Skill 31
Add and Subtract Fractions, Mixed Numbers, and Decimals

Now that you understand mixed numbers and decimals, let’s start using them in mathematical operations.

Add and Subtract Fractions with Different Denominators. Add and Adding fractions with different denominators is like mixing apples and oranges. Before you can add them, you need to rewrite one or both fractions so that they both have the same denominator. You can change to now both fractions have a denominator of 4. Add the numerators: Convert that to a mixed number to get Subtract those same numbers: Don’t forget the minus sign!

Now let’s get a little more complicated. Add and You need to put these fractions into common terms. Convert both to fractions with a denominator of 6. To convert to a fraction with a denominator of 6, you need to multiply the denominator 2 by 3. But if you multiply the denominator of a fraction by a number, you have to multiply the numerator by the same number; otherwise you change the value of the fraction. Multiply both numerator and denominator of by 3 to get Convert to a fraction with a denominator of 6. Multiply both numerator and denominator by 2. The result is Add: Change to a mixed number to get

Add and Subtract Mixed Numbers. Add and Add both whole numbers: 3 + 7 = 10. Then deal with the fractions. As always, you need to put them into common terms. Convert into a fraction with a denominator of 8 by multiplying both numerator and denominator by 2. The result is Now add: Add that number to the whole number that you calculated previously: Let’s try subtraction. is the same as Subtract the 3 from 7 to get 4. Then subtract the from the to get . Because that fraction is a negative number, you need to subtract it from your whole number total of 4. The number 4 is the same as Subtract:

A second way to perform this calculation is to transform each mixed number into a fraction. Then subtract:

Decimals are easy! Just add or subtract as you would normally. For example: 32.45 + 3.75 = 36.2. Or try 32.45 − 3.75. Subtract as normal to get 28.7.

Test Yourself!

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66.66 + 33.2 =

66.66 − 33.2 =

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997.43 − 38.96 =

4,446.98 + 37.3471 =

37.34 + 0.947423 =

0.08041 − 0.02009 =

3.046 − 2.981 =