Multiply and Divide Mixed Fractions 2

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Question 1 of 5

1. Question

Multiply the following:

$2 5/6xx1 1/3$

1. $9 3/7$
2. $3 1/9$
3. $7 1/3$
4. $3 7/9$

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Transforming a Fraction from Mixed to Improper

$=$

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

Transforming an Improper to Mixed Fraction

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

$($ $b$

$-:$ $c$

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

First, convert the mixed numbers into improper form

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

		$\color{#00880A}{2}\frac{\color{#007DDC}{5}}{\color{#9a00c7}{6}}\times\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}$

	$=$	$\frac{(\color{#9a00c7}{6}\times\color{#00880A}{2})+\color{#007DDC}{5}}{\color{#9a00c7}{6}} \times \frac{(\color{#9a00c7}{3}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}$

	$=$	$(12+5)/6 xx (3+1)/3$

	$=$	$17/6 xx 4/3$

Proceed with multiplying the fractions and then simplify.

	$17/6 xx 4/3$

$=$	$68/18$

$=$	$\frac{68\color{#CC0000}{\div2}}{18\color{#CC0000}{\div2}}$	Reduce to lowest terms

$=$	$34/9$

Convert the fraction from improper to mixed

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$9$ goes into

$34$ three times. So write

$3$ above the line.

Multiply

$3$ to

$9$ and write the answer below

$34$

Subtract

$27$ from

$34$ and write the answer one line below

Since

$9$ cannot go into

$7$ anymore, $7$ is left as the Remainder and $3$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{34}}{\color{#9a00c7}{9}}$	$=$	$\color{#00880A}{3}\frac{\color{#e65021}{7}}{\color{#9a00c7}{9}}$

$3 7/9$

Question 2 of 5

2. Question

Multiply the following:

$7xx4 3/4$

1. $33 3/4$
2. $33 1/3$
3. $33 1/4$
4. $133 1/4$

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Transforming a Fraction from Mixed to Improper

$=$

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

Transforming an Improper to Mixed Fraction

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

$($ $b$

$-:$ $c$

$)=$ $Q$ and $R$ 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

		$7\times\color{#00880A}{4}\frac{\color{#007DDC}{3}}{\color{#9a00c7}{4}}$

	$=$	$7\times\frac{(\color{#9a00c7}{4}\times\color{#00880A}{4})+\color{#007DDC}{3}}{\color{#9a00c7}{4}}$

	$=$	$7xx(16+3)/4$

	$=$	$7xx 19/4$

Proceed with multiplying the fractions and then simplify.

	$7xx 19/4$

	$7/1xx 19/4$	A whole number can be a fraction with $1$ as the denominator

$=$	$133/4$

Convert the fraction from improper to mixed

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$4$ goes into

$13$ three times. So write

$3$ above the line.

Multiply

$3$ to

$4$ and write the answer below

$13$

Subtract

$12$ from

$13$ and write the answer one line below

Drop down

$3$

$4$ goes into

$13$ three times. So again write

$3$ above the line.

Multiply

$3$ to

$4$ and write the answer below

$13$

Subtract

$12$ from

$13$ and write the answer one line below

Since

$4$ cannot go into

$1$ anymore, $1$ is left as the Remainder and $33$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{133}}{\color{#9a00c7}{4}}$	$=$	$\color{#00880A}{33}\frac{\color{#e65021}{1}}{\color{#9a00c7}{4}}$

$33 1/4$

Question 3 of 5

3. Question

Multiply the following:

$7 1/5xx2 1/2$

(18)

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Transforming a Fraction from Mixed to Improper

$=$

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

First, convert the mixed number into improper form

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

		$\color{#00880A}{7}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{5}}\times\color{#00880A}{2}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}$

	$=$	$\frac{(\color{#9a00c7}{5}\times\color{#00880A}{7})+\color{#007DDC}{1}}{\color{#9a00c7}{5}}\times\frac{(\color{#9a00c7}{2}\times\color{#00880A}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}$

	$=$	$(35+1)/5xx(4+1)/2$

	$=$	$36/5 xx 5/2$

Proceed with multiplying the fractions and then simplify.

