Multiply and Divide Mixed Numbers 2

Years

Year 7

Fractions

Multiply and Divide Mixed Numbers

Multiply and Divide Mixed Numbers 2

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Question 1 of 5

1. Question

Multiply the following:

`2 5/6xx1 1/3`

`3 7/9`
`7 1/3`
`9 3/7`
`3 1/9`

Hint

Help Video

Correct

Correct!

Incorrect

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`

`33 1/4`
`133 1/4`
`33 3/4`
`33 1/3`

Hint

Help Video

Correct

Well Done!

Incorrect

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)

Hint

Help Video

Correct

Excellent!

Incorrect

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`

`7 1/3`
`3 1/7`
`1 3/7`
`7 2/3`

Hint

Help Video

Correct

Great Work!

Incorrect

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`

Hint

Help Video

Correct

Correct!

Incorrect

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`

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