This calculator converts an improper fraction to a mixed number in its simplest form. Just enter an improper fraction and click the “Convert” button to get instant results with step-by-step explanation.
Enter an improper fraction you want to convert to a mixed number
How to Use the Improper to Mixed Number Calculator
To convert any improper fraction to a mixed number using this calculator, follow these steps:
- Step 1: Enter the improper fraction
- Step 2: Click the “Convert” button
The calculator will instantly show the equivalent mixed fraction in its simplest form. It will also display a step-by-step explanation to help you learn how to convert any improper fraction to a mixed number by hand.
Want to convert a mixed number back to an improper fraction? Try the mixed to improper fraction calculator now!
What is an Improper Fraction?
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). Every improper fraction should have at least one whole number when converted to a mixed fraction. Examples of improper fractions include 7/4, 9/5, 12/12, etc.
However, if the numerator (top number) is smaller than the denominator (bottom number), the fraction is said to be a proper fraction and cannot be converted into a mixed fraction.
What is a Mixed Fraction?
A mixed fraction (or mixed number) is a type of fraction that combines a whole number and a proper fraction. For instance, $2 \tfrac{1}{3}$, $4 \tfrac{3}{5}$, and $7 \tfrac{2}{9}$ are all mixed fractions because each includes a whole number and a proper fraction side by side.
Mixed fractions are more useful when dealing with measurements and quantities than improper fractions because they show the quantity more naturally. For instance, it is clearer to say $2 \tfrac{1}{2}$ cups of flour, instead of 5/2 cups of flour.
How to Convert an Improper Fraction into a Mixed Number
To convert any improper fraction to a mixed number manually, follow these steps:
- Identify the numerator and denominator. In an improper fraction, the numerator (top number) is larger than or equal to the denominator (bottom number).
- Divide the numerator by the denominator. For example, for
7/4, divide 7 by 4. - Find the Whole Number. The whole number part of your answer is the quotient. You need to ask yourself how many times the denominator fits into the numerator. In 7÷4, the quotient is 1.
- Find the Remainder. The remainder from the division becomes the new numerator. In 7÷4, the remainder is 3 (since 1×4 = 4, and 7−4 = 3).
- Keep the Denominator. The denominator stays the same as the original fraction. For 7/4, the denominator is 4.
- Form the Mixed Fraction. To form the mixed fraction, put the whole number, the new numerator, and the original denominator together. So, 7/4 becomes (read as “one and three-fourths”).
Example: Converting Improper Fractions to Mixed Fractions
Convert 13/5 into a mixed fraction.
Solution
To convert 13/5 into a mixed number by hand, follow these steps:
Step 1: Identify the numerator and denominator
From the question:
- Numerator (top number) = 13
- Denominator (bottom number) = 5
Step 2: Divide the numerator by the denominator
In this case, you need to divide 13 by 5. That’s 13÷5
Step 3: Find the whole number
Ask yourself, how many times can 5 fit into 13? It can go two times since 2 * 5 = 10
Therefore, the quotient is 2, and this value will form the whole number part of the mixed fraction.
Step 4: Find the remainder
Since 2*5 = 10, the remainder will be 13-10 = 3
This will be the numerator of the proper fraction.
Step 5: Keep the denominator
The denominator will stay the same. Thus, the denominator for the proper fraction part will be 5.
Step 6: Form the mixed fraction
To form the mixed fraction, you need to convert the quotient, the remainder, and the denominator.
Therefore, the improper fraction (13/5), when converted to a mixed number, becomes 2(3/5).
However, if you prefer instant results, use the improper fraction to mixed fraction calculator and enter 13/5 as the improper fraction. The calculator converts 13/5 to a mixed number, and gives the results as 2(3/5)
Frequently Asked Questions
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). For example, $\tfrac{7}{4}$, $\tfrac{12}{12}$, and $\tfrac{9}{3}$ are improper fractions because the numerator is not less than the denominator.
A mixed fraction, or mixed number, is a number made up of a whole number plus a proper fraction. It looks like $2 \tfrac{1}{3}$ or $5 \tfrac{4}{7}$. The proper fraction part always has its numerator smaller than its denominator.
Here’s the manual method for converting any improper fraction to mixed fraction:
– Divide the numerator by the denominator.
– The quotient becomes the whole number.
– The remainder becomes the numerator of the fraction part.
– Use the same denominator.
No — a proper fraction is already in the simplest form in terms of mixed vs improper. It has numerator < denominator. With no whole number part, it is less than 1. Therefore, a “proper fraction” doesn’t convert into a mixed number since it doesn’t produce a whole number + fraction.
To write an improper fraction as a mixed fraction, first divide the numerator by the denominator. The whole number part of the quotient becomes the whole number in the mixed fraction, while the remainder becomes the new numerator placed over the original denominator. Finally, if the fractional part can be simplified, reduce it to lowest terms. For example,
$\dfrac{14}{6} = 2 \dfrac{2}{6} = 2 \dfrac{1}{3}$.