	$36/5 xx 5/2$

$=$	$\frac{36}{5\div\color{#CC0000}{5}} \times \frac{5\div\color{#CC0000}{5}}{2}$	Reduce the fractions

$=$	$36/1xx1/2$

$=$	$\frac{36\div\color{#CC0000}{2}}{1} \times \frac{1}{2\div\color{#CC0000}{2}}$	Reduce the fractions further

$=$	$18/1xx1/1$

$=$	$18/1$

$=$	$18$

$18$

Question 4 of 5

4. Question

Multiply the following:

$2xx1 2/3xx2 1/5$

1. $7 1/3$
2. $3 1/7$
3. $1 3/7$
4. $7 2/3$

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Transforming a Fraction from Mixed to Improper

$=$

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

Transforming an Improper to Mixed Fraction

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

$($ $b$

$-:$ $c$

$)=$ $Q$ and $R$ 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

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

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

	$=$	$2/1xx(3+2)/3xx(10+1)/5$

	$=$	$2/1xx5/3 xx 11/5$

Proceed with multiplying the fractions and then simplify.

	$2/1xx5/3 xx 11/5$

$=$	$(2xx5xx11)/(1xx3xx5)$

$=$	$110/15$

$=$	$\frac{110\div\color{#CC0000}{5}}{15\div\color{#CC0000}{5}}$	Simplify the fraction

$=$	$22/3$

Convert the fraction from improper to mixed

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$3$ goes into

$22$ seven times. So write

$7$ above the line.

Multiply

$7$ to

$3$ and write the answer below

$22$

Subtract

$21$ from

$22$ and write the answer one line below

Since

$3$ cannot go into

$1$ anymore, $1$ is left as the Remainder and $7$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{22}}{\color{#9a00c7}{3}}$	$=$	$\color{#00880A}{7}\frac{\color{#e65021}{1}}{\color{#9a00c7}{3}}$

$7 1/3$

Question 5 of 5

5. Question

Divide the following:

$2 2/3-:1/3$

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Transforming a Fraction from Mixed to Improper

$=$

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

To divide fractions, flip the divisor and then multiply as normal

First, convert the mixed numbers into improper form

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

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

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

	$=$	$(6+2)/3 -: 1/3$

	$=$	$8/3 -: 1/3$

First, get the reciprocal (flip) of the divisor

$1/3$ becomes

$3/1$

Proceed with multiplying this to the dividend.

		$8/3-:$ $1/3$

	$=$	$8/3xx$ $3/1$

	$=$	$24/3$

	$=$	$24-:3$
	$=$	$8$

$8$

Quizzes

Shaded Fractions 1
Shaded Fractions 2
Equivalent Fractions 1
Equivalent Fractions 2
Equivalent Fractions 3
Equivalent Fractions 4
Simplify Fractions 1
Simplify Fractions 2
Simplify Fractions 3
Find the LCM
Comparing Fractions 1
Comparing Fractions 2
Comparing Fractions 3
Mixed and Improper Fractions 1
Mixed and Improper Fractions 2
Mixed and Improper Fractions 3
Add and Subtract Fractions 1
Add and Subtract Fractions 2
Add and Subtract Fractions 3
Add and Subtract Fractions 4
Multiply and Divide Fractions 1
Multiply and Divide Fractions 2
Multiply and Divide Fractions 3
Add and Subtract Mixed Numbers 1
Add and Subtract Mixed Numbers 2
Add and Subtract Mixed Numbers 3
Multiply and Divide Mixed Fractions 1
Multiply and Divide Mixed Fractions 2
Multiply and Divide Mixed Fractions 3
Multiply and Divide Mixed Fractions 4
Fraction Word Problems: Addition and Subtraction 1
Fraction Word Problems: Addition and Subtraction 2
Fraction Word Problems: Addition and Subtraction 3
Fraction Word Problems: Addition and Subtraction 4
Fraction Word Problems: Multiplication and Division
Find the Fraction of a Quantity
Find the Quantity of a Quantity 1
Find the Quantity of a Quantity 2
Find the Fraction of a Quantity: Word Problems 1
Find the Fraction of a Quantity: Word Problems 2
Find the Fraction of a Quantity: Word Problems 3
Find the Fraction of a Quantity: Word Problems 4
Find the Quantity of a Quantity: Word Problems
Order of Operations Involving Fractions 1
Order of Operations Involving Fractions 2