Mixed to Improper Fractions Calculator

Published on: May 12, 2024
Final Answer: Free • Full Steps: Free

This Mixed to Improper Fractions Calculator helps you turn a whole number and a fraction into a single improper fraction, and shows the working clearly at every step. Multiply the whole number by the denominator to see how many pieces those whole ones are worth, then add the numerator to get the total. That total goes over the same denominator. Following the same pattern every time is what makes converting fractions easy to picture, check, and repeat on your own with any mixed number.

Step-by-step method

  1. Set up the problem.
  2. Multiply the whole number by the denominator.
  3. Add the numerator to that, and put the total over the same denominator.
  4. Put the minus sign back if the mixed number was negative.
  5. Do a simplifying of fractions at the end if you can.
See Example 1 Hide Example 1

Problem

\(4\tfrac{1}{2}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Multiply the whole number by the denominator.
  3. Add the numerator to that, and put the total over the same denominator.
  4. Put the minus sign back if the mixed number was negative.
  5. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Set up the problem.

In this problem: We convert \(4\tfrac{1}{2}\) into an improper fraction.

\(4\tfrac{1}{2}\)

Step 2

Step 2 - Multiply the whole number by the denominator.

In this problem: The whole number times the denominator gives \(4 \times 2 = 8\).

\(4 \times 2 = 8\)

Step 3

Step 3 - Add the numerator to that, and put the total over the same denominator.

In this problem: Adding the numerator gives \(8 + 1 = 9\), which becomes the new numerator. The denominator stays \(2\). We only counted how many pieces there are, and the pieces are still the same size, so the denominator never changes.

\(8 + 1 = 9 \;\rightarrow\; \frac{9}{2}\)

Step 4

Step 4 - Put the minus sign back if the mixed number was negative.

In this problem: The mixed number was positive, so the answer stays \(\frac{9}{2}\).

\(\frac{9}{2}\)

Step 5

Step 5 - Do a simplifying of fractions at the end if you can.

In this problem: The only number that divides both \(9\) and \(2\) is \(1\), so nothing changes.

\(\frac{9}{2}\)

Final Answer

\(4\tfrac{1}{2} = \frac{9}{2}\)
See Example 2 Hide Example 2

Problem

\(-3\tfrac{2}{5}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Multiply the whole number by the denominator.
  3. Add the numerator to that, and put the total over the same denominator.
  4. Put the minus sign back if the mixed number was negative.
  5. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Set up the problem.

In this problem: We convert \(-3\tfrac{2}{5}\) into an improper fraction.

\(-3\tfrac{2}{5}\)

Step 2

Step 2 - Multiply the whole number by the denominator.

In this problem: The whole number times the denominator gives \(3 \times 5 = 15\).

\(3 \times 5 = 15\)

Step 3

Step 3 - Add the numerator to that, and put the total over the same denominator.

In this problem: Adding the numerator gives \(15 + 2 = 17\), which becomes the new numerator. The denominator stays \(5\). We only counted how many pieces there are, and the pieces are still the same size, so the denominator never changes.

\(15 + 2 = 17 \;\rightarrow\; \frac{17}{5}\)

Step 4

Step 4 - Put the minus sign back if the mixed number was negative.

In this problem: The mixed number was negative, so the answer is \(-\frac{17}{5}\).

\(\frac{17}{5} \;\rightarrow\; -\frac{17}{5}\)

Step 5

Step 5 - Do a simplifying of fractions at the end if you can.

In this problem: The only number that divides both \(17\) and \(5\) is \(1\), so nothing changes.

\(-\frac{17}{5}\)

Final Answer

\(-3\tfrac{2}{5} = -\frac{17}{5}\)

Example Problems

Click one to load it into the box and solve it.