how many 3 3/4 inch wires can be cut from a spool of wire that is 100 inches long will there be any wire left over? if so how much?
3 3/4 = 15/4.
Wires=100in/(15/4) = 100 * 4/15 = 26 2/3
2/3 * 3 3/4 = 2/3 * 15/4 = 2.5 Inches left over.
So we have 26-3 3/4 inch wires with 2.5
inches left over.
To determine the number of 3 3/4 inch wires that can be cut from a 100-inch spool of wire, we need to divide the length of the spool by the length of each wire.
First, let's convert 3 3/4 inches to a proper fraction. 3 is equivalent to 12/4, so we have 12/4 + 3/4 = 15/4.
Now, we divide the length of the spool (100 inches) by the length of each wire (15/4 inches):
100 ÷ (15/4)
To divide by a fraction, we can multiply by its reciprocal:
100 × (4/15)
Now, multiply the numerators and denominators:
(100 × 4) / 15
This simplifies to:
400 / 15
Simplify further by finding the greatest common divisor (GCD) of 400 and 15, which is 5:
(400 ÷ 5) / (15 ÷ 5)
80 / 3
This means we can cut 80 wires of 3 3/4 inches from a 100-inch spool of wire.
To determine if there will be any wire left over, we need to find the remainder when the length of the spool is divided by the length of each wire:
100 mod (15/4)
To calculate the modulus value, we convert the 15/4 inches to a decimal:
15 ÷ 4 = 3.75
Now, we calculate the modulus:
100 mod 3.75
The modulus or remainder here is 2.5 inches.
Therefore, there will be a remaining wire of 2.5 inches left over after cutting the 80 wires.