When we talk about numbers, there are a few types we should know: proper fractions, improper fractions, and mixed numbers. Understanding what each of these types means is important, especially when we want to change them into decimals.

Proper Fractions

A proper fraction is when the top number (numerator) is smaller than the bottom number (denominator).

For example, $\frac{3}{4}$ and $\frac{1}{2}$ are proper fractions.

These fractions are always less than 1. To change a proper fraction to a decimal, we need to divide:

• For $\frac{3}{4}$:
  • Divide 3 by 4: $3 \div 4 = 0.75$.
• So, $\frac{3}{4}$ equals $0.75$.

Improper Fractions

Next, we have improper fractions. In this case, the top number is bigger than or equal to the bottom number.

Examples include $\frac{5}{3}$ and $\frac{4}{4}$.

These fractions can be equal to or greater than 1. For instance, the number 4 can be written as $\frac{4}{4}$, and $\frac{5}{3}$ can be changed into a decimal:

• For $\frac{5}{3}$:
  • Divide 5 by 3: $5 \div 3 \approx 1.67$ (this looks like $1.666...$, which repeats).
• So, $\frac{5}{3}$ is about $1.67$ when rounded.

Mixed Numbers

A mixed number combines a whole number and a proper fraction.

For example, $2 \frac{1}{2}$ has the whole number 2 and the fraction $\frac{1}{2}$.

To turn a mixed number into a decimal, we can first change it into an improper fraction and then into a decimal. Here’s how:

• Change $2 \frac{1}{2}$ to an improper fraction:
  • First, multiply the whole number (2) by the bottom number (2): $2 \times 2 = 4$.
  • Then add the top number (1): $4 + 1 = 5$.
  • So, $2 \frac{1}{2} = \frac{5}{2}$.
• Now change $\frac{5}{2}$ to a decimal:
  • Divide 5 by 2: $5 \div 2 = 2.5$.
• Therefore, $2 \frac{1}{2}$ equals $2.5$ in decimal form.

Quick Reference

Here’s a simple way to remember:

• Proper fractions (less than 1) change to decimals (less than 1).
• Improper fractions (equal to or greater than 1) also change to decimals (equal to or greater than 1).
• Mixed numbers can first be turned into improper fractions and then into decimals.

Knowing how proper fractions, improper fractions, and mixed numbers turn into decimals helps us see how fractions and decimals are related. This is really important in math, especially when we work with measurements, percentages, and real-life problems!