To multiply the fractions [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{5}{4}\)[/tex], we follow several well-defined steps. Let's go through each one carefully.
### Step 1: Multiply the Numerators
First, we multiply the numerators (top numbers) of the given fractions.
So, the numerators are:
[tex]\[ 2 \times 5 = 10 \][/tex]
### Step 2: Multiply the Denominators
Next, we multiply the denominators (bottom numbers).
So, the denominators are:
[tex]\[ 8 \times 4 = 32 \][/tex]
Therefore, the resulting fraction from multiplying [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{5}{4}\)[/tex] is:
[tex]\[ \frac{10}{32} \][/tex]
### Step 3: Simplify the Fraction
Now, we need to simplify the resulting fraction [tex]\(\frac{10}{32}\)[/tex]. To do this, we find the greatest common divisor (GCD) of 10 and 32, which helps us reduce the fraction to its simplest form.
The GCD of 10 and 32 is 2.
To simplify the fraction:
1. Divide the numerator by the GCD:
[tex]\[ \frac{10}{2} = 5 \][/tex]
2. Divide the denominator by the GCD:
[tex]\[ \frac{32}{2} = 16 \][/tex]
So, the simplified fraction is:
[tex]\[ \frac{5}{16} \][/tex]
### Summary
The step-by-step multiplication of the given fractions [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{5}{4}\)[/tex] and simplification process leads us to the following results:
- The product before simplification: [tex]\(\frac{10}{32}\)[/tex]
- The simplified product: [tex]\(\frac{5}{16}\)[/tex]
Thus, the fraction [tex]\(\frac{2}{8} \times \frac{5}{4}\)[/tex] simplifies to:
[tex]\[ \frac{5}{16} \][/tex]
