what is 850/100 as a fraction

Natashya

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23-12-2024

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The question "What is 850/100 as a fraction?" is a straightforward one involving simplifying fractions. Let's break down how to solve this and understand the underlying principles.

Understanding Fractions

A fraction represents a part of a whole. It's written as a numerator (the top number) over a denominator (the bottom number). The numerator shows how many parts you have, and the denominator shows how many parts make up the whole.

Simplifying 850/100

The fraction 850/100 represents 850 parts out of a total of 100 parts. To simplify this fraction, we need to find the greatest common divisor (GCD) of both the numerator (850) and the denominator (100). The GCD is the largest number that divides both numbers evenly.

Finding the GCD:

One way to find the GCD is to list the factors of each number and identify the largest one they share. Alternatively, you can use the Euclidean algorithm, a more efficient method for larger numbers. For 850 and 100, we can see that 50 is the GCD.

Simplifying the Fraction:

Now that we know the GCD is 50, we divide both the numerator and the denominator by 50:

850 ÷ 50 = 17 100 ÷ 50 = 2

Therefore, the simplified fraction is 17/2.

Converting to a Mixed Number (Optional)

The fraction 17/2 is an improper fraction (the numerator is larger than the denominator). We can convert it to a mixed number, which combines a whole number and a proper fraction.

To do this, divide the numerator (17) by the denominator (2):

17 ÷ 2 = 8 with a remainder of 1

This means that 17/2 is equal to 8 1/2. This represents 8 whole units and an additional half unit.

Summary: 850/100 as a Fraction

• Improper Fraction: 17/2
• Mixed Number: 8 1/2

Both representations are correct and equivalent to the original fraction 850/100. The choice of which form to use often depends on the context of the problem. For calculations, the improper fraction (17/2) might be more convenient. For understanding the magnitude of the value, the mixed number (8 1/2) might be easier to grasp.