Sure! Let's solve these multiplication problems step-by-step.
1. First Expression: [tex]\(\frac{3}{4} \times \frac{4}{6}\)[/tex]
To multiply two fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{3}{4} \times \frac{4}{6} = \frac{3 \times 4}{4 \times 6} = \frac{12}{24} = \frac{1}{2} = 0.5
\][/tex]
So, [tex]\(\frac{3}{4} \times \frac{4}{6} = 0.5\)[/tex].
2. Second Expression: [tex]\(\frac{5}{7} \times \frac{3}{8}\)[/tex]
Similarly, multiply the numerators and the denominators together:
[tex]\[
\frac{5}{7} \times \frac{3}{8} = \frac{5 \times 3}{7 \times 8} = \frac{15}{56}
\][/tex]
Simplifying [tex]\(\frac{15}{56}\)[/tex] to a decimal:
[tex]\[
\frac{15}{56} \approx 0.26785714285714285
\][/tex]
So, [tex]\(\frac{5}{7} \times \frac{3}{8} \approx 0.26785714285714285\)[/tex].
3. Third Expression: [tex]\(3 \cdot \frac{7}{9} \times \frac{4}{10}\)[/tex]
First, convert the whole number 3 to a fraction:
[tex]\[
3 = \frac{3}{1}
\][/tex]
Now, multiply all the fractions:
[tex]\[
\frac{3}{1} \times \frac{7}{9} \times \frac{4}{10} = \frac{3 \times 7 \times 4}{1 \times 9 \times 10} = \frac{84}{90}
\][/tex]
Simplifying [tex]\(\frac{84}{90}\)[/tex]:
[tex]\[
\frac{84}{90} = \frac{42}{45} = \frac{14}{15} \approx 0.9333333333333335
\][/tex]
So, [tex]\(3 \cdot \frac{7}{9} \times \frac{4}{10} \approx 0.9333333333333335\)[/tex].
4. Fourth Expression: [tex]\(4 \cdot \frac{4}{5} \times \frac{4}{7}\)[/tex]
Convert the whole number 4 to a fraction:
[tex]\[
4 = \frac{4}{1}
\][/tex]
Multiply all the fractions:
[tex]\[
\frac{4}{1} \times \frac{4}{5} \times \frac{4}{7} = \frac{4 \times 4 \times 4}{1 \times 5 \times 7} = \frac{64}{35} \approx 1.8285714285714285
\][/tex]
So, [tex]\(4 \cdot \frac{4}{5} \times \frac{4}{7} \approx 1.8285714285714285\)[/tex].
5. Fifth Expression: [tex]\(\frac{5.2}{6} \times \frac{2}{9}\)[/tex]
Multiply the numerators and the denominators together:
[tex]\[
\frac{5.2}{6} \times \frac{2}{9} = \frac{5.2 \times 2}{6 \times 9} = \frac{10.4}{54}
\][/tex]
Simplifying [tex]\(\frac{10.4}{54}\)[/tex] to a decimal:
[tex]\[
\frac{10.4}{54} \approx 0.1925925925925926
\][/tex]
So, [tex]\(\frac{5.2}{6} \times \frac{2}{9} \approx 0.1925925925925926\)[/tex].
Therefore, the final results are:
[tex]\[
\begin{array}{l}
\frac{3}{4} \times \frac{4}{6} = 0.5 \\
\frac{5}{7} \times \frac{3}{8} \approx 0.26785714285714285 \\
3 \cdot \frac{7}{9} \times \frac{4}{10} \approx 0.9333333333333335 \\
4 \cdot \frac{4}{5} \times \frac{4}{7} \approx 1.8285714285714285 \\
\frac{5.2}{6} \times \frac{2}{9} \approx 0.1925925925925926 \\
\end{array}
\][/tex]
