Add and Subtract Mixed Numbers 3

Years

Year 10

Fractions

Add and Subtract Mixed Numbers

Add and Subtract Mixed Numbers 3

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Question 1 of 4

1. Question

Add the following:

9 \frac{7}{8} + 3 \frac{5}{24}

$9 7/8+3 5/24$

1. $12 \frac{1}{13}$ $12 1/13$
2. $13 \frac{7}{24}$ $13 7/24$
3. $13 \frac{1}{12}$ $13 1/12$
4. $12 \frac{1}{24}$ $12 1/24$

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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

A mixed number consists of a whole number and a fraction.

First, add the whole numbers

9 + 3

$9+3$

=

$=$

12

$12$

Notice that the fractions have different denominators.

Find the

L C D

$LCD$ of

8

$8$ and

24

$24$ so we can add the fractions.

Multiples of

8

$8$ :

8162432

$8\;\;16\;\;\color{#004ec4}{24}\;\;32$

Multiples of

24

$24$ :

244872

$\color{#004ec4}{24}\;\;48\;\;72$

The

L C D

$LCD$ of

8

$8$ and

24

$24$ is

24

$24$

Proceed with adding the fractions

	$\frac{7}{8} + \frac{5}{24}$ $7/8+5/24$

$=$ $=$	$\frac{7\times\color{#CC0000}{3}}{8\times\color{#CC0000}{3}}+\frac{5}{24}$	Multiply by $3$ $3$ so that the denominator becomes $24$ $24$

$=$ $=$	$\frac{21}{\color{#004ec4}{24}}+\frac{5}{\color{#004ec4}{24}}$

$=$ $=$	$\frac{26}{24}$

Change the improper fraction to a mixed fraction

Divide the numerator by the denominator

Arrange the numbers for long division

24

$24$ goes into

26

$26$ one time. So write

1

$1$ above the line.

Multiply

1

$1$ to

24

$24$ and write the answer below

26

$26$

Subtract

24

$24$ from

26

$26$ and write the answer one line below

[add colors: $1$ $1$ , $2$ $2$ ]

Since

24

$24$ cannot go into

2

$2$ anymore, $2$ $2$ is left as the Remainder and $1$ $1$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{26}}{\color{#9a00c7}{24}}$	$=$ $=$	$\color{#00880A}{1}\frac{\color{#e65021}{2}}{\color{#9a00c7}{24}}$

	$=$ $=$	$1\frac{2\div\color{#CC0000}{2}}{24\div\color{#CC0000}{2}}$	Express in lowest terms

	$=$ $=$	$1 \frac{1}{12}$ $1 1/12$

Finally, combine the sum of the whole numbers and the sum of the fractions

$9 \frac{7}{8} + 3 \frac{5}{24}$ $9 7/8+3 5/24$	$=$ $=$	$12 + 1 \frac{1}{12}$ $12+1 1/12$

	$=$ $=$	$13 \frac{1}{12}$ $13 1/12$

13 \frac{1}{12}

$13 1/12$

Question 2 of 4

2. Question

Subtract the following:

7 - 3 \frac{3}{8}

$7-3 3/8$

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

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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

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, transform the mixed fractions to improper fractions

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

	$=$ $=$	$\frac{7}{1}-\frac{(\color{#9a00c7}{8}\times\color{#00880A}{3})+\color{#007DDC}{3}}{\color{#9a00c7}{8}}$

	$=$ $=$	$\frac{7}{1}-\frac{24+3}{8}$

	$=$ $=$	$\frac{7}{1}-\frac{27}{8}$

Use cross method to subtract the fractions.

Start by multiplying the two denominators. Use the product as a denominator for a new fraction.

\frac{7}{1} - \frac{27}{8}

$7/1-27/8$

=

$=$

$☐/(1times8)$

$=$

$☐/8$

To get the numerator, cross multiply the given addition problem and subtract the products.

$\frac{\color{#00880A}{7}}{\color{#9a00c7}{1}}-\frac{\color{#9a00c7}{27}}{\color{#00880A}{8}}$	$=$	$\frac{(\color{#00880A}{7\times8})-(\color{#9a00c7}{1\times27})}{8}$

	$=$	$(56-27)/8$

	$=$	$29/8$

Transform the fraction back to a mixed fraction

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$8$ goes into

$29$ six times. So write

$6$ above the line.

