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

$2 3/4$ glasses of orange juice and

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

1. $3 7/8$
2. $7 1/8$
3. $8 3/7$
4. $7 3/8$

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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, list down the values stated in the problem

Orange Juice	$=$	$3 1/2$

Apple Juice	$=$	$4 5/8$

Add these

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

First, add the whole numbers

$2$

$+$ $4$

$=$

$6$

Now add the fractions

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

$8$ is the

$LCD$

	$3/4$ $+$ $5/8$

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

$=$	$\frac{6}{8}+\frac{5}{8}$	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

$8$ goes into

$11$ once. So write

$1$ above the line.

Multiply

$1$ to

$8$ and write the answer below

$11$

Subtract

$8$ from

$11$ and write the answer one line below

Since

$8$ cannot go into

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

Substitute values into the given formula

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

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

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

$6+1 3/8$

$=$

$7 3/8$

Question 2 of 4

2. Question

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

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

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

1. $7/8$
2. $1 5/8$
3. $8/7$
4. $5 1/8$

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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, list down the values stated in the problem

Pizzas Eaten by 1st Group	$=$	$1 7/8$

Pizzas Eaten by 2nd Group	$=$	$3 1/4$

First, add the whole numbers

$1$

$+$ $3$

$=$

$4$

Now add the fractions

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

$8$ is the

$LCD$

	$7/8$ $+$ $1/4$

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

$=$	$\frac{7}{8}+\frac{2}{8}$	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

$8$ goes into

$9$ once. So write

$1$ above the line.

Multiply

$1$ to

$8$ and write the answer below

$9$

Subtract

$8$ from

$9$ and write the answer one line below

Since

$8$ cannot go into

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

Substitute values into the given formula

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

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

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

$4+1 1/8$

$=$

$5 1/8$

Convert

$5 1/8$ into an improper fraction

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

$6$ .

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

$6-5 1/8$	$=$	$6-41/8$	Convert $5 1/8$ into an improper fraction

	$=$	$6/1-41/8$

$4+1 1/8$	$=$	$5 1/8$

Since

$8$ is a multiple of

$1$ ,

$8$ is the

$LCD$

	$6/1-41/8$

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

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

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

$7/8$

Question 3 of 4

3. Question

From a reel of ribbon that is

$9 1/2$ m long, a

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

1. $7 5/6$ m
2. $6 5/7$ m
3. $5 6/7$ m
4. $7 1/6$ m

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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, list down the values stated in the problem

Total ribbon	$=$	$9 1/2$ m

Removed piece	$=$	$1 2/3$ m

Subtract these

$2$ 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.

$19/2-5/3$

$=$

$☐/(2times3)$

$=$

$☐/6$

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

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