Adding Rational Numbers

Master adding fractions, decimals, and mixed numbers. Grade 9 Alberta mathematics with step-by-step examples.

Lesson 3.2 of Rational Numbers in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Understanding Addition with Rational Numbers. Learn what it means to add rational numbers using both positive and negative values.
• Adding Fractions with Like and Unlike Denominators. Add fractions and mixed numbers by finding common denominators and simplifying results.
• Real-World Problems. Apply addition of rational numbers to everyday word problems and real-life situations.

Inside the lesson — a free preview

Integer Rules for Adding

To add rational numbers, we follow the same rules used for adding integers and fractions.

Integer Rules for Adding:• To add a positive integer, move to the right on the number line (increase in value).• To add a negative integer, move to the left on the number line (decrease in value).Remember: the first number is your starting position.

Decimal Rules for Adding

When adding decimals, the rules are the same as with integers — but you must line up the decimal points carefully.

• A positive decimal increases the total.• A negative decimal decreases the total.

Tip: How to Add Decimals

When working with decimals, follow these simple steps:1. Check the signs.If both are positive, add normally. If one is negative, subtract.2. Rewrite the problem.Stack the numbers vertically.3. Line up the decimals!This keeps each place value (tenths, hundredths) in order.4. Add from right to left.Just like whole numbers.

Example:

Fraction Rules for Adding

Fraction Rules for Adding:• To add fractions, we need a common denominator.• Once we have a common denominator, we add the numerators only (using the integer rules).• The denominator stays the same.• Reduce to lowest terms if possible.

Common Mistake

Don't add denominators!1/2 + 1/3 ≠ 2/5Always find a common denominator first, then add the numerators.

Understanding Real-World Applications

Adding rational numbers isn't just about math problems — it's used in everyday situations like measuring distances, calculating time, or keeping track of money.

In word problems, always:

Identify what's being added. Write an addition sentence. Solve and explain what the result means.

Worked example: – Adding Integers

Let's add:. −2 + 5

1. Start at −2 on the number line.2. Since you're adding +5, move 5 units to the right.3. You land on +3.So: −2 + 5 = 3This shows that adding a positive number moves you to the right, while adding a negative moves you left.

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