Add and Subtract Mixed Numbers 2

Topics

Pre - Algebra

Fractions

Add and Subtract Mixed Numbers

Add and Subtract Mixed Numbers 2

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Question 1 of 3

1. Question

Add the following:

$8 1/2+10 3/4$

1. $18 3/4$
2. $19 3/4$
3. $18 1/4$
4. $19 1/4$

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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

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

Method One

First, add the whole numbers

$8+10$

$=$

$18$

Notice that the fractions have different denominators.

Find the

$LCD$ of

$2$ and

$4$ so we can add the fractions.

Multiples of

$2$ :

$2\;\;\color{#004ec4}{4}\;\;6\;\;8$

Multiples of

$4$ :

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

The

$LCD$ of

$2$ and

$4$ is

$4$

Use the $LCD$ as the denominator for both fractions then proceed with adding.

	$1/2+3/4$

$=$	$\frac{1\times\color{#CC0000}{2}}{2\times\color{#CC0000}{2}}+\frac{3}{4}$	Multiply by $2$ so that the denominator becomes $4$

$=$	$\frac{2}{\color{#004ec4}{4}}+\frac{3}{\color{#004ec4}{4}}$	Add the numerators

$=$	$\frac{5}{4}$	Keep the same denominator

Change the improper fraction to a mixed fraction

Divide the numerator by the denominator

Arrange the numbers for long division

$4$ goes into

$5$ one time. So write

$1$ above the line.

Multiply

$1$ to

$4$ and write the answer below

$5$

Subtract

$4$ from

$5$ and write the answer one line below

Since

$4$ cannot go into

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

Substitute values into the given formula

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

$\frac{\color{#007DDC}{5}}{\color{#9a00c7}{4}}$	$=$	$\color{#00880A}{1}\frac{\color{#e65021}{1}}{\color{#9a00c7}{4}}$

	$=$	$1 1/4$

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

$8 1/2+10 3/4$	$=$	$18+1 1/4$

	$=$	$19 1/4$

$19 1/4$

Method Two

First, add the whole numbers

$8+10$

$=$

$18$

Add the fractions using cross method.

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

$1/2+3/4$

$=$

$☐/(2times4)$

$=$

$☐/8$

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

$\frac{\color{#00880A}{1}}{\color{#9a00c7}{2}}+\frac{\color{#9a00c7}{3}}{\color{#00880A}{4}}$	$=$	$\frac{(\color{#00880A}{1\times4})+(\color{#9a00c7}{2\times3})}{8}$

	$=$	$(4+6)/8$

	$=$	$10/8$

	$=$	$\frac{10\div\color{#CC0000}{2}}{8\div\color{#CC0000}{2}}$	Express in lowest terms

	$=$	$5/4$

	$=$	$1 1/4$	We know this from Method One

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

$8 1/2+10 3/4$	$=$	$18+1 1/4$

	$=$	$19 1/4$

$19 1/4$

Question 2 of 3

2. Question

Add the following:

$7 2/3+3 5/7$

1. $8 11/21$
2. $11 8/21$
3. $21 8/11$
4. $10 8/21$

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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

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

First, add the whole numbers

$7+3$

$=$

$10$

Add the fractions using cross method.

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

$2/3+5/7$

$=$

$☐/(3times7)$

$=$

$☐/21$

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

$\frac{\color{#00880A}{2}}{\color{#9a00c7}{3}}+\frac{\color{#9a00c7}{5}}{\color{#00880A}{7}}$	$=$	$\frac{(\color{#00880A}{2\times7})+(\color{#9a00c7}{3\times5})}{21}$

	$=$	$(14+15)/21$

	$=$	$29/21$

Change the improper fraction to a mixed fraction

Divide the numerator by the denominator

Arrange the numbers for long division

$21$ goes into

$29$ one time. So write

$1$ above the line.

Multiply

$1$ to

$21$ and write the answer below

$29$

Subtract

$21$ from

$29$ and write the answer one line below

Since

$21$ cannot go into

$8$ anymore, $8$ is left as the Remainder and $1$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{29}}{\color{#9a00c7}{21}}$	$=$	$\color{#00880A}{1}\frac{\color{#e65021}{8}}{\color{#9a00c7}{21}}$

	$=$	$1 8/21$

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

$7 2/3+3 5/7$	$=$	$10+1 8/21$

	$=$	$11 8/21$

$11 8/21$

Question 3 of 3

3. Question

Subtract the following:

$4 1/2-2 1/10$

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

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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

		$\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\color{#00880A}{2} \frac{\color{#007DDC}{1}}{\color{#9a00c7}{10}}$

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

	$=$	$\frac{8+1}{2}-\frac{20+1}{10}$

	$=$	$\frac{9}{2}-\frac{21}{10}$

Notice that the fractions have different denominators.

Find the

$LCD$ of

$2$ and

$10$ so we can subtract the fractions.

Multiples of

$2$ :

$2\;\;4\;\;6\;\;8\;\;\color{#004ec4}{10}\;\;12$

Multiples of

$10$ :

$\color{#004ec4}{10}\;\;20\;\;30$

The

$LCD$ of

$2$ and

$10$ is

$10$

Next, we get the same denominator and subtract the fractions

	$9/2-21/10$

$=$	$\frac{9\times\color{#CC0000}{5}}{2\times\color{#CC0000}{5}}-\frac{21}{10}$	Multiply $5$ so that the denominator becomes $10$

$=$	$\frac{45}{\color{#004ec4}{10}}-\frac{21}{\color{#004ec4}{10}}$

$=$	$\frac{24}{10}$

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

$24$ two times. So write

$2$ above the line.

Multiply

$2$ to

$10$ and write the answer below

$24$

Subtract

$20$ from

$24$ and write the answer one line below

[add colors: $2$ ]

Since

$10$ cannot go into

$4$ anymore, $4$ is left as the Remainder and $2$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{24}}{\color{#9a00c7}{10}}$	$=$	$\color{#00880A}{2}\frac{\color{#e65021}{4}}{\color{#9a00c7}{10}}$

	$=$	$2\frac{4\div\color{#CC0000}{2}}{10\div\color{#CC0000}{2}}$	Reduce to lowest terms

	$=$	$2 2/5$

$2 2/5$

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