Final answer:
To determine the number of lengths of 4 1/5 yard ribbons in 58 4/5 yards, we convert mixed numbers to improper fractions and divide.
Step-by-step explanation:
The question is about finding how many lengths of ribbon Justin can get from his total length of ribbon. Since Justin had 58 4/5 yards of ribbon and wants to divide it into lengths of 4 1/5 yards, the calculation is similar to dividing two fractions. To solve this, we first need to convert the mixed numbers into improper fractions.
58 4/5 becomes (58 × 5 + 4)/5 = 294/5.
Next, 4 1/5 becomes (4 × 5 + 1)/5 = 21/5.
To find out how many lengths of 4 1/5 yards can be made from 58 4/5 yards, we divide the first fraction by the second:
(294/5) ÷ (21/5) = (294/5) × (5/21) = 294/21 = 14. Hence, Justin can get 14 lengths of 4 1/5 yards from his total ribbon.
It's important to remember that when dividing fractions, we multiply by the reciprocal of the divisor.