Question

To convert a positive improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number part of the mixed number and the remainder becomes the numerator of the fraction part; the denominator remains unchanged.

Short answer

Question: Convert the improper fraction \(\frac{25}{7}\) to a mixed number using the step-by-step solution provided. Answer: To convert \(\frac{25}{7}\) to a mixed number, follow the steps: Step 1: Identify the improper fraction given The improper fraction we are working with is \(\frac{25}{7}\), where the numerator (a) is 25 and the denominator (b) is 7. Step 2: Divide the numerator by the denominator Divide the numerator (25) by the denominator (7), to find the quotient (Q) and the remainder (R): \(25 = 7 \cdot Q + R\) When dividing 25 by 7, we get a quotient of Q = 3 and a remainder of R = 4. Step 3: Write the mixed number Using the quotient and remainder found in step 2, we can write the mixed number: \(Q\frac{R}{b} = 3\frac{4}{7}\) So, the mixed number equivalent of the improper fraction \(\frac{25}{7}\) is \(3\frac{4}{7}\).

Step-by-step solution

Identify the improper fraction given

First, let's identify the improper fraction that needs to be converted into a mixed number. Assume we have a positive improper fraction of the form: \(\frac{a}{b}\), where \(a> b\).

Divide the numerator by the denominator

Next, divide the numerator (a) by the denominator (b), to find the quotient (Q) and the remainder (R): \(a = b \cdot Q + R\). In this situation, Q is the whole number part of the mixed number, R is the new numerator, and b remains the same as the denominator.

Write the mixed number

Finally, write down the mixed number using the quotient (Q) as the whole number part and the remainder (R) as the numerator, while the denominator remains the same (b): \(Q\frac{R}{b}\). Now you have successfully converted a positive improper fraction to a mixed number using a step-by-step solution.