When adding two fractions with the same denominator, we

  • add their numerators, and

  • keep the denominator the same.

For example, let's compute the following sum:

\dfrac 1 3 + \dfrac 1 3

To add these numbers, we add the numerators and keep the denominators the same. Therefore,

\begin{align*} \dfrac 1 3 + \dfrac 1 3 = \dfrac{1+1}{3} = \dfrac 2 3. \end{align*}

We can use a fraction model to confirm this result:

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Find the value of \dfrac 2 9 + \dfrac 3 9.

EXPLANATION

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

\begin{align*} \dfrac 2 9 + \dfrac 3 9 = \dfrac{2+3}{9} = \dfrac 5 9. \end{align*}

FLAG
Practice: Adding Fractions

$\dfrac 3 7 + \dfrac 2 7 = $

a
$\dfrac 5 7$
b
$\dfrac 5 {14}$
c
$\dfrac 4 7$
d
$\dfrac 2 7$
e
$\dfrac 6 7$
Practice: Adding Fractions

$\dfrac{4}{7} + \dfrac{5}{7} =$

a
b
c
d
e

What is the value of \dfrac 3 8 + \dfrac 1 8 ?

EXPLANATION

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

\begin{align*} \dfrac 3 8 + \dfrac 1 8 = \dfrac{3+1}{8} = \dfrac 4 8. \end{align*}

We can simplify this fraction by dividing the numerator and the denominator by 4{:}

\dfrac{4}{8} = \dfrac{4\div 4}{8\div 4} = \dfrac{1}{2}

Therefore, we conclude that

\dfrac 3 8 + \dfrac 1 8 = \dfrac 1 2.

FLAG

$\dfrac 1 4 + \dfrac 1 4 =$

a
$\dfrac 1 2$
b
$\dfrac 1 4$
c
$\dfrac 1 8$
d
$\dfrac{1}{16}$
e
$\dfrac 2 8$

Expressed as a fraction in lowest terms,

a
b
c
d
e

Expressed as a fraction in lowest terms,

a
b
c
d
e

Find the value of \dfrac 2 3 + \dfrac 2 3.

EXPLANATION

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

\begin{align*} \dfrac 2 3 + \dfrac 2 3 = \dfrac{2+2}{3} = \dfrac 4 3. \end{align*}

We then convert \dfrac 4 3 to a mixed number:

4\div 3 = 1\,\textrm{R}1 = 1\,\dfrac 1 3

Therefore, we conclude that

\dfrac 2 3 + \dfrac 2 3 = 1\,\dfrac 1 3.

FLAG

$\dfrac 3 5 + \dfrac 3 5 = $

a
$1\,\dfrac 1 5$
b
$\dfrac 1 5$
c
$1$
d
$\dfrac{6}{10}$
e
$1\,\dfrac 2 5$

Expressed as a mixed number in lowest terms,

a
b
c
d
e
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