Order of Operations Involving Fractions 2

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Question 1 of 3

1. Question

Solve the following.

\frac{3}{4} \times \frac{2}{3} + (3 - \frac{2}{3})

$3/4xx2/3+(3-2/3)$

1. $6 \frac{2}{5}$ $6 2/5$
2. $5 \frac{2}{6}$ $5 2/6$
3. $2 \frac{5}{6}$ $2 5/6$
4. $2 \frac{6}{5}$ $2 6/5$

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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{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

According to BODMAS, Bracket is prioritized over Multiplication, then followed by Addition.

Ignore the other operations for now and only do the operation inside the bracket, which is subtraction.

\frac{3}{4} \times \frac{2}{3} + (3 - \frac{2}{3})

$\color{#9E9E9E}{\frac{3}{4}\times\frac{2}{3}+}\color{#00880A}{\left({3-\frac{2}{3}}\right)}$

First, make

3

$3$ into a fraction. Recall that all whole numbers has

1

$1$ as a denominator

3

$3$

=

$=$

\frac{3}{1}

$3/1$

To proceed with Subtraction, find the

L C D

$LCD$ of

1

$1$ and

3

$3$

Multiples of

1

$1$ :

12345

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

Multiples of

3

$3$ :

3691215

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

The

L C D

$LCD$ of

1

$1$ and

3

$3$ is

3

$3$

Use the

L C D

$LCD$ as the denominator and then subtract.

		$\frac{3}{1} - \frac{2}{3}$ $3/1-2/3$

	$=$ $=$	$\frac{(\color{#004ec4}{3}\div1)\times3}{\color{#004ec4}{3}}-\frac{(\color{#004ec4}{3}\div3)\times2}{\color{#004ec4}{3}}$

	$=$ $=$	$\frac{3 \times 3}{3} - \frac{1 \times 2}{3}$ $(3xx3)/3-(1xx2)/3$

	$=$ $=$	$\frac{9}{2} - \frac{2}{3}$ $9/2-2/3$

	$=$ $=$	$\frac{7}{3}$ $7/3$

Next, ignore the addition for now and only do Multiplication.

	$\color{#CC0000}{\frac{3}{4}\times\frac{2}{3}}\color{#9E9E9E}{+\frac{7}{3}}$

$=$ $=$	$\frac{6}{12}\color{#9E9E9E}{+\frac{7}{3}}$

$=$ $=$	$\frac{1}{2}\color{#9E9E9E}{+\frac{7}{3}}$	Simplify`

Next, to proceed with Addition, find the

L C D

$LCD$ of

2

$2$ and

3

$3$

Multiples of

2

$2$ :

246810

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

Multiples of

3

$3$ :

3691215

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

The

L C D

$LCD$ of

2

$2$ and

3

$3$ is

6

$6$

Use the

L C D

$LCD$ as the denominator and then add.

		$\frac{1}{2} + \frac{7}{3}$ $1/2+7/3$

	$=$ $=$	$\frac{(\color{#004ec4}{6}\div2)\times1}{\color{#004ec4}{6}}+\frac{(\color{#004ec4}{6}\div3)\times7}{\color{#004ec4}{6}}$

	$=$ $=$	$\frac{3 \times 1}{6} + \frac{2 \times 7}{6}$ $(3xx1)/6+(2xx7)/6$

	$=$ $=$	$\frac{3}{6} + \frac{14}{6}$ $3/6+14/6$

	$=$ $=$	$\frac{17}{6}$ $17/6$

Finally, convert the improper fraction into a mixed number.

Arrange the numbers for long division

6

$6$ goes into

17

$17$ two times. So write

2

$2$ above the line.

Multiply

2

$2$ to

6

$6$ and write the answer below

17

$17$

Subtract

12

$12$ from

17

$17$ and write the answer one line below

Since

6

$6$ cannot go into

5

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

Substitute values into the given formula

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

$\frac{\color{#007DDC}{17}}{\color{#9a00c7}{6}}$	$=$ $=$	$\color{#00880A}{2}\frac{\color{#e65021}{5}}{\color{#9a00c7}{6}}$

2 \frac{5}{6}

$2 5/6$

Question 2 of 3

2. Question

Solve the following.

