- Equivalent Fractions
- Reducing Fractions To Lowest Terms
- Raising Fractions To Higher Terms

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- Equivalent Fractions
- Reducing Fractions To Lowest Terms
- Raising Fractions To Higher Terms

Fractions that have the same value are called equivalent fractions.

For example,

It is often useful to convert one fraction to an equivalent fraction that has reduced values in the numerator and denominator. When a fraction is converted to an equivalent fraction that has the smallest numerator and denominator in the collection of equivalent fractions, it is said to be reduced to lowest terms. The conversion process is called reducing a fraction.

We can reduce a fraction to lowest terms by

- Expressing the numerator and denominator as a product of prime numbers. (Find the prime factorization of the numerator and denominator. See Section R.2 for this technique.)
- Divide the numerator and denominator by all common factors. (This technique is commonly called “cancelling.”)

Reduce each fraction to lowest terms.

Equally important as reducing fractions is raising fractions to higher terms. Raising a fraction to higher terms is the process of constructing an equivalent fraction that has higher values in the numerator and denominator. The higher, equivalent fraction is constructed by multiplying the original fraction by 1.

Notice that

This observation helps us suggest the following method for raising a fraction to higher terms.

A fraction can be raised to higher terms by multiplying both the numerator and denominator by the same nonzero number.

For example,

How did we know to choose 8 as the proper factor? Since we wish to convert 4 to 32 by multiplying it by some number, we know that 4 must be a factor of 32. This means that 4 divides into 32. In fact,

Determine the missing numerator or denominator.

For the following problems, reduce, if possible, each fraction lowest terms.

3

For the following problems, determine the missing numerator or denominator.

6

12

20

75

48