Fractions & Decimals: Two Sides of a Coin

In the world of whole numbers, life is simple. You have 1 apple, 2 cars, or 5 friends. But real life is messy. Sometimes you have half a sandwich, or something costs $19.99. This is where Fractions & Decimals come in.

These two concepts are actually just two different languages for describing the same thing: parts of a whole. Whether you say "one half" or "0.5," you are describing the exact same amount. Mastering both languages is essential for science, cooking, and finance.

1. What is a Fraction?

A fraction represents a part of a whole. It is written as two numbers separated by a line.

[Image of parts of a fraction diagram]

• Numerator (Top): Tells you how many parts you have.
• Denominator (Bottom): Tells you how many parts make up a whole.

Example: In the fraction 3/4, the denominator says the pizza is cut into 4 slices. The numerator says you have 3 of them.

Types of Fractions

• Proper Fraction: Numerator is smaller than denominator (e.g., 1/2). Value is less than 1.
• Improper Fraction: Numerator is larger than denominator (e.g., 5/2). Value is greater than 1.
• Mixed Number: A whole number plus a fraction (e.g., 2 1/2).

2. What is a Decimal?

A decimal is another way to write a fraction, but it is limited to specific denominators: 10, 100, 1000, etc. It uses a "decimal point" to separate the whole number part from the fractional part.

[Image of place value chart with decimals]

In the number 0.75:
- The 7 is in the tenths place (7/10).
- The 5 is in the hundredths place (5/100).
So, 0.75 is literally "seventy-five hundredths" or 75/100.

3. Converting Fractions to Decimals

Every fraction is actually a secret division problem. The line in the middle literally means "divided by."

To convert a fraction to a decimal, divide the numerator by the denominator.

• 1/2 becomes 1 divided by 2 = 0.5
• 3/4 becomes 3 divided by 4 = 0.75
• 1/8 becomes 1 divided by 8 = 0.125

Repeating Decimals

Sometimes, the division never ends.
1 divided by 3 = 0.333333...
We write this as 0.3 with a bar over the 3.

4. Converting Decimals to Fractions

To turn a decimal back into a fraction, you just need to say its name out loud.

Example: Convert 0.6 to a fraction.
1. Say it: "Six tenths."
2. Write it: 6/10.
3. Simplify it: Divide both top and bottom by 2 to get 3/5.

Example: Convert 0.25 to a fraction.
1. Say it: "Twenty-five hundredths."
2. Write it: 25/100.
3. Simplify it: Divide both by 25 to get 1/4.

5. Operations with Fractions & Decimals

Arithmetic works differently for each system.

Adding Fractions

You MUST have a common denominator. You cannot add slices of different sizes.

Adding Decimals

You MUST line up the decimal points. This ensures you are adding tenths to tenths and whole numbers to whole numbers.

6. When to Use Which?

Why do we keep both systems if they do the same thing?

• Use Fractions for Precision: In carpentry, cooking, and algebra, fractions are preferred because they are exact. 1/3 is perfect, while 0.333... is messy.
• Use Decimals for Comparison and Money: It is much easier to tell that 0.45 is bigger than 0.39 than to compare 9/20 and 39/100. Science and finance almost always use decimals.

7. Conclusion

Fractions and Decimals are the bilingual twins of mathematics. They express the same values in different cultures. Fractions are the language of ratios and exact division, while decimals are the language of measurement and currency. Being fluent in both allows you to navigate the world of numbers with confidence.