Fraction Word Problems: Addition and Subtraction 3

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Question 1 of 4

1. Question

Adrian juices some oranges and apples. He got

2 \frac{3}{4}

$2 3/4$ glasses of orange juice and

4 \frac{5}{8}

$4 5/8$ glasses of apple juice. How many glasses of juice did he get altogether?

1. $7 \frac{3}{8}$ $7 3/8$
2. $8 \frac{3}{7}$ $8 3/7$
3. $3 \frac{7}{8}$ $3 7/8$
4. $7 \frac{1}{8}$ $7 1/8$

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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

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

First, list down the values stated in the problem

Orange Juice	$=$ $=$	$3 \frac{1}{2}$ $3 1/2$

Apple Juice	$=$ $=$	$4 \frac{5}{8}$ $4 5/8$

Add these

2

$2$ fractions to get the total number of glasses Adrian juiced.

First, add the whole numbers

$2$ $2$

+

$+$ $4$ $4$

=

$=$

6

$6$

Now add the fractions

Since $8$ $8$ is a multiple of $4$ $4$ ,

8

$8$ is the

L C D

$LCD$

	$\frac{3}{4}$ $3/4$ $+$ $+$ $\frac{5}{8}$ $5/8$

$=$ $=$	$\frac{3\times\color{#CC0000}{2}}{4\times\color{#CC0000}{2}}+\frac{5}{8}$	Multiply by $2$ $2$ so that the denominator becomes $8$ $8$

$=$ $=$	$\frac{6}{8}+\frac{5}{8}$	Add the numerators

$=$ $=$	$\frac{11}{8}$	Keep the same denominator

Transform the fraction back to a mixed fraction

Start by dividing the numerator by the denominator

Arrange the numbers for long division

8

$8$ goes into

11

$11$ once. So write

1

$1$ above the line.

Multiply

1

$1$ to

8

$8$ and write the answer below

11

$11$

Subtract

8

$8$ from

11

$11$ and write the answer one line below

Since

8

$8$ cannot go into

3

$3$ anymore, $3$ $3$ is left as the Remainder and $1$ $1$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{11}}{\color{#9a00c7}{8}}$	$=$ $=$	$\color{#00880A}{1}\frac{\color{#e65021}{3}}{\color{#9a00c7}{8}}$

Finally, add the two sums (whole number and mixed fraction).

6 + 1 \frac{3}{8}

$6+1 3/8$

=

$=$

7 \frac{3}{8}

$7 3/8$

7 \frac{3}{8}

$7 3/8$

Question 2 of 4

2. Question

At a party, 2 groups ordered a total of 6 pizzas. The first group ate

1 \frac{7}{8}

$1 7/8$ of the pizzas and the second group ate

3 \frac{1}{4}

$3 1/4$ of the pizzas. How many pizzas were left?

1. $\frac{7}{8}$ $7/8$
2. $\frac{8}{7}$ $8/7$
3. $5 \frac{1}{8}$ $5 1/8$
4. $1 \frac{5}{8}$ $1 5/8$

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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

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

First, list down the values stated in the problem

Pizzas Eaten by 1st Group	$=$ $=$	$1 \frac{7}{8}$ $1 7/8$

Pizzas Eaten by 2nd Group	$=$ $=$	$3 \frac{1}{4}$ $3 1/4$

First, add the whole numbers

$1$ $1$

+

$+$ $3$ $3$

=

$=$

4

$4$

Now add the fractions

Since $8$ $8$ is a multiple of $4$ $4$ ,

8

$8$ is the

L C D

$LCD$

	$\frac{7}{8}$ $7/8$ $+$ $+$ $\frac{1}{4}$ $1/4$

$=$ $=$	$\frac{5}{8}+\frac{1\times\color{#CC0000}{2}}{4\times\color{#CC0000}{2}}$	Multiply by $2$ $2$ so that the denominator becomes $8$ $8$

$=$ $=$	$\frac{7}{8}+\frac{2}{8}$	Add the numerators

$=$ $=$	$\frac{9}{8}$	Keep the same denominator

Transform the fraction back to a mixed fraction

Start by dividing the numerator by the denominator

Arrange the numbers for long division

8

$8$ goes into

9

$9$ once. So write

1

$1$ above the line.

Multiply

1

$1$ to

8

$8$ and write the answer below

9

$9$

Subtract

8

$8$ from

9

$9$ and write the answer one line below

Since

8

$8$ cannot go into

9

$9$ anymore, $1$ $1$ is left as the Remainder and $1$ $1$ is the Quotient

Substitute values into the given formula

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

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

Next, add the two sums (whole number and mixed fraction).

4 + 1 \frac{1}{8}

$4+1 1/8$

=

$=$

5 \frac{1}{8}

$5 1/8$

Convert

5 \frac{1}{8}

$5 1/8$ into an improper fraction

Finally, subtract the sum of the fractions from the total number of pizzas, which is

6

$6$ .

It will be easier to compute if you change the sum of the fractions into an improper fraction.

