Example 2
Completion requirements
| Example 2 |
Simplify the expression \(\frac{6\thinspace 380}{13\thinspace 050}\).
Method 1: GCF
Step 1: Determine the GCF.
\(\begin{align}
6\thinspace 380 &= {\color{red}2} \times 2 \times {\color{red}5} \times 11 \times {\color{red}29} \\
13\thinspace 050 &= {\color{red}2} \times 3 \times 3 \times {\color{red}5} \times 5 \times {\color{red}29} \\
{\rm{GCF}} &= 2 \times 5 \times 29 = 290 \\
\end{align}\)
Step 2: Divide the numerator and denominator by the GCF.
Method 2: Prime Factorization
Step 1: Write out the prime factors of each number.
Step 2: Reduce the numerator and denominator. Then, simplify.
Step 1: Determine the GCF.
\(\begin{align}
6\thinspace 380 &= {\color{red}2} \times 2 \times {\color{red}5} \times 11 \times {\color{red}29} \\
13\thinspace 050 &= {\color{red}2} \times 3 \times 3 \times {\color{red}5} \times 5 \times {\color{red}29} \\
{\rm{GCF}} &= 2 \times 5 \times 29 = 290 \\
\end{align}\)
Step 2: Divide the numerator and denominator by the GCF.
\[\frac{{6\thinspace 380 \div 290}}{{13\thinspace 050 \div 290}} = \frac{22}{45}\]
Method 2: Prime Factorization
Step 1: Write out the prime factors of each number.
\[\frac{{6\thinspace 380}}{{13\thinspace 050}} = \frac{{2 \times 2
\times 5 \times 11 \times 29}}{{2 \times 3 \times 3 \times 5 \times 5
\times 29}}\]
Step 2: Reduce the numerator and denominator. Then, simplify.
\[\frac{{{\color{red} \cancel {\color{#444}2}} \times 2 \times{\color{red}
\cancel {\color{#444}{5}}} \times 11 \times {\color{red} \cancel {\color{#444}{29}}}}}{{{\color{red} \cancel
{\color{#444}2}} \times 3 \times 3 \times{\color{red} \cancel {\color{#444}{5}}} \times 5 \times
{\color{red} \cancel {\color{#444}{29}}}}} = \frac{{22}}{{45}}\]