Sure! Let's simplify each side of the equation step-by-step.
1. Simplify the fraction on the left side:
[tex]\[
\frac{6}{15}
\][/tex]
- To simplify this fraction, find the greatest common divisor (GCD) of 6 and 15, which is 3.
- Divide the numerator and denominator by 3.
[tex]\[
\frac{6 \div 3}{15 \div 3} = \frac{2}{5}
\][/tex]
- Simplifying [tex]\(\frac{2}{5}\)[/tex] as a decimal, we get:
[tex]\[
\frac{2}{5} = 0.4
\][/tex]
So, the simplified left side is:
[tex]\[
\frac{6}{15} = 0.4
\][/tex]
2. Simplify the multiplication on the right side:
[tex]\[
3 \cdot \frac{16}{12}
\][/tex]
- First, simplify the fraction [tex]\(\frac{16}{12}\)[/tex]. Find the GCD of 16 and 12, which is 4.
- Divide the numerator and denominator by 4.
[tex]\[
\frac{16 \div 4}{12 \div 4} = \frac{4}{3}
\][/tex]
- Now multiply 3 by the simplified fraction:
[tex]\[
3 \cdot \frac{4}{3}
\][/tex]
- The 3's in the numerator and the denominator cancel each other out, leaving:
[tex]\[
4
\][/tex]
So, the simplified right side is:
[tex]\[
3 \cdot \frac{16}{12} = 4
\][/tex]
Thus, comparing both sides, we have:
[tex]\[
\frac{6}{15} = 0.4
\][/tex]
and
[tex]\[
3 \cdot \frac{16}{12} = 4
\][/tex]
So, the simplified forms are:
[tex]\[
0.4 \text{ and } 4
\][/tex]
