From a stick 2y metres long, I cut a piece of length 4y centimetres. What fraction of the original stick remains?
2y m = 200y cm
we cut off 4y cm, leaving us with 196y cm
fraction of original left = 196y/200y = 49/50
To find the fraction of the original stick that remains, we need to compare the length of the piece that was cut to the original length of the stick.
1. Convert the length of the stick and the piece that was cut to the same unit. Since the piece was given in centimeters, convert the length of the stick to centimeters:
Original length of the stick = 2y meters = 2y * 100 centimeters = 200y centimeters.
2. Calculate the length of the remaining stick by subtracting the length of the piece that was cut from the original length of the stick:
Length of the remaining stick = 200y centimeters - 4y centimeters = 196y centimeters.
3. Finally, express the length of the remaining stick as a fraction of the original stick:
Fraction of the original stick that remains = (Length of remaining stick) / (Original length of the stick)
= 196y / 200y.
Therefore, the fraction of the original stick that remains is 196y / 200y.
To find the fraction of the original stick that remains, we need to compare the length of the remaining stick to the length of the original stick.
Given that the original stick is 2y meters long, we can convert the length of the cut piece from centimeters to meters. There are 100 centimeters in a meter, so 4y centimeters is equal to (4y/100) meters.
Now, to find the length of the remaining stick in meters, we need to subtract the length of the cut piece from the original length: 2y - (4y/100).
To express this as a fraction, we need to find a common denominator. The denominator will be 100, since we are dealing with meters. Multiplying the fraction (4y/100) by (1/1) doesn't change its value, so we can rewrite it as (4y/100) * (1/1) = (4y/100).
Now, we can subtract the fractions: 2y - (4y/100) = (200y/100) - (4y/100) = (196y/100).
Simplifying the fraction (196y/100), we can divide both the numerator and denominator by their greatest common divisor, which is 4: (196y/100) ÷ 4 = (49y/25).
Therefore, the fraction of the original stick that remains is (49y/25).