Multiply

$3$ to

$8$ and write the answer below

$29$

Subtract

$24$ from

$29$ and write the answer one line below

Since

$8$ cannot go into

$5$ anymore, $5$ is left as the Remainder and $3$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{29}}{\color{#9a00c7}{8}}$	$=$	$\color{#00880A}{3}\frac{\color{#e65021}{5}}{\color{#9a00c7}{8}}$

$3 5/8$

Question 3 of 4

3. Question

Subtract the following:

$5 1/4-3 2/3$

1. $1 7/12$
2. $7 1/12$
3. $2 5/12$
4. $1 1/12$

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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

Transforming a Fraction from Mixed to Improper

$=$

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

First, transform the mixed fractions to improper fractions

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

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

	$=$	$\frac{20+1}{4}-\frac{9+2}{3}$

	$=$	$\frac{21}{4}-\frac{11}{3}$

Notice that the fractions have different denominators.

Find the

$LCD$ of

$4$ and

$3$ so we can subtract the fractions.

Multiples of

$4$ :

$4\;\;8\;\;\color{#004ec4}{12}\;\;16\;\;20$

Multiples of

$3$ :

$3\;\;6\;\;9\;\;\color{#004ec4}{12}\;\;15\;\;18$

The

$LCD$ of

$4$ and

$3$ is

$12$

Next, we get the same denominator and subtract the fractions

	$21/4-11/3$

$=$	$\frac{21\times\color{#CC0000}{3}}{4\times\color{#CC0000}{3}}-\frac{11\times\color{#CC0000}{4}}{3\times\color{#CC0000}{4}}$	Multiply each fraction so that the denominator becomes $12$

$=$	$\frac{63}{\color{#004ec4}{12}}-\frac{44}{\color{#004ec4}{12}}$

$=$	$\frac{19}{12}$

Transform the fraction back to a mixed fraction

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$12$ goes into

$19$ once. So write

$1$ above the line.

Multiply

$1$ to

$12$ and write the answer below

$19$

Subtract

$12$ from

$19$ and write the answer one line below

Since

$12$ cannot go into

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

Substitute values into the given formula

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

$\frac{\color{#007DDC}{19}}{\color{#9a00c7}{12}}$	$=$	$\color{#00880A}{1}\frac{\color{#e65021}{7}}{\color{#9a00c7}{12}}$

$1 7/12$

Question 4 of 4

4. Question

Subtract the following:

$9-2 7/10$

1. $6 1/10$
2. $10 1/2$
3. $3 3/5$
4. $6 3/10$

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Chapters

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

Transforming a Fraction from Mixed to Improper

$=$

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

First, transform the mixed fractions to improper fractions

		$9-\color{#00880A}{2} \frac{\color{#007DDC}{7}}{\color{#9a00c7}{10}}$

	$=$	$\frac{9}{1}-\frac{(\color{#9a00c7}{10}\times\color{#00880A}{2})+\color{#007DDC}{7}}{\color{#9a00c7}{10}}$

	$=$	$\frac{9}{1}-\frac{20+7}{10}$

	$=$	$\frac{9}{1}-\frac{27}{10}$

Use cross method to subtract the fractions.

Start by multiplying the two denominators. Use the product as a denominator for a new fraction.

$9/1-27/10$

$=$

$☐/(1times10)$

$=$

$☐/10$

To get the numerator, cross multiply the given addition problem and subtract the products.

$\frac{\color{#00880A}{9}}{\color{#9a00c7}{1}}-\frac{\color{#9a00c7}{27}}{\color{#00880A}{10}}$	$=$	$\frac{(\color{#00880A}{9\times10})-(\color{#9a00c7}{1\times27})}{10}$

	$=$	$(90-27)/10$

	$=$	$63/10$

Transform the fraction back to a mixed fraction

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$10$ goes into

$63$ six times. So write

$6$ above the line.

Multiply

$6$ to

$10$ and write the answer below

$63$

Subtract

$60$ from

$63$ and write the answer one line below

Since

$10$ cannot go into

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

Substitute values into the given formula

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

$\frac{\color{#007DDC}{63}}{\color{#9a00c7}{10}}$	$=$	$\color{#00880A}{6}\frac{\color{#e65021}{3}}{\color{#9a00c7}{10}}$

$6 3/10$

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 Lowest Common Denominator
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 Numbers 1
Multiply and Divide Mixed Numbers 2
Multiply and Divide Mixed Numbers 3
Multiply and Divide Mixed Numbers 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