{2}

$5 1/3xx4 1/2$

(24)

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Transforming a Fraction from Mixed to Improper

=

$=$

\frac{(c \times A) + b}{c}

$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$

First, convert the mixed number into improper form

Multiply the denominator by the whole number and then add it to the numerator

		$\color{#00880A}{5}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}\times\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}$

	$=$ $=$	$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{5})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}\times\frac{(\color{#9a00c7}{2}\times\color{#00880A}{4})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}$

	$=$ $=$	$\frac{15 + 1}{3} \times \frac{8 + 1}{2}$ $(15+1)/3xx(8+1)/2$

	$=$ $=$	$\frac{16}{3} \times \frac{9}{2}$ $16/3 xx 9/2$

Proceed with multiplying the fractions and then simplify.

	$\frac{16}{3} \times \frac{9}{2}$ $16/3 xx 9/2$

$=$ $=$	$\frac{16\div\color{#CC0000}{2}}{3} \times \frac{9}{2\div\color{#CC0000}{2}}$	Reduce the fractions

$=$ $=$	$\frac{8}{3} \times \frac{9}{1}$ $8/3xx9/1$

$=$ $=$	$\frac{8}{3\div\color{#CC0000}{3}} \times \frac{9\div\color{#CC0000}{3}}{1}$	Reduce the fractions further

$=$ $=$	$\frac{8}{1} \times \frac{3}{1}$ $8/1xx3/1$

$=$ $=$	$\frac{24}{1}$ $24/1$

$=$ $=$	$24$ $24$

24

$24$

Multiply and Divide Mixed Fractions 1

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Quiz summary

Information

1. Question

Hint

Keep Going!

Transforming a Fraction from Mixed to Improper

2. Question

Hint

Great Work!

Transforming a Fraction from Mixed to Improper

3. Question

Hint

Nice Job!

Transforming a Fraction from Mixed to Improper

Transforming an Improper to Mixed Fraction

4. Question

Hint

Well Done!

Transforming a Fraction from Mixed to Improper

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