\frac{4}{5} + 3 \frac{2}{3} \div \frac{1}{6}

$4/5+3 2/3-:1/6$

1. $5 \frac{4}{22}$ $5 4/22$
2. $4 \frac{5}{22}$ $4 5/22$
3. $22 \frac{4}{5}$ $22 4/5$
4. $22 \frac{5}{4}$ $22 5/4$

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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{(c \times A) + b}{c}

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

First, convert the mixed number in a fraction by multiplying the denominator by the whole number and then adding the numerator

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

	$=$ $=$	$\frac{9+2}{3}$

	$=$ $=$	$\frac{11}{3}$

According to BODMAS, Division is prioritized over Addition.

Ignore the addition for now and only do division.

	$\color{#9E9E9E}{\frac{4}{5}+}\frac{11}{3}\div\frac{1}{6}$

$=$ $=$	$\color{#9E9E9E}{\frac{4}{5}+}\color{#e85e00}{\frac{11}{3}\div\frac{6}{1}}$	Find the reciprocal of $\frac{1}{6}$ $1/6$ then proceed with multiplication

$=$ $=$	$\color{#9E9E9E}{\frac{4}{5}+}\frac{66}{3}$

$=$ $=$	$\color{#9E9E9E}{\frac{4}{5}+}22$	Simplify

Simply combine the two remaining values to make a mixed number

\frac{4}{5} + 22

$4/5+22$

=

$=$

22 \frac{4}{5}

$22 4/5$

22 \frac{4}{5}

$22 4/5$

Question 3 of 3

3. Question

Solve the following.

\frac{5}{8} + 1 \frac{1}{2} \div 1 \frac{1}{3}

$5/8+1 1/2-:1 1/3$

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

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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}

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

Order of Operations (BODMAS)

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

First, convert the mixed numbers in fractions by multiplying the denominator by the whole number and then adding the numerator

1 \frac{1}{2}

$1 1/2$

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

	$=$ $=$	$\frac{2+1}{2}$

	$=$ $=$	$\frac{3}{2}$

1 \frac{1}{3}

$1 1/3$

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

	$=$ $=$	$\frac{3+1}{3}$

	$=$ $=$	$\frac{4}{3}$

According to BODMAS, Division is prioritized over Addition.

Ignore the addition for now and only do division.

	$\color{#9E9E9E}{\frac{5}{8}+}\color{#e85e00}{\frac{3}{2}\div\frac{4}{3}}$

$=$ $=$	$\color{#9E9E9E}{\frac{5}{8}+}\frac{3}{2}\times\frac{3}{4}$	Find the reciprocal of $\frac{4}{3}$ $4/3$ then proceed with multiplication

$=$ $=$	$\color{#9E9E9E}{\frac{5}{8}+}\frac{9}{8}$

Next, proceed with the Addition

Since the denominators of the remaining values are the same, add only the numerators

\frac{5}{8} + \frac{9}{8}

$\frac{5}{8}+\frac{9}{8}$

=

$=$

\frac{14}{8}

$\frac{14}{8}$

Finally, convert the improper fraction into a mixed number.

Arrange the numbers for long division

8

$8$ goes into

14

$14$ one time. So write

1

$1$ above the line.

Multiply

1

$1$ to

8

$8$ and write the answer below

14

$14$

Subtract

8

$8$ from

14

$14$ and write the answer one line below

Since

8

$8$ cannot go into

6

$6$ anymore, $6$ $6$ is left as the Remainder and $1$ $1$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{14}}{\color{#9a00c7}{8}}$	$=$ $=$	$\color{#00880A}{1}\frac{\color{#e65021}{6}}{\color{#9a00c7}{8}}$

	$=$ $=$	$1 \frac{3}{4}$ $1 3/4$	Simplify the fraction

1 \frac{3}{4}

$1 3/4$

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