The method of subtracting fractions and whole numbers is very similar to the one we use for addition.

For example, suppose that we want to find the value of 2-\dfrac{5}{\color{blue}6}. We first write 2 as an improper fraction: \dfrac{2}{1}

Then, we put this fraction over a denominator of \color{blue}6 by multiplying the numerator and denominator by {\color{blue}{6}} :

\dfrac{2 \times {\color{blue}{6}}}{1\times{\color{blue}{6}}} = \dfrac{12}{6}

So now, we have to find:

\underbrace{\dfrac{12}{6}}_{2} - \dfrac{5}{6}

To subtract two fractions with like denominators, we subtract the numerators and keep the denominators the same.

\begin{align*} \dfrac{12}{6} - \dfrac{5}{6} =\dfrac{7}{6} \end{align*}

So our final answer is \dfrac 7 {6}.

We can always check our answer using a fraction model:


FLAG

What is 3 - \dfrac{1}{7} expressed as an improper fraction?

EXPLANATION

To subtract \dfrac{1}{\color{blue}{7}} from 3 , we need to express the whole number 3 as an equivalent fraction with a denominator of {\color{blue}{7}}.

First, we write 3 as an improper fraction:

\dfrac{3}{1}

Then, we put this fraction over a denominator of \color{blue}7 by multiplying the numerator and denominator by {\color{blue}{7}} :

\dfrac{3 \times {\color{blue}{7}}}{1\times{\color{blue}{7}}} = \dfrac{21}{7}

So now, we have to find:

\dfrac{21}{7} - \dfrac{1}{7}

To subtract two fractions with like denominators, we subtract the numerators and keep the denominators the same:

\begin{align*} \dfrac{21}{7} - \dfrac{1}{7} = \dfrac{20}{7} \end{align*}

FLAG

What is $2-\dfrac{4}{7}?$

a
$\dfrac{8}{7}$
b
$\dfrac{12}{7}$
c
$\dfrac{9}{7}$
d
$\dfrac{10}{7}$
e
$\dfrac{11}{7}$

$1 - \dfrac{5}{7} = $

a
$\dfrac{5}{7}$
b
$\dfrac{3}{7}$
c
$\dfrac{1}{7}$
d
$\dfrac{4}{7}$
e
$\dfrac{2}{7}$

What is \dfrac{31}{9} - 2 expressed as a mixed number?

EXPLANATION

To subtract 2 from \dfrac{31}{\color{blue}{9}} , we need to express the whole number 2 as an equivalent fraction with a denominator of {\color{blue}{9}}.

First, we write 2 as an improper fraction:

\dfrac{2}{1}

Then, we put this fraction over a denominator of \color{blue}9 by multiplying the numerator and denominator by {\color{blue}{9}} :

\dfrac{2 \times {\color{blue}{9}}}{1\times{\color{blue}{9}}} = \dfrac{18}{9}

So now, we have to find:

\dfrac{31}{9} - \dfrac{18}{9}

To subtract two fractions with like denominators, we subtract the numerators and keep the denominators the same:

\begin{align*} \dfrac{31}{9} - \dfrac{18}{9} = \dfrac{31 - 18}{9} = \dfrac{13}{9} \end{align*}

Finally, we convert to a mixed number:

13 \div 9 = 1 \, \textrm{R} \, 4

So our final answer is 1 \, \dfrac{4}{9}.

FLAG

Expressed as a mixed number, what is $\dfrac{17}{3}-4?$

a
$3\,\dfrac{1}{3}$
b
$1\,\dfrac{2}{3}$
c
$2\,\dfrac{1}{3}$
d
$2\,\dfrac{2}{3}$
e
$1\,\dfrac{1}{3}$

$3-\dfrac{2}{5}=$

a
$2\,\dfrac{3}{5}$
b
$3\,\dfrac{1}{5}$
c
$2\,\dfrac{1}{5}$
d
$2\,\dfrac{2}{5}$
e
$3\,\dfrac{2}{5}$

Julia had 4 liters of orange juice, but she accidentally spilled \dfrac{15}{8} liters of juice. Expressed as a mixed number, how much juice is left?

EXPLANATION

To find out how much juice is left, we have to calculate the difference 4 - \dfrac{15}{8}.

To subtract \dfrac{15}{\color{blue}{8}} from 4 , we need to express the whole number 4 as an equivalent fraction with a denominator of {\color{blue}{8}}.

First, we write 4 as an improper fraction:

\dfrac{4}{1}

Then, we put this fraction over a denominator of \color{blue}8 by multiplying the numerator and denominator by {\color{blue}{8}} :

\dfrac{4 \times {\color{blue}{8}}}{1\times{\color{blue}{8}}} = \dfrac{32}{8}

So now, we have to find:

\dfrac{32}{8} - \dfrac{15}{8}

To subtract two fractions with like denominators, we subtract the numerators and keep the denominators the same:

\begin{align*} \dfrac{32}{8} - \dfrac{15}{8} = \dfrac{32 - 15}{8} = \dfrac{17}{8} \end{align*}

Finally, we convert to a mixed number:

17 \div 8 = 2 \, \textrm{R} \, 1

Therefore, 2 \, \dfrac{1}{8} liters of juice is left.

FLAG

George went to the beach with his family in a car. Along the way, George stopped at a store and bought $3$ kilograms of almonds. When they arrived, $\dfrac{7}{5}$ kilograms remained. Expressed as a mixed number, how many kilograms of almonds did George and his family eat on their way to the beach?

a
$2 \, \dfrac{4}{5}$ kilograms
b
$1 \, \dfrac{4}{5}$ kilograms
c
$1 \, \dfrac{1}{5}$ kilograms
d
$1 \, \dfrac{3}{5}$ kilograms
e
$2 \, \dfrac{2}{5}$ kilograms

Jeremy decides to visit a Zoo that is $4$ miles away from his home, on a straight road. After leaving home, Jeremy travels for $\dfrac{3}{8}$ miles and stops at a convenience store to buy ice cream. What is the distance from the store to the Zoo?

a
$3\,\dfrac 3 4$ miles
b
$3\,\dfrac 5 8$ miles
c
$3\,\dfrac 3 8$ miles
d
$3\,\dfrac 1 2$ miles
e
$3\,\dfrac 7 8$ miles
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