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Methods for Multiplying Decimals

Solve [tex]$6.25 \cdot 5.7$[/tex] using fractions.

\[
\begin{aligned}
& 6.25 \cdot 5.7 \\
= & \frac{625}{100} \cdot \frac{57}{10} \\
= & \frac{625 \cdot 57}{100 \cdot 10}
\end{aligned}
\]

[tex]625 \cdot 57 = 35,625[/tex]

Answer :

Sure! Let's solve [tex]\(6.25 \cdot 5.7\)[/tex] using fractions by following a detailed, step-by-step approach:

1. Convert Decimals to Fractions:

- Convert [tex]\(6.25\)[/tex] to a fraction.
[tex]\[
6.25 = \frac{625}{100}
\][/tex]
Here, 6.25 is the same as 625 divided by 100.

- Convert [tex]\(5.7\)[/tex] to a fraction.
[tex]\[
5.7 = \frac{57}{10}
\][/tex]
This is because 5.7 is the same as 57 divided by 10.

2. Multiply the Fractions:

- Multiply the two fractions:
[tex]\[
\frac{625}{100} \cdot \frac{57}{10} = \frac{625 \cdot 57}{100 \cdot 10}
\][/tex]

3. Calculate the Multiplication in the Numerators:

- Multiply the numerators, [tex]\(625 \times 57\)[/tex]:
[tex]\[
625 \times 57 = 35,625
\][/tex]
So, the fraction becomes:
[tex]\[
\frac{35,625}{1,000}
\][/tex]

4. Simplify the Fraction:

- Divide the numerator by the denominator to simplify:
[tex]\[
\frac{35,625}{1,000} = 35.625
\][/tex]

Therefore, the result of multiplying [tex]\(6.25\)[/tex] by [tex]\(5.7\)[/tex] is [tex]\(35.625\)[/tex].

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