Fraction Word Problems: Addition and Subtraction 1

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Question 1 of 4

Three people share a sum of money. The

1

$1$ st person receives

\frac{2}{5}

$2/5$ of the sum and the

2

$2$ nd person receives

\frac{1}{2}

$1/2$ . What fraction of the money does the

3

$3$ rd person receive?

Write fractions in the format “a/b”

(1/10)

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Add fractions with unlike denominators by transforming the fractions so that they have like denominators

First, list down the values stated in the problem

$1$ $1$ st person	$=$ $=$	$\frac{2}{5}$ $2/5$

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

Use cross method to add the two fractions.

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

$\frac{2}{5}$ $2/5$

+

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

=

$=$

$☐/(5times2)$

$=$

$☐/10$

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

$\frac{\color{#00880A}{2}}{\color{#9a00c7}{5}}+\frac{\color{#9a00c7}{1}}{\color{#00880A}{2}}$	$=$	$\frac{(\color{#00880A}{2\times2})+(\color{#9a00c7}{5\times1})}{10}$

	$=$	$(4+5)/10$

	$=$	$9/10$

Finally, subtract this fraction from

$1$ .

$1$ represents the whole sum of money

	$1-9/10$

$=$	$10/10-9/10$	Subtract the numerators

$=$	$1/10$	Keep the same denominator

The

$3$ rd person gets

$1/10$ of the money.

$1/10$

Question 2 of 4

A rain tank is three fifths full. Heavy rain over a period of

$3$ nights filled it with one tenths of water each night. What fraction of the tank’s capacity is filled after the

$3$ nights of rainfall?

Write fractions in the format “a/b”

(9/10)

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Add fractions with unlike denominators by transforming the fractions so that they have like denominators

First, list down the values stated in the problem

Starting amount of water	$=$	$3/5$

Additional amount of water	$=$	$3times1/10=3/1times1/10=$ $3/10$

Add the two values to get the total amount of water after 3 days

Since

$10$ is a multiple of

$5$ , it is the

$LCD$ of

$5$ and

$10$

	$3/5$ $+$ $3/10$

$=$	$\frac{3\color{#CC0000}{\times2}}{5\color{#CC0000}{\times2}}+\frac{3}{10}$	Multiply $2$ to $5$ so it becomes $10$

$=$	$6/10+3/10$

$=$	$9/10$	Keep the same denominator

$9/10$

Question 3 of 4

A concrete truck contains a concrete mixture that consists of

$1/4$ cement,

$1/3$ sand,

$1/6$ water and the rest is gravel. What fraction of the mixture is gravel?

Write fractions in the format “a/b”

(1/4)

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Add fractions with unlike denominators by transforming the fractions so that they have like denominators

First, list down the values stated in the problem

Cement	$=$	$1/4$

Sand	$=$	$1/3$

Water	$=$	$1/6$

Add the three fractions.

Start by finding the

$LCD$ of the $4$ , $3$ and $6$

Multiples of

$4$ :

$4\;\;8\;\;\color{#004ec4}{12}\;\;16\;\;20$

Multiples of

$3$ :

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

Multiples of

$6$ :

$6\;\;\color{#004ec4}{12}\;\;18\;\;24$

The

$LCD$ of

$4$ ,

$3$ and

$6$ is $12$

Use the $LCD$ as the denominator for the three fractions then add them.

	$1/4$ $+$ $1/3$ $+$ $1/6$

$=$	$\frac{1\times\color{#CC0000}{3}}{4\times\color{#CC0000}{3}}+\frac{1\times\color{#CC0000}{4}}{4\times\color{#CC0000}{4}}+\frac{1\times\color{#CC0000}{2}}{6\times\color{#CC0000}{2}}$	Multiply the fractions so that the denominator becomes $12$

$=$	$\frac{3}{\color{#004ec4}{12}}+\frac{4}{\color{#004ec4}{12}}+\frac{2}{\color{#004ec4}{12}}$	Add only the numerators

$=$	$\frac{9}{12}$	Keep the same denominator

$=$	$\frac{9\div\color{#CC0000}{3}}{12\div\color{#CC0000}{3}}$	Express in lowest terms

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

Finally, subtract this fraction from

$1$ . Here,

$1$ represents the whole mixture

	$1-3/4$

$=$	$4/4-3/4$	Subtract the numerators

$=$	$1/4$	Keep the same denominator

$1/4$ of the concrete mixture is gravel.

$1/4$

Question 4 of 4

4. Question
Eddie ordered $2$ pizzas, each sliced in $8$ pieces. He ate $5$ pieces. Find the following:

Write fractions in the format “a/b”
- $(i)$ Fraction that Eddie ate: (5/16)
  
  $(ii)$ Fraction of remaining pizza: (11/16)
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$(i)$ Find the fraction of pizza that Eddie ate.

First, list down the values stated in the problem

Slices Eddie ate $=$ $5$

Total slices of pizza $=$ $2$ pizzas $xx8$ slices $=$ $16$

Since we are looking for the fraction that Eddie ate, the numerator must be the no. of slices he ate while the denominator must be the total no. of slices

$\mathsf{\frac{\color{#9E8600}{no.\;of\;slices\;he\;ate}}{\color{#007DDC}{total\;no.\;of\;slices}}}$ $=$ $\frac{\color{#9E8600}{5}}{\color{#007DDC}{16}}$

Eddie ate $5/16$ of the pizza he ordered.

$(ii)$ Find the fraction of pizza that remains.

Simply subtract the fraction that Eddie ate from $1$ . Here, $1$ represents the total pizza that he ordered.

$1-5/16$

$=$ $16/16-5/16$ Subtract the numerators

$=$ $11/16$ Keep the same denominator

$11/16$ of the pizza Eddie ordered remains.

$(i) 5/16$

$(ii) 11/16$

Fraction Word Problems: Addition and Subtraction 1

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

Slices Eddie ate	$=$	$5$

Total slices of pizza	$=$	$2$ pizzas $xx8$ slices $=$ $16$

	$1-5/16$

$=$	$16/16-5/16$	Subtract the numerators

$=$	$11/16$	Keep the same denominator