Final answer:
To multiply the mixed numbers 4 5/8 by 1 1/7, first convert them to improper fractions, then multiply the numerators and denominators, simplify the resulting fraction, and if necessary, convert back to a mixed number. The result is 5 2/7.
Step-by-step explanation:
The student is asking how to multiply the mixed numbers 4 5/8 and 1 1/7. First, we need to convert these mixed numbers into improper fractions. To do this, multiply the whole number by the denominator and add the numerator. For 4 5/8, that's (4 × 8) + 5, which equals 37/8. For 1 1/7, it's (1 × 7) + 1, which is 8/7.
With the improper fractions 37/8 and 8/7, the multiplication process involves multiplying the numerators together and the denominators together, giving us (37 × 8)/(8 × 7). This simplifies to 296/56. Since both 296 and 56 are divisible by 8, we can reduce this fraction further to 37/7 or 5 2/7 when converted back to a mixed number.
Therefore, 4 5/8 multiplied by 1 1/7 equals 5 2/7.