Fraction Word Problems: Addition and Subtraction 2

Question 1 of 4

Arnold decided to give out a certain amount of money. He gave

\frac{1}{4}

$1/4$ of this money to his daughter,

\frac{3}{5}

$3/5$ to his wife and the rest to a charity. What fraction of the money is left for the charity?

Write fractions in the format “a/b”

(3/20)

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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

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

Wife	$=$ $=$	$\frac{3}{5}$ $3/5$

Use cross method to add the two fractions.

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

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

+

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

=

$=$

\frac{☐}{4 \times 5}

$☐/(4times5)$

=

$=$

\frac{☐}{20}

$☐/20$

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

$\frac{\color{#00880A}{1}}{\color{#9a00c7}{4}}+\frac{\color{#9a00c7}{3}}{\color{#00880A}{5}}$	$=$ $=$	$\frac{(\color{#00880A}{1\times5})+(\color{#9a00c7}{4\times3})}{20}$

	$=$ $=$	$\frac{5 + 12}{20}$ $(5+12)/20$

	$=$ $=$	$\frac{17}{20}$ $17/20$

Finally, subtract this fraction from

1

$1$ .

1

$1$ represents the whole sum of money

	$1 - \frac{17}{20}$ $1-17/20$

$=$ $=$	$\frac{20}{20} - \frac{17}{20}$ $20/20-17/20$	Subtract the numerators

$=$ $=$	$\frac{3}{20}$ $3/20$	Keep the same denominator

Arnold would be giving

\frac{3}{20}

$3/20$ of the money to charity.

\frac{3}{20}

$3/20$

Question 2 of 4

Georgia loves chocolate. She ate

\frac{1}{3}

$1/3$ of her chocolate bar, then gave away

\frac{1}{4}

$1/4$ to her friend. How much remains of her chocolate bar?

Write fractions in the format “a/b”

(5/12)

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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

Ate	$=$ $=$	$1/3$

Gave	$=$	$1/4$

Use cross method to add the two fractions.

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

$1/3$

$+$ $1/4$

$=$

$☐/(3times4)$

$=$

$☐/12$

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

$\frac{\color{#00880A}{1}}{\color{#9a00c7}{3}}+\frac{\color{#9a00c7}{1}}{\color{#00880A}{4}}$	$=$	$\frac{(\color{#00880A}{1\times4})+(\color{#9a00c7}{3\times1})}{12}$

	$=$	$(4+3)/12$

	$=$	$7/12$

Finally, subtract this fraction from

$1$ .

$1$ represents the whole chocolate bar

	$1-7/12$

$=$	$12/12-7/12$	Subtract the numerators

$=$	$5/12$	Keep the same denominator

$5/12$ remains of Georgia’s chocolate bar.

$5/12$

Question 3 of 4

Julie’s fuel tank is half full. She went to some shops and used a further

$1/5$ of the tank. How much fuel remains in the tank?

Write fractions in the format “a/b”

(3/10)

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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

Initial amount of fuel that was used	$=$	$1/2$ (Since the tank was half full)

Further fuel used	$=$	$1/5$

Use cross method to add the two fractions.

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

$1/2$

$+$ $1/5$

$=$

$☐/(2times5)$

$=$

$☐/10$

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

$\frac{\color{#00880A}{1}}{\color{#9a00c7}{2}}+\frac{\color{#9a00c7}{1}}{\color{#00880A}{5}}$	$=$	$\frac{(\color{#00880A}{1\times5})+(\color{#9a00c7}{2\times1})}{10}$

	$=$	$(5+2)/10$

	$=$	$7/10$

Finally, subtract this fraction from

$1$ .

$1$ represents the whole sum of money

	$1-7/10$

$=$	$10/10-7/10$	Subtract the numerators

$=$	$3/10$	Keep the same denominator

$3/10$ of the fuel tank remains.

$3/10$

Question 4 of 4

A bucket is half full. If

$1$ litre is added it becomes three quarters full. How many litres is in the bucket when it is full?

(4) $L$

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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

Initial amount	$=$	$1/2$ (half full)

Amount after adding $1L$	$=$	$3/4$ (three quarters full)

We can find the fraction that is equivalent to

$1L$ by subtracting these fractions

Since $4$ is a multiple of $2$ ,

$4$ is the

$LCD$

	$3/4$ $-$ $1/2$

$=$	$\frac{3}{4}-\frac{1\times\color{#CC0000}{2}}{2\times\color{#CC0000}{2}}$	Multiply by $2$ so that the denominator becomes $4$

$=$	$\frac{3}{4}-\frac{2}{4}$	Subtract the numerators

$=$	$\frac{1}{4}$	Keep the same denominator

This means that

$1L$ is equivalent to

$1/4$ of the bucket.

Equate

$1/4$ and

$1L$ and multiply both sides so that

$1/4$ becomes

$1$ . Here,

$1$ represents a full bucket.

$1/4$	$=$	$1L$

$1/4$ $xx4$	$=$	$1L$ $xx4$

$1/4xx4/1$	$=$	$4L$

$4/4$	$=$	$4L$

$1$	$=$	$4L$

A full bucket contains

$4L$ .

$4L$

Fraction Word Problems: Addition and Subtraction 2

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