Mixed & Improper Fractions
Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
What a learner can do afterwards
- Add, subtract, multiply, and divide with positive and negative integers
- Apply formal written methods to calculations with decimals of any size
- Perform all four operations with proper fractions, improper fractions, and mixed numbers
The lesson
You already know how to add, multiply, and divide fractions. Now you will work with two ways of writing fractions bigger than one whole. A mixed number, like 2 1/4, shows a whole number next to a fraction. An improper fraction, like 9/4, shows the same amount with one fraction where the top number is bigger than the bottom number.
To change an improper fraction to a mixed number, divide the top number by the bottom number. For 9/4: 9 divided by 4 is 2, remainder 1. So 9/4 = 2 1/4.
To change a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. For 2 1/4: 2 x 4 = 8, then 8 + 1 = 9. Keep the same denominator, so 2 1/4 = 9/4.
A negative sign in front of a mixed number covers the whole thing, not just the whole number part. -1 1/2 means the same as -(3/2). Convert to an improper fraction first, keeping the negative sign, before you add, subtract, multiply, or divide.
Change mixed numbers and improper fractions into the same form first, keep negative signs with the whole amount, then use the written methods you already know.
Watch it
Where it sits
Learn first
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Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.