Compute: 6/7 ÷ 3/5 . Simplify the answer if possible.
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 3/5 = 5/3
6/7 ÷ 3/5 = 6/7 × 5/3
Now, we can multiply the numerators together and the denominators together:
= (6 × 5) / (7 × 3)
= 30/21
The fraction 30/21 cannot be simplified any further because 30 and 21 do not share a common factor other than 1.
George has a wooden board that is 3 1/4 feet long. He needs to cut it into sections that are 3/4 foot long. How many sections can he cut from this board?
To find out how many sections George can cut from the wooden board, we need to divide the length of the board by the length of each section.
First, we need to convert the mixed number 3 1/4 into an improper fraction.
3 1/4 = (4 × 3 + 1) / 4 = 13/4
Now, we can divide 13/4 by 3/4:
(13/4) ÷ (3/4) = 13/4 × 4/3
Next, we multiply the numerators and the denominators together:
= (13 × 4) / (4 × 3)
= 52/12
Now, we can simplify the fraction, if possible:
52/12 = 4 × (13/3)
So, George can cut 4 sections from this board.