64 Part 1: The World of Numbers
WORLDLY WISDOM
To quickly convert a mixed number to an improper fraction, multiply the denominator
by the whole number and add to the numerator. 6
5
8865
848 5
853(^558)
111
5. To change
an improper fraction to a mixed number, divide numerator by denominator and make
any remainder the numerator of the fraction.^47356 with 1 left over, so 617.
CHECK POINT
Perform each multiplication or division problem.
11.^2332150
12. 1584252
13. 49631415
- (^4834178)
- (^5473423)
Adding and Subtracting Fractions
Adding and subtracting fractions requires that the fractions have the same denominator.
Denominators tell you what kind of things you have, and it’s difficult to even think about adding
unless you have the same kind of things, or a common denominator. When you have a common
denominator, you simply add the numerators and keep the denominator. 113111751011. Three of
these things plus 7 of these things equals 10 of these same things.
DEFINITION
A common denominator is one that is a multiple of each of the denominators of two
or more fractions. The least common denominator is the least common multiple of the
denominators.
Your real work comes when the fractions don’t have a common denominator to start out. It’s not
impossible to add or subtract fractions with different denominators, but you must change their
appearance first. You have to change them to equivalent fractions with a common denominator.
A common denominator is a number that is a multiple of each of the denominators you were
given. Ideally, you should choose the lowest number that can be evenly divided by each of the
denominators in your equation. That’s called the lowest or least common denominator. Larger
multiples will work, but you will have to simplify at the end. Let’s look at some examples.