Online Calculators

Adding Fractions Calculator

Add and Subtract Fractions
\[ = \frac{1}{16} \]Showing the Work:
With different bottom numbers find the Least Common Denominator (LCD)

LCD = 16

Multiplying top and bottom numbers to get the LCD in all of the denominators\[ = \frac{-1 \times 2}{8 \times 2} - \frac{1}{16} - \frac{3 \times 2}{8 \times 2} + \frac{5 \times 2}{8 \times 2} \]Rewriting the math problem with the equivalent fractions\[ = \frac{-2}{16} - \frac{1}{16} - \frac{6}{16} + \frac{10}{16} \]With the same denominators we can do math on just the numerators\[ = \frac{-2 - 1 - 6 + 10}{16} \]\[ = \frac{1}{16} \]

Calculator Use

Add and subtract fractions with this calculator and see the work to solve the problem.

Select the number of fractions in your problem and input numerators (top numbers) and denominators (bottom numbers) in the calculator fields. Click the Calculate button to solve the equation and show the work.

You can add and subtract 3 fractions, 4 fractions, 5 fractions or up to 9 fractions at once.

How to Add and Subtract Fractions

When the Denominators are the Same

When fractions have the same bottom numbers you can add or subtract the top numbers and put the result over the common denominator. If possible you can simplify the fraction to lowest terms or a mixed number.

When the Denominators are Different

When fractions have unlike denominators (bottom numbers) the first step is to find equivalent fractions so all of the denominators become the same number. Find the Least Common Denominator (LCD) and rewrite all fractions as equivalent fractions using the LCD as the denominator.

When the denominators are the same you can add or subtract the numerators and put the result over the common denominator. If possible you can simplify the fraction to lowest terms or a mixed number.

How to Work With Negative Fractions

When you are adding a negative fraction you can rewrite the equation as subtracting a positive fraction. For example 4/5 + -3/10 = 4/5 - 3/10.

When you are subtracting a negative fraction it is the same as adding a positive fraction. You can rewrite the problem this way. For example 4/5 - -3/10 = 4/5 + 3/10.

This calculator rewrites negative fractions when it shows the work to find the answer.

Simplifying Operations on Negative Numbers

Whether you are working with fractions, whole numbers or decimals, use these guidelines when adding and subtracting positive and negative numbers.

Rules for Number Signs
Add positive or subtract negative
(+ and +) or (- and -)
Add the numbers +
Sign of the resulting number is the same as the operation, + or
Add negative or subtract positive
(+ and -) or (- and +)
Subtract the numbers
Sign of the resulting number is the same as the sign of the larger number

Why is it Important to Understand Fractions?

Fractions come up everywhere in everyday life. When following cooking recipes you'll usually see fractions in ingredient quantities. You might need a 1/2 cup of flour or 3/4 teaspoon of salt. If you're making twice the recipe you will need to know how to add fractions together so your dish turns out as expected.

Or say you wanted to make 2/3 a recipe. You would need to subtract 1/3 from each of the ingredient amounts to come up with accurate measurements for your adjusted recipe.

Fractions can also be important in budgeting your finances. Say you wanted to allocate your income into 6 categories of expenses: housing, utilities, groceries, transportation, entertainment and savings. Maybe you already know that 1/4 of your income goes toward housing, 1/8 goes toward utilites, and another 1/8 goes toward groceries. You need to be able to work with fractions to figure out how to optimize your budget to put the rest of your money toward the remaining categories where you have flexibility: transportation, entertainment and savings.

You can add 1/8 + 1/8 to get 2/8. And you can reduce this fraction to 1/4, so you see that the amount of your income that goes toward predictable expenses is 1/4 + 1/4 = 1/2. If half of your income is accounted for, you can continue to use fractions to make the most of your remaining money, in ways that are important to you.


Cite this content, page or calculator as:

Furey, Edward "Adding and Subtracting Fractions Step by Step - CalculatorSoup" at https://www.calculatorsoup.com/calculators/math/adding-fractions-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: April 10, 2024

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