Simplifying fractions can seem daunting, but with a clear step-by-step approach, you'll be a pro in no time. Here's how to simplify 17/51 in three easy steps:
Step 1: Find the Greatest Common Divisor (GCD)
The first step in simplifying a fraction is to find the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers without leaving a remainder. To find the GCD of 17 and 51, we can list the factors of each number:
- Factors of 17: 1, 17
- Factors of 51: 1, 3, 17, 51
As we can see, the only common factor is 1 and 17. Since 17 is the largest common factor, it is the GCD of 17 and 51.
What is the GCD?
- GCD of 17 and 51 is 17.
Step 2: Divide Both Numbers by the GCD
Now that we have found the GCD, we can simplify the fraction by dividing both the numerator and denominator by the GCD.
- Numerator: 17 ÷ 17 = 1
- Denominator: 51 ÷ 17 = 3
So, the simplified fraction is 1/3.
What is the Simplified Fraction?
- Simplified fraction: 1/3.
Step 3: Check for Further Simplification
The final step is to check if the fraction can be further simplified. Since the numerator is 1, we cannot simplify it any further. However, we can check if the denominator can be divided by a common factor.
In this case, the denominator 3 has no common factors with the numerator 1, so the fraction 1/3 is already in its simplest form.
Is the Fraction Fully Simplified?
- Yes, the fraction 1/3 is fully simplified.
And that's it! By following these three easy steps, we simplified the fraction 17/51 to its simplest form, which is 1/3.
What is the purpose of simplifying fractions?
+Simplifying fractions makes it easier to work with them in mathematical operations and reduces errors.
How do I find the GCD of two numbers?
+To find the GCD, list the factors of each number and identify the largest common factor.
Can I simplify a fraction if the numerator is 1?
+No, if the numerator is 1, the fraction is already in its simplest form.