Add, Subtract, Multiply & Divide Fractions & Mixed Numbers

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  • 0:01 Operations with Fractions
  • 0:39 Adding Fractions &…
  • 1:30 Subtracting Fractions…
  • 1:59 Multiplying Fractions…
  • 2:30 Dividing Fractions &…
  • 3:02 Lesson Summary
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Lesson Transcript
Instructor: Bethany Calderwood

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

Fractions and mixed numbers are very important in math. Do you know how to use them? In this lesson you'll learn how to work with fractions and mixed numbers while using the four basic operations of arithmetic: addition, subtraction, multiplication, and division.

Operations with Fractions.

Suzanne is baking a cake, but someone scrambled her recipe. Instead of the measurement for each ingredient, she has a math equation. Can you use the clues to find out how much of each ingredient to include in the cake?


Each equation in Suzanne's recipe includes fractions, or parts of numbers, and some of the equations also include mixed numbers, or a whole number and a fraction. Fractions and mixed numbers follow some of the same rules when we add, subtract, multiply, and divide, but there are some other rules we follow too. Let's use the rules for fractions to fix Suzanne's recipe.

Adding Fractions and Mixed Numbers

Take a look at this equation for the cups of flour, which asks us to add fractions together.

adding fractions

Since the original fractions, shown in green, have different denominators (remember, the denominators are bottom numbers), you'll have to convert them to equivalent fractions with a common denominator. Here, 6 is the common denominator, so the equivalent fractions are shown in red. They are equal to the same part of the whole number, but now you can add them together.

When adding fractions, add all of the numerators (top numbers), and keep the same denominator (bottom numbers), like in the blue fraction. Put your answer in simplest terms. For example, if the numerator is larger than the denominator, divide the numerator by the denominator to get a mixed number, like the answer in black (1 5/6).

Subtracting Fractions and Mixed Numbers

Now let's take a look at this equation for cups of sugar and subtract some mixed numbers.

subtracting fractions

The fractions in green have different denominators: 2 and 4. Here, you'll have to find the common denominator, or 4, to get the fractions in red. Subtract the whole numbers. When you subtract the fractions, subtract the numerators and keep the denominator the same. This answer is already in simplest terms, so you don't need to do anymore work.

Multiplying Fractions and Mixed Numbers

Let's move onto this equation for teaspoons of baking powder, which asks us to multiply some mixed numbers.

multiplying fractions

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