Navigating Mixed Numbers and Improper Fractions

Fractions can come in different forms. Sometimes we see them with a whole number alongside a fraction, and other times the fraction’s numerator is larger than the denominator. These are Mixed Numbers and Improper Fractions.

What is a Mixed Number?

A Mixed Number is a combination of a whole number and a proper fraction (where the numerator is smaller than the denominator).

For example:

• $2\frac{1}{3}$ is a mixed number because it combines the whole number $2$ with the fraction $\frac{1}{3}$

What is an Improper Fraction?

An Improper Fraction is a fraction where the numerator (top number) is equal to or greater than the denominator (bottom number).

For example:

• $\frac{7}{3}$ is an improper fraction because the numerator $7$ is greater than the denominator $3$.

 

Converting Between Mixed Numbers and Improper Fractions

To work with fractions more easily, we often need to switch between mixed numbers and improper fractions. Here’s how!

Converting a Mixed Number to an Improper Fraction

1. Multiply the whole number by the denominator.
2. Add the result to the numerator.
3. Place this new number over the original denominator.

For example, to convert $3\frac{2}{5}$ to an improper fraction:

1. Multiply the whole number by the denominator: $3 \times 5 = 15$
2. Add the numerator: $15 + 2 = 17$
3. Write it over the original denominator: $\frac{17}{5}$.

So, $$3 \frac{2}{5} = \frac{17}{5}$$

 

 

 

 

Converting an Improper Fraction to a Mixed Number

1. Divide the numerator by the denominator.
2. The quotient (whole number part) is the whole number.
3. The remainder becomes the new numerator, over the original denominator.

For example, to convert $\frac{11}{4}$ to a mixed number:

1. Divide $11$ by $4$: $11 \div 4 = 2$ remainder $3$.
2. The quotient $2$ is the whole number, and the remainder $3$ is the new numerator.

So, $$\frac{11}{4} = 2 \frac{3}{4}$$