Mixed Fraction Calculator

This calculator performs mixed number to improper fraction conversions. A fraction is called proper when its numerator is smaller than its denominator. A fraction is called improper, when its numerator is equal to denominator or is larger than the denominator.

Finally, a mixed number consists of a whole number and a proper fraction. Any mixed number can be converted to an improper fraction; this conversion doesn’t change the value of the number.

Directions for use

To use the mixed number to improper fraction calculator, enter all parts of a given mixed number into the corresponding fields. You will need to enter the whole number, the numerator, and the denominator of the given number. Then press “Calculate.” The calculator will convert the given mixed number to an improper fraction and simplify the resulting fraction, if possible. The answer, as well as the solution algorithm, will be presented.

Converting mixed numbers to improper fractions

Definitions

• Proper fraction – a fraction, where the numerator is smaller than the denominator; for example, \$\frac{3}{5}\$, \$\frac{6}{26}\$, \$\frac{7}{15}\$.
• Improper fraction – a fraction, where the numerator is larger than the denominator; for example, \$\frac{11}{4}\$, \$\frac{9}{2}\$.
• Mixed number – a number, consisting of two parts: a whole number and a proper fraction. For example, \$6 \frac{1}{2}\$, \$9 \frac{5}{9}\$.

Since in a proper fraction a numerator is always smaller than a denominator, the value of a proper fraction is always less than 1. Similarly, the value of any improper fraction is always greater than 1. Therefore, any improper fraction can be converted to a mixed number and vice versa.

Conversion algorithm

To express a mixed number as an improper fraction, follow the steps below:

1. Multiply the whole number part of the mixed number by the denominator of the fractional part of the mixed number.
2. Add the result of the multiplication in step 1 to the numerator of the fractional part of the mixed number.
3. Use the result of step 2 as the numerator of the new improper fraction, and the original denominator of the fractional part of the mixed number as the denominator of the new improper fraction.
4. Check, if the numerator and the denominator of the new improper fraction have any common factors. If yes, simplify the improper fraction by dividing both the numerator and the denominator by the greatest common factor (GCF).

For example, let’s express \$1 \frac{2}{5}\$ as an improper fraction, following the above algorithm.

1. 5 × 1 = 5
2. 5 + 2 = 7
3. Improper fraction = \$\frac{7}{5}\$
4. 7 and 5 do not have any common factors, therefore, simplification is not possible.

Finally, \$1 \frac{2}{5}\$ = \$\frac{7}{5}\$.

Converting mixed number to an improper fraction by addition

Any mixed number can be presented as a sum of its whole number part and its fractional part. Therefore, another way to convert a mixed number to an improper fraction is by adding the fractional part to the whole number part. For example, let’s express \$3 \frac{2}{5}\$ as an improper fraction.

\$3 \frac{2}{5}\$ = 3 + \$\frac{2}{5}\$ = \$\frac{3}{1}\$ + \$\frac{2}{5}\$ = \$\frac{15 + 2}{5}\$ = \$\frac{17}{5}\$

17 and 5 do not have any common factors, therefore, it is the final answer.

Calculation examples

Ordering pizza

Converting mixed numbers to improper fractions is often used when adding a mixed number to a fraction.

Imagine, you are ordering pizza for a group of 5 kids. You know that 3 of the kids can eat half-a-pizza each, 1 kid eats a whole pizza, and 1 kid eats a pizza and a half. How many pizzas will you have to order?

Solution

To figure out how many pizzas you have to order, you have to sum the amount of pizza each child can eat, and then round up the final number. Let’s first look at the known data:

• 1 child – 1 pizza
• 1 child – 1 pizza and a half
• 3 children – \$\frac{1}{2}\$ pizza each

The final sum will be:

1 + (1 + \$\frac{1}{2}\$) + 3 × (\$\frac{1}{2}\$) = 1 + \$1 \frac{1}{2}\$ + \$\frac{3}{2}\$

To be able to calculate the sum above, we need to convert \$1 \frac{1}{2}\$ to an improper fraction. Following the steps of the algorithm above, we get:

1. 2 × 1 = 2
2. 2 + 1 = 3
3. Improper fraction = \$\frac{3}{2}\$
4. 3 and 2 don’t have any common factors.

Taking into account that 1 can be written as \$\frac{2}{2}\$, and \$1\frac{1}{2}\$ can be expressed as an improper fraction \$\frac{3}{2}\$, the above sum can be re-written as follows:

1 + \$1 \frac{1}{2}\$ + \$\frac{3}{2}\$ = \$\frac{2}{2}\$ + \$\frac{3}{2}\$ + \$\frac{3}{2}\$ = \$\frac{2 + 3 + 3}{2}\$ = \$\frac{8}{2}\$ = 4

Answer

You will need to order 4 pizzas.

A recipe

Similarly to addition, multiplication is also easier when performed on improper fractions, not on mixed numbers.

Imagine, you are organizing a dinner party, and you want to impress your guests with some cheese pies. You have found a really nice recipe, that uses \$2 \frac{1}{2}\$ cups of flour and yields 4 portions. You are expecting 7 guests to attend the party, and you also need a piece of pie for yourself. How much flour will you need to make enough pies?

Solution

To figure out the final amount of flour, let’s first calculate how much more flour you will need, compared to the original recipe. The original recipe yields 4 portions, but you have 7 guests and yourself, resulting in (7 + 1) = 8 portions. \$\frac{8}{4}\$ = 2. You will need twice as much flour as in the original recipe.

To calculate the final amount, we need to multiply the original amount by 2. The original amount was \$2 \frac{1}{2}\$ cups. To be able to perform the multiplication, let’s first convert \$2 \frac{1}{2}\$ to an improper fraction:

1. 2 × 2 = 4
2. 4 + 1 = 5
3. Improper fraction = \$\frac{5}{2}\$
4. 5 and 2 don’t have any common factors

Final amount of flour = 2 × \$\frac{5}{2}\$ = \$\frac{10}{2}\$. Note that 10 can be divided by 2 without any remainder: \$\frac{10}{2}\$ = 5.

Answer

You will need 5 cups of flour.