Order of Operations Involving Fractions 1

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Question 1 of 4

1. Question

Solve the following.

$2/3-1/2xx3/4$

Write fractions in the format “a/b”

(7/24)

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Order of Operations (BODMAS)

B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – Subtraction

According to BODMAS, Multiplication is prioritized over Subtraction.

Ignore the subtraction for now and only do multiplication.

		$\color{#9E9E9E}{\frac{2}{3}-}\color{#CC0000}{\frac{1}{2}\times\frac{3}{4}}$

	$=$	$\color{#9E9E9E}{\frac{2}{3}-}\frac{3}{8}$

To proceed with Subtraction, find the

$LCD$ of

$3$ and

$8$

Multiples of

$3$ :

$3\;\;6\;\;9\;\;12\;\;15\;\;18\;\;21\;\;\color{#004ec4}{24}\;\;27$

Multiples of

$8$ :

$8\;\;16\;\;\color{#004ec4}{24}\;\;32\;\;40\;\;48$

The

$LCD$ of

$3$ and

$8$ is

$24$

Use the

$LCD$ as the denominator and then subtract.

		$2/3-3/8$

	$=$	$\frac{(\color{#004ec4}{24}\div3)\times2}{\color{#004ec4}{24}}-\frac{(\color{#004ec4}{24}\div8)\times3}{\color{#004ec4}{24}}$

	$=$	$(8xx2)/24-(3xx3)/24$

	$=$	$16/24-9/24$

	$=$	$7/24$

$7/24$

Question 2 of 4

2. Question
Solve the following.

$3/7+1/4xx3+1/4$
- 1. $7 1/3$
- 2. $1 3/7$
- 3. $3 1/7$
- 4. $3 3/7$
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Order of Operations (BODMAS)

B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – Subtraction

According to BODMAS, Multiplication is prioritized over Addition.

Ignore the addition for now and only do multiplication.

$\color{#9E9E9E}{\frac{3}{7}+}\color{#CC0000}{\frac{1}{4}\times3}\color{#9E9E9E}{+\frac{1}{4}}$

$=$ $\color{#9E9E9E}{\frac{3}{7}+}\frac{3}{4}\color{#9E9E9E}{+\frac{1}{4}}$

Next, proceed with the Addition

Since the denominators of the second and third value are the same, add only the numerators

$\color{#9E9E9E}{\frac{3}{7}+}\color{#A57200}{\frac{3}{4}+\frac{1}{4}}$ $=$ $\color{#9E9E9E}{\frac{3}{7}+}\frac{4}{4}$

$=$ $\color{#9E9E9E}{\frac{3}{7}+}1$

Simply combine the two remaining values to make a mixed number

$3/7+1$ $=$ $1 3/7$

$1 3/7$

Question 3 of 4

3. Question

Solve the following.

$5-2/5-:7/10$

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

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Chapters

Order of Operations (BODMAS)

B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – Subtraction

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

According to BODMAS, Division is prioritized over Subtraction.

Ignore the subtraction for now and only do division.

	$\color{#9E9E9E}{5-}\color{#e85e00}{\frac{2}{5}\div\frac{7}{10}}$

$=$	$\color{#9E9E9E}{5-}\frac{2}{5}\times\frac{10}{7}$	Find the reciprocal of $7/10$ then proceed with multiplication

$=$	$\color{#9E9E9E}{5-}\frac{2}{1}\times\frac{2}{7}$	Simplify

$=$	$\color{#9E9E9E}{5-}\frac{4}{7}$

Make

$5$ into a fraction. Recall that all whole numbers has

$1$ as a denominator

$5$

$=$

$5/1$

To proceed with Subtraction, find the

$LCD$ of

$1$ and

$7$

Multiples of

$1$ :

$1\;\;2\;\;3\;\;4\;\;5\;\;6\;\;\color{#004ec4}{7}$

Multiples of

$7$ :

$\color{#004ec4}{7}\;\;14\;\;21\;\;28\;\;35$

The

$LCD$ of

$1$ and

$7$ is

$7$

Use the

$LCD$ as the denominator and then subtract.

		$5/1-4/7$

	$=$	$\frac{(\color{#004ec4}{7}\div1)\times5}{\color{#004ec4}{7}}-\frac{(\color{#004ec4}{7}\div7)\times4}{\color{#004ec4}{7}}$

	$=$	$(7xx5)/7-(1xx4)/7$

	$=$	$35/7-4/7$

	$=$	$31/7$

Finally, convert the improper fraction into a mixed number.

Arrange the numbers for long division

$7$ goes into

$31$ four times. So write

$4$ above the line.

Multiply

$4$ to

$7$ and write the answer below

$31$

Subtract

$28$ from

$31$ and write the answer one line below

Since

$7$ cannot go into

$3$ anymore, $3$ is left as the Remainder and $4$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{31}}{\color{#9a00c7}{7}}$	$=$	$\color{#00880A}{4}\frac{\color{#e65021}{3}}{\color{#9a00c7}{7}}$

$4 3/7$

Question 4 of 4

4. Question

Solve the following.

$1 1/5-:2+4$

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

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Chapters

Chapters

Order of Operations (BODMAS)

B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – Subtraction

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 in a fraction by multiplying the denominator by the whole number and then adding the numerator

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

	$=$	$\frac{5+1}{5}$

	$=$	$\frac{6}{5}$

Next, make

$2$ into a fractions. Recall that all whole numbers has

$1$ as a denominator

$2$

$=$

$2/1$

According to BODMAS, Division is prioritized over Addition.

Ignore the addition for now and only do division.

	$\color{#e85e00}{\frac{6}{5}\div\frac{2}{1}}\color{#9E9E9E}{+4}$

$=$	$\frac{6}{5}\times\frac{1}{2}\color{#9E9E9E}{+4}$	Find the reciprocal of $2/1$ then proceed with multiplication

$=$	$\frac{6}{10}\color{#9E9E9E}{+4}$

$=$	$\frac{3}{5}\color{#9E9E9E}{+4}$	Simplify

Simply combine the two remaining values to make a mixed number

$3/5+4$

$=$

$4 3/5$

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

		$\color{#9E9E9E}{\frac{3}{7}+}\color{#CC0000}{\frac{1}{4}\times3}\color{#9E9E9E}{+\frac{1}{4}}$

	$=$	$\color{#9E9E9E}{\frac{3}{7}+}\frac{3}{4}\color{#9E9E9E}{+\frac{1}{4}}$

$\color{#9E9E9E}{\frac{3}{7}+}\color{#A57200}{\frac{3}{4}+\frac{1}{4}}$	$=$	$\color{#9E9E9E}{\frac{3}{7}+}\frac{4}{4}$
	$=$	$\color{#9E9E9E}{\frac{3}{7}+}1$

Order of Operations Involving Fractions 1

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Quiz summary

Information

1. Question

Hint

Excellent!

Order of Operations (BODMAS)

2. Question

Hint

Well Done!

Order of Operations (BODMAS)

3. Question

Hint

Nice Job!

Order of Operations (BODMAS)

Transforming an Improper to Mixed Fraction

4. Question

Hint

Correct!

Order of Operations (BODMAS)

Transforming a Fraction from Mixed to Improper

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