Certainly! Let's go through the problem step by step to find the solution.
We start with the expression:
[tex]\[
\frac{22}{55} \times 124
\][/tex]
### Step 1: Simplify the Fraction
First, we need to simplify the fraction [tex]\(\frac{22}{55}\)[/tex]. To do this, we look for the greatest common divisor (GCD) of 22 and 55.
- Both 22 and 55 can be divided by 11.
So, we can simplify the fraction by dividing both the numerator and the denominator by their GCD:
[tex]\[
\frac{22 \div 11}{55 \div 11} = \frac{2}{5}
\][/tex]
Therefore, [tex]\(\frac{22}{55}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex].
### Step 2: Multiply by 124
Now, we take our simplified fraction [tex]\(\frac{2}{5}\)[/tex] and multiply it by 124:
[tex]\[
\frac{2}{5} \times 124
\][/tex]
### Step 3: Perform the Multiplication
Multiply the numerator of the fraction by 124:
[tex]\[
2 \times 124 = 248
\][/tex]
And place this over the original denominator:
[tex]\[
\frac{248}{5}
\][/tex]
### Step 4: Simplify the Result
We can simplify [tex]\(\frac{248}{5}\)[/tex] by performing the division:
[tex]\[
248 \div 5 = 49.6
\][/tex]
### Conclusion
So, the value of the expression [tex]\(\frac{22}{55} \times 124\)[/tex] is:
[tex]\[
49.6
\][/tex]
Additionally, during our calculations, we observed that the simplified fraction [tex]\(\frac{22}{55}\)[/tex] equals [tex]\(0.4\)[/tex]. Therefore, we have:
[tex]\[
\frac{22}{55} = 0.4
\][/tex]
So, multiplying this by 124, we get:
[tex]\[
0.4 \times 124 = 49.6
\][/tex]
Thus, the solution to the problem [tex]\(\frac{22}{55} \times 124\)[/tex] is [tex]\(0.4\)[/tex] and the resulting product is [tex]\(49.6\)[/tex].
