A ribbon is 3 2/3 long. Mae needs to cut the ribbon into pieces that are 2/3 yard long. How much ribbon will be left after she cuts these pieces?
Is that 3 2/3 yards?
To find out how much ribbon will be left after cutting it into pieces, follow these steps:
Step 1: Convert the length of the ribbon into a mixed number
The length of the ribbon is given as 3 2/3 yards. To convert this into a mixed number, multiply the whole number (3) by the denominator of the fraction (3) and add the numerator (2).
3 * 3 + 2 = 9 + 2 = 11
So, the length of the ribbon is 11/3 yards.
Step 2: Divide the length of the ribbon by the length of a single piece
The length of a single piece is given as 2/3 yards. To find out how many pieces can be cut from the ribbon, divide the length of the ribbon (11/3) by the length of a single piece (2/3).
(11/3) / (2/3) = (11/3) * (3/2) = 33/6 = 5 3/6
Step 3: Subtract the total length of the pieces from the length of the ribbon
To find out how much ribbon will be left, subtract the total length of the pieces (5 3/6) from the length of the ribbon (11/3).
11/3 - 5 3/6
To subtract mixed numbers, convert them into improper fractions:
11/3 - (5 * 6/6 + 3/6)
11/3 - 33/6
(11 * 6 - 33)/(3 * 6)
(66 - 33)/18
33/18
Step 4: Simplify the fraction
To simplify the fraction 33/18, find a common factor for both the numerator and denominator.
The greatest common factor of 33 and 18 is 3.
33/18 = (33/3) / (18/3) = 11/6
Therefore, Mae will have 11/6 yards of ribbon left after cutting these pieces.
To figure out how much ribbon will be left after cutting pieces that are 2/3 yard long, we need to divide the total length of the ribbon by the length of each piece.
The length of the ribbon is given as 3 2/3 yards. To convert this mixed number into an improper fraction, we multiply the whole number (3) by the denominator of the fraction (3) and add the numerator (2), which gives us a numerator of 11. The denominator remains the same. So, the length of the ribbon in fraction form is 11/3 yards.
Now, we need to divide the length of the ribbon by the length of each piece, which is 2/3 yard. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have:
(11/3) ÷ (2/3)
To simplify, we can cancel out the denominator of 3 in both fractions. This leaves us with:
(11/1) ÷ (2/1)
Dividing 11 by 2 gives us 5 with a remainder of 1. So, we have:
5 remainder 1
This means that Mae can cut out 5 pieces of ribbon that are 2/3 yard long, with 1/3 yard of ribbon left over as a remainder.
Therefore, Mae will have 1/3 yard of ribbon left after cutting the desired pieces.