Let's solve the given expression step by step:
1. First, identify the fractions:
- The first fraction is [tex]\(\frac{4}{5}\)[/tex].
- The second fraction is [tex]\(\frac{7}{5}\)[/tex].
- The third fraction is [tex]\(\frac{5}{25}\)[/tex].
2. Multiply the first two fractions:
- We need to multiply [tex]\(\frac{4}{5}\)[/tex] by [tex]\(\frac{7}{5}\)[/tex].
- Multiplying numerators together: [tex]\(4 \times 7 = 28\)[/tex].
- Multiplying denominators together: [tex]\(5 \times 5 = 25\)[/tex].
- This gives us: [tex]\(\frac{4}{5} \times \frac{7}{5} = \frac{28}{25}\)[/tex].
3. Now multiply the result by the third fraction:
- We have [tex]\(\frac{28}{25} \times \frac{5}{25}\)[/tex].
- Multiplying numerators together: [tex]\(28 \times 5 = 140\)[/tex].
- Multiplying denominators together: [tex]\(25 \times 25 = 625\)[/tex].
- This gives us: [tex]\(\frac{28}{25} \times \frac{5}{25} = \frac{140}{625}\)[/tex].
4. Simplify the final fraction:
- The fraction [tex]\(\frac{140}{625}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 140 and 625 is 5.
- Simplifying [tex]\(\frac{140}{625}\)[/tex] by dividing both the numerator and the denominator by 5, we get [tex]\(\frac{140 \div 5}{625 \div 5} = \frac{28}{125}\)[/tex].
5. Convert the simplified fraction to a decimal:
- [tex]\(\frac{28}{125}\)[/tex] in decimal form is [tex]\(0.224\)[/tex] (approximate).
### Summary:
- The intermediate result of [tex]\(\frac{4}{5} \times \frac{7}{5}\)[/tex] is [tex]\(\frac{28}{25}\)[/tex] or [tex]\(1.12\)[/tex].
- The final result of [tex]\(\frac{28}{25} \times \frac{5}{25}\)[/tex] is [tex]\(\frac{28}{125}\)[/tex] or approximately [tex]\(0.224\)[/tex].
Therefore, the step-by-step multiplication of [tex]\(\frac{4}{5} \times \frac{7}{5} \times \frac{5}{25}\)[/tex] results in approximately [tex]\(0.224\)[/tex].