$6 - 5 \frac{1}{8}$ $6-5 1/8$	$=$ $=$	$6 - \frac{41}{8}$ $6-41/8$	Convert $5 \frac{1}{8}$ $5 1/8$ into an improper fraction

	$=$ $=$	$\frac{6}{1} - \frac{41}{8}$ $6/1-41/8$

$4 + 1 \frac{1}{8}$ $4+1 1/8$	$=$ $=$	$5 \frac{1}{8}$ $5 1/8$

Since

8

$8$ is a multiple of

1

$1$ ,

8

$8$ is the

L C D

$LCD$

	$\frac{6}{1} - \frac{41}{8}$ $6/1-41/8$

$=$ $=$	$\frac{6\times\color{#CC0000}{8}}{1\times\color{#CC0000}{8}}-\frac{41}{8}$	Multiply by $8$ $8$ so that the denominator becomes $8$ $8$

$=$ $=$	$\frac{48}{8}-\frac{41}{8}$	Add the numerators

$=$ $=$	$\frac{7}{8}$	Keep the same denominator

\frac{7}{8}

$7/8$

Question 3 of 4

3. Question

From a reel of ribbon that is

9 \frac{1}{2}

$9 1/2$ m long, a

1 \frac{2}{3}

$1 2/3$ m long piece is cut. How much of the ribbon remains?

1. $7 \frac{5}{6}$ $7 5/6$ m
2. $5 \frac{6}{7}$ $5 6/7$ m
3. $7 \frac{1}{6}$ $7 1/6$ m
4. $6 \frac{5}{7}$ $6 5/7$ m

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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, list down the values stated in the problem

Total ribbon	$=$ $=$	$9 \frac{1}{2}$ $9 1/2$ m

Removed piece	$=$ $=$	$1 \frac{2}{3}$ $1 2/3$ m

Subtract these

2

$2$ fractions to get the remaining length of ribbon.

First, transform the mixed fractions to improper fractions

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

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

	$=$ $=$	$\frac{18+1}{2}-\frac{3+2}{3}$

	$=$ $=$	$\frac{19}{2}-\frac{5}{3}$

Use cross method to subtract the two fractions.

First, multiply the two denominators. Use the product as a denominator for a new fraction.

\frac{19}{2} - \frac{5}{3}

$19/2-5/3$

=

$=$

$☐/(2times3)$

$=$

$☐/6$

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

$\frac{\color{#00880A}{19}}{\color{#9a00c7}{2}}-\frac{\color{#9a00c7}{5}}{\color{#00880A}{3}}$	$=$	$\frac{(\color{#00880A}{19\times3})-(\color{#9a00c7}{2\times5})}{6}$

	$=$	$(57-10)/6$

	$=$	$47/6$

Transform the fraction back to a mixed fraction

Start by dividing the numerator by the denominator

Arrange the numbers for long division

$6$ goes into

$47$ seven times. So write

$7$ above the line.

Multiply

$7$ to

$6$ and write the answer below

$47$

Subtract

$42$ from

$47$ and write the answer one line below

Since

$6$ cannot go into

$5$ anymore, $5$ is left as the Remainder and $7$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{47}}{\color{#9a00c7}{6}}$	$=$	$\color{#00880A}{7}\frac{\color{#e65021}{5}}{\color{#9a00c7}{6}}$

$7 5/6$ m

Question 4 of 4

4. Question

Doug plans to dig a hole

$4 1/3$ m deep. So far, he has dug

$3 4/5$ m deep. How much deeper does he need to dig?

Write fractions in the form “a/b”

(8/15)m

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Transforming a Fraction from Mixed to Improper

$=$

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

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

First, list down the values stated in the problem

Target depth	$=$	$4 1/3$ m

Dug so far	$=$	$3 4/5$ m

Subtract these

$2$ fractions to get the remaining depth to be dug.

First, transform the mixed fractions to improper fractions

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

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

	$=$	$\frac{12+1}{3}-\frac{15+4}{5}$

	$=$	$\frac{13}{3}-\frac{19}{5}$

Use cross method to subtract the two fractions.

First, multiply the two denominators. Use the product as a denominator for a new fraction.

$13/3-19/5$

$=$

$☐/(3times5)$

$=$

$☐/15$

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

$\frac{\color{#00880A}{13}}{\color{#9a00c7}{3}}-\frac{\color{#9a00c7}{19}}{\color{#00880A}{5}}$	$=$	$\frac{(\color{#00880A}{13\times5})-(\color{#9a00c7}{3\times19})}{15}$

	$=$	$(65-57)/15$

	$=$	$8/15$

$8/15$ m

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
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Fraction Word Problems: Addition and Subtraction 2
Fraction Word Problems: Addition and Subtraction 3
Fraction Word Problems: Addition and Subtraction 4
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Find the Fraction of a Quantity: Word Problems 1
Find the Fraction of a Quantity: Word Problems 2
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Find the Fraction of a Quantity: Word Problems 4
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Order of Operations Involving Fractions 2