To divide the mixed numbers 3 4 (which is 3 + 4/7) by 4 7 (which is 4 + 7/7), we first need to convert them into improper fractions.
For 3 4, we calculate:
3 4 = 3 + 4/7 = (3 * 7 + 4)/7 = (21 + 4)/7 = 25/7
For 4 7, we have:
4 7 = 4 + 7/7 = (4 * 7 + 7)/7 = (28 + 7)/7 = 35/7
Now, we can perform the division:
(25/7) ÷ (35/7)
Dividing by a fraction is the same as multiplying by its reciprocal:
(25/7) * (7/35)
The sevens in the numerator and denominator cancel out:
(25/1) * (1/35) = 25/35
This fraction can be simplified:
25 and 35 have a common factor of 5.
So, 25 ÷ 5 = 5 and 35 ÷ 5 = 7, giving us:
5/7
Therefore, 3 4 divided by 4 7 equals 5/7.