What is 28/40 in simplest form?
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{28}{40} ), we need to divide both the numerator (28) and the denominator (40) by their greatest common divisor (GCD). The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: Find the GCD of 28 and 40
We can find the GCD using the prime factorization method:
- Prime Factorization of 28:
- 28 can be divided by 2: ( 28 \div 2 = 14 )
- 14 can again be divided by 2: ( 14 \div 2 = 7 )
- 7 is a prime number.
- So, the prime factorization of 28 is ( 2^2 \times 7 ).
- Prime Factorization of 40:
- 40 can be divided by 2: ( 40 \div 2 = 20 )
- 20 can again be divided by 2: ( 20 \div 2 = 10 )
- 10 can again be divided by 2: ( 10 \div 2 = 5 )
- 5 is a prime number.
- So, the prime factorization of 40 is ( 2^3 \times 5 ).
Step 2: Identify the common factors
From the prime factorizations:
- The prime factors of 28 are ( 2^2 ) and ( 7 ).
- The prime factors of 40 are ( 2^3 ) and ( 5 ).
The common factor is ( 2^2 ) (or 4). Therefore, the GCD of 28 and 40 is 4.
Step 3: Divide both the numerator and denominator by the GCD
Now, we simplify the fraction:
[
\frac{28 \div 4}{40 \div 4} = \frac{7}{10}
]
Conclusion
Thus, the fraction ( \frac{28}{40} ) simplified to its simplest form is ( \frac{7}{10} ).
Simplifying fractions is essential for mathematical accuracy and clarity, especially in scenarios involving ratios, proportions, and calculations in various fields like science, finance, and engineering. By breaking down the fraction into its simplest form, we can communicate quantities more effectively and avoid unnecessary complexity in calculations.