Get detailed and accurate responses to your questions on IDNLearn.com. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
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]
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]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.
