Convert Between Improper Fractions and Mixed Numbers

A mixed number has a fraction and a whole number.
An improper fraction has a numerator that equals or is higher than the denominator. It can be represented via a mixed number.

Step by step to convert an improper fraction to a mixed number:

Step 1: Divide the numerator by its denominator. The result is the whole number, and whatever remains is the new fraction’s numerator.
Step 2: The denominator of the new fraction is the same number as the original denominator.
Step 3: If there is no remainder, there is no fraction so a resulting number is a whole number.

Convert Between Improper Fractions and Mixed Numbers – Examples 1

Write $$4 \frac{3}{4}$$ as an improper fraction.
Solutions:
Step 1: Multiply the whole number in the denominator. $$4×4$$
Step 2: Add the result to the numerator and write in the numerator. 16+3
Step 3: The denominator is the same as the mixed number. 4
$$4 \frac{3}{4}=\frac{(4×4)+3}{4}=\frac{19}{4}$$

Convert Between Improper Fractions and Mixed Numbers – Examples 2

Write $$\frac{63}{8}$$ as a mixed fraction.
Step 1: Divide the numerator by the denominator. $$61÷8$$
Step 2: The whole number is 7.
Step 3: The rest is the new fraction’s numerator 5.
$$\frac{61}{8}=\frac{(8×7)+5}{8}=7 \frac{5}{8}$$

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