Lesson 4.4 Assignment: Multiplying and Dividing Mixed Numbers

A mixed number is a whole number combined with a fraction, such as $$2\frac{1}{2}$$ .

To multiply mixed numbers, convert them to improper fractions, multiply the fractions, and then convert back to a mixed number if necessary.

Convert the mixed numbers to improper fractions before dividing.

A reciprocal of a number is 1 divided by that number. For example, the reciprocal of 7 is $$\frac{1}{7}$$ .

Convert to improper fractions: $$\frac{20}{3} \times \frac{7}{2} = \frac{140}{6} = 23\frac{1}{3}$$ .

Convert to improper fractions: $$\frac{55}{6} \times \frac{2}{7} = \frac{110}{42} = 2\frac{2}{7}$$ .

To simplify a fraction means to reduce it to its lowest terms, where the numerator and denominator have no common factors.

Convert to improper fraction: $$\frac{17}{4} \times 2 = \frac{34}{4} = 8\frac{1}{2}$$ .

Multiply the whole number by the denominator, add the numerator, and place that over the original denominator.

Multiply by the reciprocal: $$\frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = 1\frac{1}{2}$$ .