Write the fraction 32/40 in simplest form
The Correct Answer and Explanation is:
The fraction 32/40 in its simplest form is 4/5.
Explanation:
To simplify the fraction 32/40, the goal is to reduce it to its lowest terms by dividing both the numerator (32) and the denominator (40) by their greatest common divisor (GCD), which is the largest number that divides both without leaving a remainder.
Step 1: Find the GCD of 32 and 40.
To find the GCD, first list the factors of each number:
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The common factors of 32 and 40 are 1, 2, 4, and 8. The largest of these is 8, so the GCD of 32 and 40 is 8.
Step 2: Divide both the numerator and denominator by the GCD.
Now, divide both 32 and 40 by their GCD (8):
- 32 ÷ 8 = 4
- 40 ÷ 8 = 5
Thus, the fraction 32/40 simplifies to 4/5.
Step 3: Verify the result.
To ensure the fraction is in its simplest form, check if the numerator and denominator have any common factors other than 1. The factors of 4 are 1, 2, 4, and the factors of 5 are 1, 5. Since the only common factor is 1, 4/5 is indeed the simplest form of 32/40.
Why Simplifying Matters:
Simplifying fractions makes them easier to understand and work with, particularly in math problems like adding, subtracting, or comparing fractions. It also helps in real-life applications, such as cooking or dividing resources, where simplicity leads to clearer measurements or portions.