Multiply and Divide Mixed Fractions 3

Question 1 of 4

Divide the following:

$3 3/5-:9/10$

(4)

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Transforming a Fraction from Mixed to Improper

$=$

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

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

		$\color{#00880A}{3}\frac{\color{#007DDC}{3}}{\color{#9a00c7}{5}}\div\frac{9}{10}$

	$=$	$\frac{(\color{#9a00c7}{5}\times\color{#00880A}{3})+\color{#007DDC}{3}}{\color{#9a00c7}{5}} \div \frac{9}{10}$

	$=$	$(15+3)/5 -: 9/10$

	$=$	$18/5 -: 9/10$

Now, get the reciprocal (flip) of the divisor

$9/10$ becomes

$10/9$

Proceed with multiplying this to the dividend.

	$18/5-:$ $9/10$

$=$	$18/5xx$ $10/9$

$=$	$\frac{18\div\color{#CC0000}{9}}{5}\times\frac{10}{9\div\color{#CC0000}{9}}$	Reduce the fractions

$=$	$2/5xx10/1$

$=$	$\frac{2}{5\div\color{#CC0000}{5}}\times\frac{10\div\color{#CC0000}{5}}{1}$	Reduce the fractions further

$=$	$2/1xx2/1$

$=$	$4/1$

$=$	$4$

$4$

Question 2 of 4

Divide the following:

$4 2/3-:7/8$

1. $5 1/5$
2. $1 3/5$
3. $3 1/5$
4. $5 1/3$

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Transforming a Fraction from Mixed to Improper

$=$

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

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

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

		$\color{#00880A}{4}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}\div\frac{7}{8}$

	$=$	$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{4})+\color{#007DDC}{2}}{\color{#9a00c7}{3}} \div \frac{7}{8}$

	$=$	$(12+2)/3 -: 7/8$

	$=$	$14/3 -: 7/8$

Now, get the reciprocal (flip) of the divisor

$7/8$ becomes

$8/7$

Proceed with multiplying this to the dividend.

	$14/3-:$ $7/8$

$=$	$14/3xx$ $8/7$

$=$	$\frac{14\div\color{#CC0000}{7}}{3}\times\frac{8}{7\div\color{#CC0000}{7}}$	Reduce the fractions

$=$	$2/3xx8/1$

$=$	$16/3$

Convert the fraction from improper to mixed

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$3$ goes into

$16$ five times. So write

$5$ above the line.

Multiply

$5$ to

$3$ and write the answer below

$15$

Subtract

$15$ from

$16$ and write the answer one line below

Since

$3$ cannot go into

$1$ anymore, $1$ is left as the Remainder and $5$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{16}}{\color{#9a00c7}{3}}$	$=$	$\color{#00880A}{5}\frac{\color{#e65021}{1}}{\color{#9a00c7}{3}}$

$5 1/3$

Question 3 of 4

Divide the following:

$2 3/10-:2 4/5$

Write fractions in the format “a/b”

(23/28)

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Mute

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

		$\color{#00880A}{2}\frac{\color{#007DDC}{3}}{\color{#9a00c7}{10}}\div\color{#00880A}{2}\frac{\color{#007DDC}{4}}{\color{#9a00c7}{5}}$

	$=$	$\frac{(\color{#9a00c7}{10}\times\color{#00880A}{2})+\color{#007DDC}{3}}{\color{#9a00c7}{10}} \div \frac{(\color{#9a00c7}{5}\times\color{#00880A}{2})+\color{#007DDC}{4}}{\color{#9a00c7}{5}}$

	$=$	$(20+3)/10 -: (10+4)/5$

	$=$	$23/10 -: 14/5$

Now, get the reciprocal (flip) of the divisor

$14/5$ becomes

$5/14$

Proceed with multiplying this to the dividend.

	$23/10-:$ $14/5$

$=$	$23/10xx$ $5/14$

$=$	$\frac{23}{10\div\color{#CC0000}{5}}\times\frac{5\div\color{#CC0000}{5}}{14}$	Reduce the fractions

$=$	$23/2xx1/14$

$=$	$23/28$

$23/28$

Question 4 of 4

Divide the following:

$10 1/2-:4$

1. $2 5/8$
2. $5 1/4$
3. $8 2/5$
4. $2 2/3$

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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

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

		$\color{#00880A}{10}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}\div4$

	$=$	$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{10})+\color{#007DDC}{1}}{\color{#9a00c7}{2}} \div \frac{4}{1}$

	$=$	$(20+1)/2 -: 4/1$

	$=$	$21/2 -: 4/1$

Now, get the reciprocal (flip) of the divisor

$4/1$ becomes

$1/4$

Proceed with multiplying this to the dividend.

		$21/2 -:$ $4/1$

	$=$	$21/2xx$ $1/4$

	$=$	$21/8$

Convert the fraction from improper to mixed

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$8$ goes into

$21$ two times. So write

$2$ above the line.

Multiply

$2$ to

$8$ and write the answer below

$21$

Subtract

$16$ from

$21$ and write the answer one line below

Since

$8$ cannot go into

$5$ anymore, $5$ is left as the Remainder and $2$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{21}}{\color{#9a00c7}{8}}$	$=$	$\color{#00880A}{2}\frac{\color{#e65021}{5}}{\color{#9a00c7}{8}}$

$2 5/8$

Multiply and Divide Mixed Fractions 3

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Quiz summary

Information

1. Question

Hint

Keep Going!

Transforming a Fraction from Mixed to Improper

2. Question

Hint

Fantastic!

Transforming a Fraction from Mixed to Improper

Transforming an Improper to Mixed Fraction

3. Question

Hint

Excellent!

Transforming a Fraction from Mixed to Improper

4. Question

Hint

Well Done!

Transforming a Fraction from Mixed to Improper

Transforming an Improper to Mixed Fraction

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