Question

name :
write the correct answer for each sentence.
$6\frac{1}{2} * 4\frac{2}{3} =$
$3\frac{1}{6} * 2\frac{3}{5} =$
$6\frac{3}{7} * 1\frac{2}{5} =$
$3\frac{4}{5} * 4\frac{1}{3} =$
$1\frac{3}{4} * 6\frac{6}{7} =$
$3\frac{4}{5} * 4\frac{2}{3} =$
$2\frac{2}{7} * 3\frac{5}{6} =$
$2\frac{4}{7} * 3\frac{2}{3} =$
$3\frac{1}{6} * 2\frac{1}{5} =$

Explanation:

Let's solve each problem step by step by converting mixed numbers to improper fractions, multiplying them, and then converting back to mixed numbers if needed.

1. \( 6\frac{1}{2} \times 4\frac{2}{3} \)

Step 1: Convert to improper fractions

\( 6\frac{1}{2}=\frac{6\times2 + 1}{2}=\frac{13}{2} \)
\( 4\frac{2}{3}=\frac{4\times3+2}{3}=\frac{14}{3} \)

Step 2: Multiply the fractions

\( \frac{13}{2}\times\frac{14}{3}=\frac{13\times14}{2\times3}=\frac{182}{6} \)

Step 3: Simplify

\( \frac{182}{6}=\frac{91}{3}=30\frac{1}{3} \)

2. \( 3\frac{1}{6} \times 2\frac{3}{5} \)

Step 1: Convert to improper fractions

\( 3\frac{1}{6}=\frac{3\times6 + 1}{6}=\frac{19}{6} \)
\( 2\frac{3}{5}=\frac{2\times5+3}{5}=\frac{13}{5} \)

Step 2: Multiply the fractions

\( \frac{19}{6}\times\frac{13}{5}=\frac{19\times13}{6\times5}=\frac{247}{30} \)

Step 3: Simplify

\( \frac{247}{30}=8\frac{7}{30} \)

3. \( 6\frac{3}{7} \times 1\frac{2}{5} \)

Step 1: Convert to improper fractions

\( 6\frac{3}{7}=\frac{6\times7 + 3}{7}=\frac{45}{7} \)
\( 1\frac{2}{5}=\frac{1\times5+2}{5}=\frac{7}{5} \)

Step 2: Multiply the fractions

\( \frac{45}{7}\times\frac{7}{5}=\frac{45\times7}{7\times5}=9 \)

4. \( 3\frac{4}{5} \times 4\frac{1}{3} \)

Step 1: Convert to improper fractions

\( 3\frac{4}{5}=\frac{3\times5 + 4}{5}=\frac{19}{5} \)
\( 4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{13}{3} \)

Step 2: Multiply the fractions

\( \frac{19}{5}\times\frac{13}{3}=\frac{19\times13}{5\times3}=\frac{247}{15} \)

Step 3: Simplify

\( \frac{247}{15}=16\frac{7}{15} \)

5. \( 1\frac{3}{4} \times 6\frac{6}{7} \)

Step 1: Convert to improper fractions

\( 1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4} \)
\( 6\frac{6}{7}=\frac{6\times7+6}{7}=\frac{48}{7} \)

Step 2: Multiply the fractions

\( \frac{7}{4}\times\frac{48}{7}=\frac{7\times48}{4\times7}=12 \)

6. \( 3\frac{4}{5} \times 4\frac{2}{3} \)

Step 1: Convert to improper fractions

\( 3\frac{4}{5}=\frac{3\times5 + 4}{5}=\frac{19}{5} \)
\( 4\frac{2}{3}=\frac{4\times3+2}{3}=\frac{14}{3} \)

Step 2: Multiply the fractions

\( \frac{19}{5}\times\frac{14}{3}=\frac{19\times14}{5\times3}=\frac{266}{15} \)

Step 3: Simplify

\( \frac{266}{15}=17\frac{11}{15} \)

7. \( 2\frac{2}{7} \times 3\frac{5}{6} \)

Step 1: Convert to improper fractions

\( 2\frac{2}{7}=\frac{2\times7 + 2}{7}=\frac{16}{7} \)
\( 3\frac{5}{6}=\frac{3\times6+5}{6}=\frac{23}{6} \)

Step 2: Multiply the fractions

\( \frac{16}{7}\times\frac{23}{6}=\frac{16\times23}{7\times6}=\frac{368}{42}=\frac{184}{21} \)

Step 3: Simplify

\( \frac{184}{21}=8\frac{16}{21} \)

8. \( 2\frac{4}{7} \times 3\frac{2}{3} \)

Step 1: Convert to improper fractions

\( 2\frac{4}{7}=\frac{2\times7 + 4}{7}=\frac{18}{7} \)
\( 3\frac{2}{3}=\frac{3\times3+2}{3}=\frac{11}{3} \)

Step 2: Multiply the fractions

\( \frac{18}{7}\times\frac{11}{3}=\frac{18\times11}{7\times3}=\frac{198}{21}=\frac{66}{7} \)

Step 3: Simplify

\( \frac{66}{7}=9\frac{3}{7} \)

9. \( 3\frac{1}{6} \times 2\frac{1}{5} \)

Step 1: Convert to improper fractions

\( 3\frac{1}{6}=\frac{3\times6 + 1}{6}=\frac{19}{6} \)
\( 2\frac{1}{5}=\frac{2\times5+1}{5}=\frac{11}{5} \)

Step 2: Multiply the fractions

\( \frac{19}{6}\times\frac{11}{5}=\frac{19\times11}{6\times5}=\frac{209}{30} \)

Step 3: Simplify

\( \frac{209}{30}=6\frac{29}{30} \)

Answer:

s:

1. \( 30\frac{1}{3} \)
2. \( 8\frac{7}{30} \)
3. \( 9 \)
4. \( 16\frac{7}{15} \)
5. \( 12 \)
6. \( 17\frac{11}{15} \)
7. \( 8\frac{16}{21} \)
8. \( 9\frac{3}{7} \)
9. \( 6\frac{29}{30} \)