Mixed Numbers and Improper Fractions

In math, there are two common ways to write fractions that are greater than $1$: as mixed numbers or as improper fractions. Learning how to convert between the two is an important Grade 4 math skill!

What is a Mixed Number?

A mixed number is made up of a whole number and a proper fraction combined.

• Example: $2\frac{3}{4}$ (read as "two and three-fourths"). This means you have $2$ whole parts and $\frac{3}{4}$ of another part.

What is an Improper Fraction?

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

• Example: $\frac{11}{4}$. This means you have $11$ pieces, and it takes $4$ pieces to make a whole.

Converting a Mixed Number to an Improper Fraction

To change a mixed number like $3\frac{2}{5}$ into an improper fraction, follow these three simple steps:

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

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

Converting an Improper Fraction to a Mixed Number

To change an improper fraction like $\frac{17}{4}$ back into a mixed number, treat the fraction bar like a division sign:

1. Divide the numerator by the denominator: $17 \div 4 = 4$ with a remainder of $1$.
2. The quotient ($4$) becomes your new whole number.
3. The remainder ($1$) becomes your new numerator.
4. Keep the original denominator ($4$).

So, $\frac{17}{4} = 4\frac{1}{4}$.

Placing Mixed Numbers on a Number Line

To place a mixed number like $2\frac{1}{3}$ on a number line:

1. Find the whole number $2$. You know the fraction is greater than $2$, so the point will be somewhere between $2$ and $3$.
2. Look at the denominator ($3$). Divide the space between $2$ and $3$ into $3$ equal sections.
3. Count forward $1$ section (the numerator) from $2$. That exact spot is $2\frac{1}{3}$!