To reduce the fraction [tex]\(\frac{16}{40}\)[/tex] to its lowest terms, we follow these steps:
### Step 1: Identify the Greatest Common Divisor (GCD)
First, we need to find the greatest common divisor (GCD) of the numerator (16) and the denominator (40). The GCD is the largest number that can exactly divide both 16 and 40 without leaving a remainder.
### Step 2: Calculate the GCD
The GCD of 16 and 40 is 8. This is because 8 is the highest number that divides both 16 and 40 evenly.
### Step 3: Divide the Numerator and Denominator by the GCD
Next, we divide both the numerator and the denominator by the GCD to simplify the fraction:
- Divide the numerator by the GCD: [tex]\( \frac{16}{8} = 2 \)[/tex]
- Divide the denominator by the GCD: [tex]\( \frac{40}{8} = 5 \)[/tex]
### Step 4: Write the Reduced Fraction
After dividing both the numerator and the denominator by the GCD, we get the reduced fraction:
[tex]\[
\frac{16}{40} = \frac{2}{5}
\][/tex]
Thus, the fraction [tex]\(\frac{16}{40}\)[/tex] reduced to its lowest terms is [tex]\(\frac{2}{5}\)[/tex].
