We can use fraction models to subtract fractions from whole numbers.

For example, let's find the value of 1 - \dfrac{1}{6} using the model below:

We cannot subtract the two numbers straight away because they are split into different numbers of parts (i.e., they have different denominators).

In order to subtract, we split the whole number ( 1 in this case) into \color{red}6 equal parts, as follows:

Now, both shapes are split into \color{red}6 equal parts, and we have 6-1={\color{blue}{5}} parts in total. Therefore:

1 - \dfrac{1}{6} = \dfrac{\color{blue}5}{\color{red}6}

FLAG

Use the model below to find the value of 2 - \dfrac{1}{3} as an improper fraction.

EXPLANATION

All three shapes are already split into \color{red}3 equal parts, and we have 3+3-1 = {\color{blue}{5}} parts in total.

Therefore,

2 - \dfrac{1}{3} = \dfrac{{\color{blue}5}}{{\color{red}3}}.

FLAG

Using the fraction model above, find the value of $1-\dfrac 1 4.$

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

Using the model above, what is $3-\dfrac{5}{7}$ as an improper fraction?

a
$\dfrac{15}{7}$
b
$\dfrac{16}{7}$
c
$\dfrac{12}{7}$
d
$\dfrac{9}{7}$
e
$\dfrac{18}{7}$

Use the model above to determine the missing number in the statement below.

2 - \dfrac{3}{5} = \dfrac{\fbox{[math]\,\phantom{0}\,[/math]}}{5}

EXPLANATION

The shape on the right is split into \color{red}5 equal parts. We can split the first and second shapes into \color{red}5 equal parts as follows:

We have 5 + 5 - 3=\color{blue}7 shaded parts in total.

Therefore,

2 - \dfrac{3}{5} = \dfrac{\color{blue}7}{5}.

So, the missing number is \color{blue}7.

FLAG

Use the model above to determine the missing number in the statement below. \[ 1-\dfrac{2}{6} = \dfrac{\fbox{$\,\phantom{0}\,$}}{6} \]

a
$4$
b
$1$
c
$3$
d
$5$
e
$2$

Use the model above to determine the missing number in the statement below.

\[ 2 - \dfrac{2}{9} = \dfrac{\fbox{$\,\phantom{0}\,$}}{9} \]

a
$16$
b
$14$
c
$15$
d
$13$
e
$17$

Use a visual fraction model to find the value of 2 - \dfrac{1}{6} as an improper fraction.

EXPLANATION

Writing 2 - \dfrac{1}{6} as a visual fraction model, we get:

The shape on the right is split into \color{red}6 equal parts. We can split the other two shapes into \color{red}6 equal parts as follows:

We have 6 + 6 - 1 = \color{blue}11 shaded parts in total.

Therefore,

2 - \dfrac{1}{6} = \dfrac{\color{blue}11}{\color{red}6}.

FLAG

Use a visual fraction model to find the value of $2 - \dfrac{1}{5}$ as an improper fraction.

a
$\dfrac{7}{5}$
b
$\dfrac{8}{5}$
c
$\dfrac{6}{5}$
d
$\dfrac{9}{5}$
e
$\dfrac{10}{5}$

Use a visual fraction model to find the value of $3 - \dfrac{1}{4}$ as an improper fraction.

a
$\dfrac{7}{3}$
b
$\dfrac{5}{3}$
c
$\dfrac{17}{6}$
d
$\dfrac{9}{4}$
e
$\dfrac{11}{4}$
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