Simplify Mixed Number Calculator
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How to Simplify Mixed Numbers
To simplify a mixed number, it is necessary to convert it to an improper fraction and then simplify the fraction. These are the steps to simplify a mixed number:
- Convert the mixed number to an improper fraction: To do this, you must multiply the whole part of the mixed number by the denominator of the fraction and add the numerator to the result. This will give you the new numerator of the improper fraction. The denominator remains the same.
- Simplify the improper fraction: To simplify the fraction, divide the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that evenly divides both the numerator and the denominator. Continue dividing the numerator and the denominator by the GCD until you cannot divide further. The resulting fraction is the simplified form of the mixed number.
For example, let's simplify the mixed number 3 1/2. First, we convert it to an improper fraction:
(3 x 2) + 1 = 7
So, 3 1/2 can be written as 7/2. Now, to simplify the fraction 7/2, we find the GCD of 7 and 2, which is 1. Since the GCD is 1, the fraction is already in its simplest form, and the answer is 7/2.
Note: If the numerator of the simplified fraction is greater than or equal to the denominator, you can convert the fraction back to a mixed number by dividing the numerator by the denominator and writing the whole part as an integer and the remainder as a fraction.
Examples of Simplified Mixed Numbers
| Mixed Number | Improper Fraction | Simplified Fraction |
|---|---|---|
| 2 2/6 | (2 x 6) + 2 = 14 / 6 | 7 / 3 |
| 3 6/15 | (3 x 15) + 6 = 51 / 15 | 17 / 5 |
| 4 27/54 | (4 x 54) + 27 = 243 / 54 | 9 / 2 |
| 5 4/7 | (5 x 7) + 4 = 39 / 7 | 39 / 7 |
| 1 5/8 | (1 x 8) + 5 = 13 / 8 | 13 / 8 |
Frequently Asked Questions
What is a mixed number?
A mixed number is an expression that combines a whole number with a proper fraction, such as 3 ¼. It is used to represent quantities greater than one in a more intuitive way.
What does it mean to simplify a mixed number?
Simplifying a mixed number means reducing the fractional part to its simplest form while keeping the whole number unchanged.
How do you simplify a mixed number step by step?
1. Analyze the fraction part of the mixed number.
2. If possible, divide the numerator and denominator by their greatest common divisor (GCD).
3. Keep the whole number as is.
Example: 5 8/12 → 8/12 simplifies to 2/3, so the simplified mixed number is 5 ⅔.
What is the difference between a mixed number and an improper fraction?
A mixed number combines a whole number and a proper fraction, while an improper fraction has a numerator greater than or equal to the denominator. Both represent the same value in different forms.