Fundamentals of Math

Fundamentals of Mathematics

Directions: Simplify the following fractions into their lowest forms.

5. 12 15

6. 20 30

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4 18

8. 15 45

7.

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Answer Key on Page 117

Types of Fractions Like people, fractions come in many forms - proper, improper, and mixed. A proper fraction is one whose numerator is less than its denominator (the top number is smaller than the bottom). Improper fractions are the opposite - their numerators are larger than their denominators (the top number is bigger than the bottom). Then there is the mixed case - with mixed numbers you have a fraction (traditionally proper) with its whole number counterpart.

Proper Fraction

Improper Fraction

Mixed Numbers

2 3

1 9

27 4

8

There is a rumor going around the mathematical world that improper fractions should always be converted to mixed numbers, and that is simply not true. Mixed numbers help us better understand the size of a number (for example you need 4 1 3 cup of flower vs. 13 3 ), but from an algebraic point of view, there is no real benefit to mixed numbers.

To Convert from an Improper Fraction to a Mixed Number

1. Divide the denominator into the numerator.

2. The quotient is the whole number counterpart, the remainder is the new numerator, and the denominator (the divisor) remains the same. Then simplify your remaining fractional part if possible.

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