Fraction Word Problems: Addition and Subtraction 4

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Question 1 of 4

1. Question

At a federal court, a jury was deciding whether a person accused was guilty or not.

\frac{2}{3}

$2/3$ believed the accused was guilty,

\frac{1}{6}

$1/6$ believed he was not guilty while the rest were undecided. What fraction of the jury were undecided?

Write fractions in the format “a/b”

(1/6)

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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

Believes accused is guilty	$=$ $=$	$\frac{2}{3}$ $2/3$

Believes accused is not guilty	$=$ $=$	$\frac{1}{6}$ $1/6$

Add the two fractions.

Since $6$ $6$ is a multiple of $3$ $3$ ,

6

$6$ is the

L C D

$LCD$

	$\frac{2}{3}$ $2/3$ $+$ $+$ $\frac{1}{6}$ $1/6$

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

$=$ $=$	$\frac{4}{6}+\frac{1}{6}$	Add the numerators

$=$ $=$	$\frac{5}{6}$	Keep the same denominator

Finally, subtract this fraction from

1

$1$ . Here,

1

$1$ represents the whole jury

	$1 - \frac{5}{6}$ $1-5/6$

$=$ $=$	$\frac{6}{6} - \frac{5}{6}$ $6/6-5/6$	Subtract the numerators

$=$ $=$	$\frac{1}{6}$ $1/6$	Keep the same denominator

\frac{1}{6}

$1/6$ of the jury were undecided.

\frac{1}{6}

$1/6$

Question 2 of 4

2. Question

Jack likes to run to stay fit. He runs

3 \frac{1}{2}

$3 1/2$ km on Sunday,

2 \frac{1}{4}

$2 1/4$ km on Monday, and

4 \frac{2}{3}

$4 2/3$ km on Wednesday. How far does Jack run over those

3

$3$ days?

1. $5 \frac{5}{6}$ $5 5/6$ km
2. $12 \frac{1}{2}$ $12 1/2$ km
3. $9 \frac{7}{12}$ $9 7/12$ km
4. $10 \frac{5}{12}$ $10 5/12$ km

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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

Sunday	$=$ $=$	$3 \frac{1}{2}$ $3 1/2$ km

Monday	$=$ $=$	$2 \frac{1}{4}$ $2 1/4$ km

Wednesday	$=$ $=$	$4 \frac{2}{3}$ $4 2/3$ km

Add these

3

$3$ fractions to get the total distance that Jack ran.

First, add the whole numbers

$3$ $3$

+

$+$ $2$ $2$

+

$+$ $4$ $4$

=

$=$

9

$9$

Now add the fractions

Start by finding the

L C D

$LCD$ of

2

$2$ ,

4

$4$ and

3

$3$

Multiples of

2

$2$ :

246810121416

$2\;\;4\;\;6\;\;8\;\;10\;\;\color{#004ec4}{12}\;\;14\;\;16$

Multiples of

4

$4$ :

48121620

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

Multiples of

3

$3$ :

369121518

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

The

L C D

$LCD$ of

2

$2$ ,

4

$4$ and

3

$3$ is $12$ $12$

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

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

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

$=$ $=$	$\frac{6}{\color{#004ec4}{12}}+\frac{3}{\color{#004ec4}{12}}+\frac{8}{\color{#004ec4}{12}}$	Add only the numerators

$=$ $=$	$\frac{17}{12}$	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

12

$12$ goes into

17

$17$ once. So write

1

$1$ above the line.

Multiply

1

$1$ to

12

$12$ and write the answer below

17

$17$

Subtract

12

$12$ from

17

$17$ and write the answer one line below

Since

12

$12$ cannot go into

5

$5$ anymore, $5$ $5$ is left as the Remainder and $1$ $1$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{17}}{\color{#9a00c7}{12}}$	$=$ $=$	$\color{#00880A}{1}\frac{\color{#e65021}{5}}{\color{#9a00c7}{12}}$

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

9 + 1 \frac{5}{12}

$9+1 5/12$

=

$=$

$10 5/12$ km

Question 3 of 4

3. Question

From a

$10 1/2$ m roll of fabric,

$2 1/4$ m is cut. How much fabric remains?

