Write 40/32 in simplest form.
The Correct Answer and Explanation is:
To simplify the fraction ( \frac{40}{32} ), we need to divide both the numerator (40) and the denominator (32) by their greatest common divisor (GCD). The GCD is the largest number that can divide both numbers without leaving a remainder.
Step 1: Find the GCD
To find the GCD, we can list the factors of each number:
- Factors of 40:
- 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 32:
- 1, 2, 4, 8, 16, 32
The common factors of 40 and 32 are:
1, 2, 4, 8.
The largest of these common factors is 8. Therefore, the GCD of 40 and 32 is 8.
Step 2: Divide the Numerator and Denominator by the GCD
Now we can simplify the fraction by dividing both the numerator and the denominator by their GCD:
[
\frac{40 \div 8}{32 \div 8} = \frac{5}{4}
]
Step 3: Write the Final Answer
The fraction ( \frac{40}{32} ) in its simplest form is ( \frac{5}{4} ).
Conclusion
Simplifying fractions is an important skill in mathematics that allows us to express numbers in their simplest terms, making them easier to understand and work with. The process involves finding the GCD and dividing both the numerator and the denominator by this number. This ensures that the fraction is expressed in its lowest form, which can be particularly helpful in various applications, including algebra, fractions in cooking measurements, and ratios in everyday scenarios.
Thus, the simplified form of ( \frac{40}{32} ) is ( \frac{5}{4} ), which can also be expressed as a mixed number: ( 1 \frac{1}{4} ) if needed.