1. Multiplying and Dividing Fractions
Chapter 1 / Whole Numbers and Introduction to Algebra
Section 4.3
Multiplying and Dividing Fractions

2. Multiplying Fractions
Chapter 1 / Whole Numbers and Introduction to Algebra
Multiplying Fractions of is 1
The word “of” means multiplication and “is” means equal to.
Martin-Gay, Prealgebra, 5ed

3. Martin-Gay, Prealgebra, 5edof is
means
Martin-Gay, Prealgebra, 5ed

4. Multiplying Two Fractions
Chapter 1 / Whole Numbers and Introduction to Algebra
Multiplying Two Fractions
If a, b, c, and d are numbers and b and d are not 0, then
In other words, to multiply two fractions, multiply the numerators and multiply the denominators.
Martin-Gay, Prealgebra, 5ed

5. Chapter 1 / Whole Numbers and Introduction to Algebra
Examples
If the numerators have common factors with the denominators, divide out common factors before multiplying. 1 or 2
Martin-Gay, Prealgebra, 5ed

6. Chapter 1 / Whole Numbers and Introduction to Algebra
Examples or 2 1
Martin-Gay, Prealgebra, 5ed

7. Chapter 1 / Whole Numbers and Introduction to Algebra
Helpful Hint
Recall that when the denominator of a fraction contains a variable, such as
we assume that the variable is not 0.
Martin-Gay, Prealgebra, 5ed

8. Evaluating Expressions with Fractional Bases
Chapter 1 / Whole Numbers and Introduction to Algebra
Evaluating Expressions with Fractional Bases
The base of an exponential expression can also be a fraction.
Martin-Gay, Prealgebra, 5ed

9. Reciprocal of a Fraction
Chapter 1 / Whole Numbers and Introduction to Algebra
Reciprocal of a Fraction
Two numbers are reciprocals of each other if their product is 1. The reciprocal of the fraction is
because
Martin-Gay, Prealgebra, 5ed

10. Dividing Two Fractions
Chapter 1 / Whole Numbers and Introduction to Algebra
Dividing Two Fractions
If b, c, and d are not 0, then
In other words, to divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Martin-Gay, Prealgebra, 5ed

11. Chapter 1 / Whole Numbers and Introduction to Algebra
Helpful Hint
Every number has a reciprocal except 0. The number 0 has no reciprocal. Why?
There is no number that when multiplied by 0 gives the result 1.
Martin-Gay, Prealgebra, 5ed

12. Chapter 1 / Whole Numbers and Introduction to Algebra
Helpful Hint
When dividing by a fraction, do not look for common factors to divide out until you rewrite the division as multiplication.
Do not try to divide out these two 2s.
Martin-Gay, Prealgebra, 5ed

13. Multiplying and Dividing with Fractional Replacement Values
Chapter 1 / Whole Numbers and Introduction to Algebra
Multiplying and Dividing with Fractional Replacement Values
If x = and y = , evaluate
Replace x with and y with .
Martin-Gay, Prealgebra, 5ed