Write each fraction in simplest form 63/81.
The Correct Answer and Explanation is:
To write the fraction 63/81 in its simplest form, we divide both the numerator and the denominator by their greatest common factor (GCF).
Step 1: Find the GCF of 63 and 81
Start by listing the factors of each number:
Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 81: 1, 3, 9, 27, 81
The common factors of both 63 and 81 are 1, 3, and 9.
So, the greatest common factor is 9.
Step 2: Divide both the numerator and the denominator by the GCF
63÷981÷9=79\frac{63 \div 9}{81 \div 9} = \frac{7}{9}81÷963÷9=97
Final Answer:
63/81 simplified is 7/9
Explanation
To simplify a fraction, the goal is to make it as small as possible while still keeping the same value. This is done by dividing both the top number (called the numerator) and the bottom number (called the denominator) by the same number — specifically, the greatest common factor (GCF). The GCF is the largest number that evenly divides both numbers.
In the case of the fraction 63/81, we want to find the largest number that can go into both 63 and 81 without leaving a remainder. This number is 9. Dividing both the numerator and the denominator by 9 simplifies the fraction.
When you simplify 63 divided by 9, you get 7. And when you divide 81 by 9, you get 9. So the simplified fraction becomes 7/9.
This new fraction, 7/9, is called a simplest form or lowest terms version of the original fraction. It is easier to work with, especially in math problems involving addition, subtraction, or comparison of fractions.
Another way to check if a fraction is in its simplest form is to see if the numerator and the denominator have any common factors besides 1. In the fraction 7/9, the number 7 and 9 do not have any common factors except 1. That confirms 7/9 is already in simplest form.
Simplifying fractions helps make numbers more manageable, which is useful in everyday life as well as in academic and professional settings.
