Calculations with fractions, decimals and negatives
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
1 · Read
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.
More to read
Visualize Fractions
A fraction tells you about equal parts of a whole. In this lesson you learn to picture improper fractions and mixed numbers, and to switch between them. An improper fraction like 7/4 has a numerator that is as big as or bigger than its denominator. It means more than one whole. A mixed number like 1 3/4 mixes a whole number with a fraction. To turn an improper fraction into a mixed number, divide the numerator by the denominator. The answer is the whole number part, and the remainder goes over the same denominator. So 7/4 = 1 3/4. To go the other way, multiply the whole number by the denominator, add the numerator, and keep the denominator. You also practice placing fractions on a number line and putting fractions in order from smallest to largest.
Fractions Key Concepts
A mixed number is a whole number plus a fraction, like 2 1/2. A proper fraction has a numerator smaller than its denominator, like 3/4. An improper fraction has a numerator that is equal to or bigger than its denominator, like 5/5 or 7/4. To change an improper fraction into a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder goes over the same denominator. To change a mixed number into an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the denominator. Two fractions are equivalent if they name the same amount, like 1/2 and 2/4. These two forms always name the same value, just written in different ways.
How to Change Mixed Numbers to Improper Fractions
A mixed number has a whole number and a proper fraction, like 2 1/2. You can rewrite it as one fraction, called an improper fraction. For a mixed number a b/c, multiply the whole number a by the denominator c, then add the numerator b. Write the result over the same denominator c. Try it with 2 3/4. Multiply 2 x 4 = 8. Add the 3 to get 11. Keep the denominator 4. So 2 3/4 = 11/4. Why does this work? Each whole is made of 4 fourths, so 2 wholes are 8 fourths, plus 3 more fourths makes 11 fourths. Once your numbers are improper fractions, multiplying and dividing them becomes much easier.
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2 · Watch
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Where it sits
Optional connections
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Where this leads
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11 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.