Question

Multiply four fist by 7 1/3 convert the product to be a mixed number

Answer 1

To multiply \(4 \frac{1}{5}\) by \(7 \frac{1}{3}\), we first need to convert both mixed numbers to improper fractions.

1. Convert \(4 \frac{1}{5}\) to an improper fraction:
\[
4 \frac{1}{5} = 4 \cdot 5 + 1 = 20 + 1 = 21 \quad \text{(so it's } \frac{21}{5}\text{)}
\]

2. Convert \(7 \frac{1}{3}\) to an improper fraction:
\[
7 \frac{1}{3} = 7 \cdot 3 + 1 = 21 + 1 = 22 \quad \text{(so it's } \frac{22}{3}\text{)}
\]

Now we can multiply the two improper fractions:

\[
\frac{21}{5} \times \frac{22}{3} = \frac{21 \times 22}{5 \times 3} = \frac{462}{15}
\]

Next, we convert \(\frac{462}{15}\) to a mixed number. To do this, we perform the division of \(462\) by \(15\):

- \(462 \div 15 = 30\) (since \(15 \times 30 = 450\))
- The remainder is \(462 - 450 = 12\).

Thus, \(\frac{462}{15} = 30 \frac{12}{15}\).

Finally, we can simplify \(\frac{12}{15}\):
- The greatest common divisor (GCD) of \(12\) and \(15\) is \(3\),
- Therefore, \(\frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}\).

Putting it all together, we have:

\[
30 \frac{12}{15} = 30 \frac{4}{5}
\]

So, \(4 \frac{1}{5} \times 7 \frac{1}{3} = 30 \frac{4}{5}\).