SOLUTION

Convert the improper fraction to a mixed number.

ALTERNATIVE SOLUTION

● A mixed number $\color{chocolate}a\color{black}\dfrac{\color{#3a5998}b}{\color{#3a5998}c}$ can be written as $\color{chocolate}a\color{black}+\dfrac{\color{#3a5998}b}{\color{#3a5998}c}$

$\mathrm{\color{chocolate}1\color{black}\dfrac{\color{#3a5998}2}{\color{#3a5998}3}+\dfrac{\color{#3a5998}1}{\color{#3a5998}2}}$ $=\mathrm{\color{chocolate}1\color{black}+\dfrac{\color{#3a5998}2}{\color{#3a5998}3}+\dfrac{\color{#3a5998}1}{\color{#3a5998}2}}$

● Add the whole and fraction parts separately.

$\mathrm{\color{chocolate}1\color{black}+\dfrac{\color{#3a5998}2}{\color{#3a5998}3}+\dfrac{\color{#3a5998}1}{\color{#3a5998}2}}$ $=\mathrm{\color{chocolate}1\color{black}+\left(\dfrac{\color{#3a5998}2}{\color{#3a5998}3}+\dfrac{\color{#3a5998}1}{\color{#3a5998}2}\right)}$

● Sum of the fraction parts is $\mathrm{\dfrac{\color{#3a5998}7}{\color{#3a5998}6}}$ .

$\mathrm{\dfrac{\color{#3a5998}2}{\color{#3a5998}3}+\dfrac{\color{#3a5998}1}{\color{#3a5998}2}=\dfrac{\color{#3a5998}7}{\color{#3a5998}6}}$

● Convert $\mathrm{\dfrac{\color{#3a5998}7}{\color{#3a5998}6}}$ to a mixed number.

$\mathrm{\dfrac{\color{#3a5998}7}{\color{#3a5998}6}=\color{#3a5998}1\dfrac{\color{#3a5998}1}{\color{#3a5998}6}}$

● Add this number to the sum of the whole numbers.

$\mathrm{\color{chocolate}1\color{black}+\color{#3a5998}1\color{black}\dfrac{\color{#3a5998}1}{\color{#3a5998}6}}$ $=\mathrm{\color{chocolate}1\color{black}+\color{#3a5998}1\color{black}+\dfrac{\color{#3a5998}1}{\color{#3a5998}6}}$ $=\mathrm{\color{black}2\color{black}+\dfrac{\color{black}1}{\color{black}6}}$ $=\mathrm{\color{olive}2\color{black}\dfrac{\color{olive}1}{\color{olive}6}}$

OTHER INFORMATION

👉 Click here to see how to find the LCM of 3 and 2.

👉 Click here to see how to convert $\mathrm{1\dfrac{2}{3}}$ to an improper fraction.

👉 Click here to see how to convert $\mathrm{\dfrac{13}{6}}$ to a mixed number.

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INFORMATION

There are two main methods that we use to calculate the sum of a mixed number and a fraction. In the first method, we convert the mixed number to an improper fraction and apply the same rules as the addition of fractions. In the second method, we add the whole and fractional parts, separately. The calculator above describes the solution using both methods.

WHAT IS ADDING MIXED NUMBERS WITH FRACTIONS CALCULATOR?

Adding mixed numbers with fractions calculator,

Calculates the addition of a mixed numbers with a fraction; and
Illustrates the solution steps with animations.

HOW TO USE THE ADDING MIXED NUMBERS WITH FRACTIONS CALCULATOR?

You can use the adding mixed numbers with fractions calculator in two ways.

USER INPUTS

You can enter positive or negative whole numbers, fractions or mixed numbers to the input boxes and click on the "CALCULATE" button. The result and explanations appaer below the calculator
RANDOM INPUTS

You can click on the DIE ICON next to the input boxes. If you use this property, two random numbers are generated and entered to the calculator, automatically. You can see the result and explanations below the calculator. You can create your own examples and practice using this property.
SELECTING THE INPUT TYPE

You can choose whether the first or the second addend is a mixed number using the dropdown box on top of the input boxes.
CLEARING THE INPUT BOXES

To find the summation of some other numbers you can clear the input box by clicking on the CLEAR button under the input box.
COPYING & DOWNLOADING THE SOLUTION
- You can copy the generated solution by clicking on the "Copy Text" link, appaers under the solution panel.
- Even you can download the solution as an image file with .jpg extension if you click on the "Download Solution" link at the bottom of the solution panel. You can share the downloaded image file.