Mixed and Improper Fractions 3

Years

Year 10

Fractions

Mixed and Improper Fractions

Mixed and Improper Fractions 3

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Question 1 of 4

1. Question

Convert this fraction to an improper fraction

7 \frac{5}{12}

$7 5/12$

Write fractions in the format “a/b”

(89/12)

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Transforming a Fraction from Mixed to Improper

=

$=$

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

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

An Improper Fraction is a fraction where the numerator is larger than the denominator.

Multiply the denominator by the whole number and then add the numerator

$\color{#00880A}{7}\frac{\color{#007DDC}{5}}{\color{#9a00c7}{12}}$	$=$ $=$	$\frac{(\color{#9a00c7}{12}\times\color{#00880A}{7})+\color{#007DDC}{5}}{\color{#9a00c7}{12}}$

	$=$ $=$	$\frac{84+5}{12}$

	$=$ $=$	$\frac{89}{12}$

\frac{89}{12}

$89/12$

Question 2 of 4

2. Question

Convert this fraction to a mixed fraction

\frac{41}{9}

$41/9$

1. $3 \frac{7}{9}$ $3 7/9$
2. $9 \frac{4}{5}$ $9 4/5$
3. $5 \frac{4}{9}$ $5 4/9$
4. $4 \frac{5}{9}$ $4 5/9$

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Transforming an Improper to Mixed Fraction

\frac{b}{c} = Q \frac{R}{c}

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

where $Q$ $Q$ is the quotient of

(

$($ $b$ $b$

\div

$-:$ $c$ $c$

)

$)$ and $R$ $R$ is the remainder

A Mixed Number or Mixed Fraction consists of a whole number and a fraction.

First, divide the numerator by the denominator

Arrange the numbers for long division

9

$9$ goes into

41

$41$ four times. So write

4

$4$ above the line.

Multiply

4

$4$ to

9

$9$ and write the answer below

41

$41$

Subtract

36

$36$ from

41

$41$ and write the answer one line below

Since

9

$9$ cannot go into

5

$5$ anymore, $5$ $5$ is left as the Remainder and $4$ $4$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{41}}{\color{#9a00c7}{9}}$	$=$ $=$	$\color{#00880A}{4}\frac{\color{#e65021}{5}}{\color{#9a00c7}{9}}$

4 \frac{5}{9}

$4 5/9$

Question 3 of 4

3. Question

Convert this fraction to a mixed fraction

\frac{68}{16}

$68/16$

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

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

where $Q$ $Q$ is the quotient of

(

$($ $b$ $b$

\div

$-:$ $c$ $c$

)

$)$ and $R$ $R$ is the remainder

A Mixed Number or Mixed Fraction consists of a whole number and a fraction.

First, divide the numerator by the denominator

Arrange the numbers for long division

16

$16$ goes into

68

$68$ four times. So write

4

$4$ above the line.

Multiply

4

$4$ to

16

$16$ and write the answer below

68

$68$

Subtract

64

$64$ from

68

$68$ and write the answer one line below

Since

16

$16$ cannot go into

4

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

Substitute values into the given formula

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

$\frac{\color{#007DDC}{68}}{\color{#9a00c7}{16}}$	$=$ $=$	$\color{#00880A}{4}\frac{\color{#e65021}{4}}{\color{#9a00c7}{16}}$

	$=$ $=$	$4\frac{4\div\color{#CC0000}{4}}{16\div\color{#CC0000}{4}}$	Simplify the fraction

	$=$ $=$	$4 \frac{1}{4}$ $4 1/4$

4 \frac{1}{4}

$4 1/4$

Question 4 of 4

4. Question

Convert this fraction to a mixed fraction

\frac{25}{10}

$25/10$

1. $1 \frac{3}{10}$ $1 3/10$
2. $2 \frac{1}{2}$ $2 1/2$
3. $2 \frac{3}{5}$ $2 3/5$
4. $3 \frac{7}{10}$ $3 7/10$

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Chapters

Transforming an Improper to Mixed Fraction

\frac{b}{c} = Q \frac{R}{c}

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

where $Q$ $Q$ is the quotient of

(

$($ $b$ $b$

\div

$-:$ $c$ $c$

)

$)$ and $R$ $R$ is the remainder

A Mixed Number or Mixed Fraction consists of a whole number and a fraction.

First, divide the numerator by the denominator

Arrange the numbers for long division

10

$10$ goes into

25

$25$ two times. So write

2

$2$ above the line.

Multiply

2

$2$ to

10

$10$ and write the answer below

25

$25$

Subtract

20

$20$ from

25

$25$ and write the answer one line below

Since

10

$10$ 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

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

$\frac{\color{#007DDC}{25}}{\color{#9a00c7}{10}}$	$=$ $=$	$\color{#00880A}{2}\frac{\color{#e65021}{5}}{\color{#9a00c7}{10}}$

	$=$ $=$	$2\frac{5\div\color{#CC0000}{5}}{10\div\color{#CC0000}{5}}$	Simplify the fraction

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

2 \frac{1}{2}

$2 1/2$

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