1. $4 3/7$ m
2. $7 3/4$ m
3. $7 1/4$ m
4. $3 4/7$ 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 length of fabric	$=$	$10 1/2$

Fabric that was cut	$=$	$2 3/4$

Subtract the two fractions to get the remaining length of fabric

First, transform the mixed fractions to improper fractions

		$\color{#00880A}{10}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\color{#00880A}{2} \frac{\color{#007DDC}{3}}{\color{#9a00c7}{4}}$

	$=$	$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{10})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\frac{(\color{#9a00c7}{4}\times\color{#00880A}{2})+\color{#007DDC}{3}}{\color{#9a00c7}{4}}$

	$=$	$\frac{20+1}{2}-\frac{8+3}{4}$

	$=$	$\frac{21}{2}-\frac{11}{4}$

Make sure that the fractions have the same denominators before subtracting

Since

$4$ is a multiple of

$2$ ,

$4$ is the

$LCD$

	$21/2-11/4$

$=$	$\frac{21\times\color{#CC0000}{2}}{2\times\color{#CC0000}{2}}-\frac{11}{4}$	Multiply by $2$ so that the denominator becomes $4$

$=$	$\frac{42}{4}-\frac{11}{4}$	Subtract the numerators

$=$	$\frac{31}{4}$	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

$4$ goes into

$31$ seven times. So write

$7$ above the line.

Multiply

$7$ to

$4$ and write the answer below

$31$

Subtract

$28$ from

$31$ and write the answer one line below

Since

$4$ cannot go into

$3$ anymore, $3$ is left as the Remainder and $7$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{31}}{\color{#9a00c7}{4}}$	$=$	$\color{#00880A}{7}\frac{\color{#e65021}{3}}{\color{#9a00c7}{4}}$

$7 3/4$ m

Question 4 of 4

4. Question

A cake needs

$2/3$ cup of sugar,

$1 1/2$ cups of cocoa,

$3/4$ cup of butter and

$3 1/2$ cups of flour. How many cups of ingredients are needed in total?

1. $5 3/4$
2. $5 6/12$
3. $2 1/4$
4. $6 5/12$

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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

Sugar	$=$	$2/3$

Cocoa	$=$	$1 1/2$

Butter	$=$	$3/4$

Flour	$=$	$3 1/2$

First, add the whole numbers

$3+1$

$=$

$4$

Next, notice that the cocoa and the flour both have

$1/2$ cup worth of ingredient.

These two halves can be added together to get a sum of

$1$ .

$1/2+1/2$

$=$

$1$

Now add the fractions

Since

$3$ and

$4$ are both multiples of

$12$ ,

$12$ is the

$LCD$

	$2/3+3/4$

$=$	$\frac{2\times\color{#CC0000}{4}+3\times\color{#CC0000}{3}}{12}$	Cross multiply the fractions to get the new numerators

$=$	$\frac{8+9}{12}$	Add the numerators

$=$	$\frac{17}{12}$	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

$17$ goes into

$12$ once. So write

$1$ above the line.

Multiply

$1$ to

$12$ and write the answer below

$17$

Subtract

$12$ from

$17$ and write the answer one line below

Since

$5$ cannot go into

$12$ anymore, $5$ is left as the Remainder and $1$ is the Quotient

Substitute values into the given formula

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

$\frac{\color{#007DDC}{17}}{\color{#9a00c7}{12}}$	$=$	$\color{#00880A}{1}\frac{\color{#e65021}{5}}{\color{#9a00c7}{12}}$

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

$4+1+1 5/12$

$=$

$6 5/12$

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Comparing Fractions 1
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Mixed and Improper Fractions 1
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