To multiply the mixed numbers 3 4/5 and 1 9/14, you first need to convert them into improper fractions.
Convert 3 4/5 to an improper fraction:
3 4/5 = (3 × 5 + 4)/5 = (15+4)/5 = 19/5
Convert 1 9/14 to an improper fraction:
1 9/14 = (1 × 14 + 9)/14 = (14+9)/14 = 23/14
Now multiply the two improper fractions:
(19/5) × (23/14)
To multiply fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
(19 × 23)/(5 × 14) = 437/70
Now you have the result as an improper fraction, which can be simplified or converted back to a mixed number:
437 ÷ 70 = 6 with a remainder of 17, so the improper fraction 437/70 is equivalent to the mixed number:
6 17/70
To simplify the fraction part of the mixed number, you look for the greatest common divisor (gcd) between the numerator and the denominator. However, in this case, 17 and 70 do not share any common divisors other than 1, so the fraction 17/70 is already in its simplest form.
Therefore, the final simplified answer to the multiplication of 3 4/5 and 1 9/14 is:
6 17/70
3 4/5 x 1 9/14
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