Final answer:
To calculate the division of the negative fractions − 1 3/8 and − 1 4/7, convert them to improper fractions, find the reciprocal of the second, and multiply. After simplifying, the result is a positive 7/8.
Step-by-step explanation:
To calculate the division of two negative fractions, − 1 3/8 and − 1 4/7, we first convert them to improper fractions and then divide. Convert − 1 3/8 to an improper fraction by multiplying 8 (the denominator) by 1 (the whole number) and adding the numerator: 8 × 1 + 3 = 11. So, − 1 3/8 becomes − 11/8. Secondly, − 1 4/7 becomes − 11/7 by the same process (7 × 1 + 4 = 11).
Next, the division of two fractions can be turned into multiplication by the reciprocal of the second fraction. Therefore, − 11/8 ÷ − 11/7 becomes − 11/8 × 7/− 11. The negatives cancel each other, and we can simplify before multiplying by canceling out the 11 in the numerator of the first fraction and the denominator of the second fraction.
After simplifying, we are left with 1/8 × 7/1, which equals 7/8. Therefore, − 1 3/8 ÷ − 1 4/7 equals positive 7/8.