Rojas Mills
08/13/2023 · Senior High School
Lultiply Simplify the produs \( \frac{3}{4} \times \frac{2}{3}= \) \( \frac{7}{8} \times \frac{7}{14}= \) \( 2 \frac{1}{4} \times \frac{7}{3}= \) \( 1 \frac{5}{8} \times \frac{4}{6}= \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let's simplify each of the products step by step.
1. **For \( \frac{3}{4} \times \frac{2}{3} \)**:
\[
\frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2}
\]
2. **For \( \frac{7}{8} \times \frac{7}{14} \)**:
\[
\frac{7}{8} \times \frac{7}{14} = \frac{7 \times 7}{8 \times 14} = \frac{49}{112}
\]
Now, simplify \( \frac{49}{112} \):
\[
\frac{49 \div 49}{112 \div 49} = \frac{1}{\frac{112}{49}} = \frac{1}{2.2857} \approx \frac{7}{16} \text{ (exactly, } \frac{49}{112} = \frac{7}{16} \text{)}
\]
3. **For \( 2 \frac{1}{4} \times \frac{7}{3} \)**:
First, convert \( 2 \frac{1}{4} \) to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4}
\]
Now multiply:
\[
\frac{9}{4} \times \frac{7}{3} = \frac{9 \times 7}{4 \times 3} = \frac{63}{12}
\]
Now, simplify \( \frac{63}{12} \):
\[
\frac{63 \div 21}{12 \div 21} = \frac{21}{4} \text{ (or } 5 \frac{1}{4} \text{)}
\]
4. **For \( 1 \frac{5}{8} \times \frac{4}{6} \)**:
First, convert \( 1 \frac{5}{8} \) to an improper fraction:
\[
1 \frac{5}{8} = \frac{13}{8}
\]
Now multiply:
\[
\frac{13}{8} \times \frac{4}{6} = \frac{13 \times 4}{8 \times 6} = \frac{52}{48}
\]
Now, simplify \( \frac{52}{48} \):
\[
\frac{52 \div 4}{48 \div 4} = \frac{13}{12} \text{ (or } 1 \frac{1}{12} \text{)}
\]
### Final Results:
1. \( \frac{3}{4} \times \frac{2}{3} = \frac{1}{2} \)
2. \( \frac{7}{8} \times \frac{7}{14} = \frac{7}{16} \)
3. \( 2 \frac{1}{4} \times \frac{7}{3} = \frac{21}{4} \) or \( 5 \frac{1}{4} \)
4. \( 1 \frac{5}{8} \times \frac{4}{6} = \frac{13}{12} \) or \( 1 \frac{1}{12} \)
Quick Answer
1. \( \frac{3}{4} \times \frac{2}{3} = \frac{1}{2} \)
2. \( \frac{7}{8} \times \frac{7}{14} = \frac{7}{16} \)
3. \( 2 \frac{1}{4} \times \frac{7}{3} = \frac{21}{4} \) or \( 5 \frac{1}{4} \)
4. \( 1 \frac{5}{8} \times \frac{4}{6} = \frac{13}{12} \) or \( 1 \frac{1}{12} \)
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