Question

What is the advantage of simplifying first? What would you need to do with mixed numbers before multiplying them? Explain?

Accepted Answer

To reduce a fraction to its lowest terms by cancelling to the lowest common factor for both numerator and denominator or to condense an algebraic expression by grouping and combining similar terms. Simplifying makes a fractions more understandable and solvable.

The advantage of cross-cancellation over multiplying and then simplifying is that before the numbers are multiplied they are smaller and easier to work with.

A mixed number is a number that contains a whole number and a fraction, for instance $5 \frac{3}{5}$ is a mixed number.

Mixed numbers can be multiplied by first converting them to improper fractions.

For example : Multiply $2 \frac{1}{2} \times 3 \frac{1}{5}$

Convert the mixed numbers to improper fractions first.

$2 \frac{1}{2} \times 3 \frac{1}{5} = \frac{2 \times 2 + 1}{2} \times \frac{3 \times 5 + 1}{5} = \frac{5}{2} \times \frac{16}{5}$

Multiply the numerators from each fraction to each other and place the product at the top and multiply the denominators of each fraction by each other (the numbers on the bottom). The product is the denominator of the new fraction.

$\frac{5}{2} \times \frac{16}{5} = \frac{16 \times 5}{2 \times 5} = \frac{80}{10}$

Simplify or reduce the final answer to the lowest terms possible.

$\frac{80}{10} = 8$

David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Fractions Human Connections, Exercise 9: Reflect and discuss 4

David Weber Mathematics Solutions for Exercise - David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Fractions Human Connections, Exercise 9: Reflect and discuss 4

Questions from David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Fractions Human Connections, Exercise 9: Reflect and discuss 4 with Hints & Solutions

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