a board was 24 3/8 inches long. A worker cut it into pieces that were 4 7/8 inches long. The worker cut the board into how many pieces?
4 7/8 = 39/8
24 3/8 = 195/8
195/39 = 5
Of course we have made no allowance for the saw kerf.
24 3/8 = 195/8 =24.375
4 7/8 =39/8=4.875
24.375/4.875 = 5 pieces
is it correct
5 pieces because 4875 is close to 5
To find out how many pieces the board was cut into, we need to divide the total length of the board by the length of each piece.
First, let's convert the mixed number 24 3/8 into an improper fraction. The whole number part, 24, can be written as 24/1. So, the mixed number becomes (24/1) + (3/8).
To add these fractions, we need to have a common denominator. The least common multiple (LCM) of 1 and 8 is 8. Therefore, we can rewrite the mixed number as: (24/1) + (3/8) = (24/1) + (3/8) x (8/8) = (24/1) + (24/8) = (192/8) + (3/8) = (192+3)/8 = 195/8.
Now that we have the length of the board as an improper fraction: 195/8 inches, we can divide it by the length of each piece, which is 4 7/8 inches.
To do the division, we multiply the length of the board by the reciprocal of the length of each piece.
Reciprocal of 4 7/8 is (8/39).
So, (195/8) / (8/39) = (195/8) * (39/8).
To multiply fractions, we multiply the numerators (top numbers) together and the same with the denominators (bottom numbers): (195 * 39) / (8 * 8) = 7605/64.
Therefore, the board was cut into 7605/64 pieces.
Note: If you prefer to have a whole number as the answer, you can divide the numerator by the denominator: 7605 รท 64 = 118 with a remainder of 53. This means the board was cut into 118 whole pieces and there was a remainder of 53/64 inches.
I showed you how to do your last two problems. Now it's your turn.
I'll be glad to check your answer.