Example
Multiply: [latex]3\frac{1}{3}\cdot \frac{5}{8}[/latex]
Solution:
|
[latex]3\frac{1}{3}\cdot \frac{5}{8}[/latex] |
| Convert [latex]3\frac{1}{3}[/latex] to an improper fraction. |
[latex]\frac{10}{3}\cdot \frac{5}{8}[/latex] |
| Multiply. |
[latex]\frac{10\cdot 5}{3\cdot 8}[/latex] |
| Look for common factors. |
[latex]\frac{\color{red}{2}\cdot 5\cdot 5}{3\cdot \color{red}{2} \cdot 4}[/latex] |
| Remove common factors. |
[latex]\frac{5\cdot 5}{3\cdot 4}[/latex] |
| Simplify. |
[latex]\frac{25}{12}[/latex] |
Notice that we left the answer as an improper fraction, [latex]\frac{25}{12}[/latex], and did not convert it to a mixed number. In algebra, it is preferable to write answers as improper fractions instead of mixed numbers. This avoids any possible confusion between [latex]2\frac{1}{12}[/latex] and [latex]2\cdot \frac{1}{12}[/latex].
Example
Multiply, and write your answer in simplified form: [latex]2\frac{4}{5}\left(-1\frac{7}{8}\right)[/latex]
Answer:
Solution:
| [latex]2\frac{4}{5}\left(-1\frac{7}{8}\right)[/latex] |
| Convert mixed numbers to improper fractions. |
[latex]\frac{14}{5}\left(-\frac{15}{8}\right)[/latex] |
| Multiply. |
[latex]-\frac{14\cdot 15}{5\cdot 8}[/latex] |
| Look for common factors. |
[latex]-\frac{\color{red}{2} \cdot 7\cdot \color{red}{5} \cdot 3}{\color{red}{5} \cdot \color{red}{2}\cdot 4}[/latex] |
| Remove common factors. |
[latex]-\frac{7\cdot 3}{4}[/latex] |
| Simplify. |
[latex]-\frac{21}{4}[/latex] |
Example
Divide, and write your answer in simplified form: [latex]3\frac{4}{7}\div 5[/latex]
Answer:
Solution:
|
[latex]3\frac{4}{7}\div 5[/latex] |
| Convert mixed numbers to improper fractions. |
[latex]\frac{25}{7}\div \frac{5}{1}[/latex] |
| Multiply the first fraction by the reciprocal of the second. |
[latex]\frac{25}{7}\cdot \frac{1}{5}[/latex] |
| Multiply. |
[latex]\frac{25\cdot 1}{7\cdot 5}[/latex] |
| Look for common factors. |
[latex]\frac{\color{red}{5} \cdot 5\cdot 1}{7\cdot \color{red}{5} }[/latex] |
| Remove common factors. |
[latex]\frac{5\cdot 1}{7}[/latex] |
| Simplify. |
[latex]\frac{5}{7}[/latex] |
Example
Divide: [latex]2\frac{1}{2}\div 1\frac{1}{4}[/latex]
Answer:
Solution:
| [latex]2\frac{1}{2}\div 1\frac{1}{4}[/latex] |
| Convert mixed numbers to improper fractions. |
[latex]\frac{5}{2}\div \frac{5}{4}[/latex] |
| Multiply the first fraction by the reciprocal of the second. |
[latex]\frac{5}{2}\cdot \frac{4}{5}[/latex] |
| Multiply. |
[latex]\frac{5\cdot 4}{2\cdot 5}[/latex] |
| Look for common factors. |
[latex]\frac{\color{red}{5} \cdot \color{red}{2} \cdot 2}{\color{red}{2} \cdot 1\cdot \color{red}{5}}[/latex] |
| Remove common factors. |
[latex]\frac{2}{1}[/latex] |
| Simplify. |
[latex]2[/latex] |
