Adding and Subtracting Rational Numbers
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Examples, solutions, videos, worksheets, stories and songs to help Grade 6 students learn how to add and subtract rational numbers.
Adding and subtracting rational numbers involves similar principles to adding and subtracting fractions. Remember that rational numbers can be expressed as fractions ( \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \) ≠ 0) or decimals that can be converted to fractions.
Check out the following lesson if you need to review what is a rational number:
Rational Numbers
The following diagram gives some examples of adding rational numbers. Scroll down the page for more examples and solutions.
Fraction, Decimal & Rational Number Worksheets
Practice your skills with the following worksheets:
Online & Printable Fraction Worksheets
Online & Printable Decimal Worksheets
Online & Printable Rational Number Worksheets
Adding and Subtracting Rational Numbers in Fraction Form
Case 1: Same Denominator
To add or subtract fractions with the same denominator, add or subtract the numerators and keep the denominator the same.
Case 2: Different Denominators
To add or subtract fractions with different denominators, you must first find a common denominator. The least common multiple (LCM) of the denominators is usually the most efficient common denominator. Convert to equivalent fractions with same denominator. Then, add or subtract the numerators and keep the denominator the same.
Adding and Subtracting Mixed Numbers
Mixed numbers can be added or subtracted in two main ways:
Method 1: Convert to Improper Fractions
- Convert each mixed number to an improper fraction.
- Find a common denominator (if necessary).
- Add or subtract the numerators.
- Keep the common denominator.
- Convert the result back to a mixed number if desired.
Method 2: Work with Whole and Fractional Parts Separately - Add or subtract the whole number parts.
- Add or subtract the fractional parts (find a common denominator if necessary).
- Combine the results. If the fractional part of the sum is an improper fraction, convert it to a mixed number and add the whole number part to the sum of the whole numbers. For subtraction, you may need to borrow from the whole number part to perform the subtraction of the fractions.
Adding and Subtracting Rational Numbers in Decimal Form
To add or subtract rational numbers in decimal form, follow the same rules as adding or subtracting whole numbers, making sure to align the decimal points vertically.
Steps:
- Align the Decimal Points: Write the numbers vertically so that their decimal points are directly below each other.
- Add Trailing Zeros (Optional): If the numbers have a different number of decimal places, you can add trailing zeros to the shorter number(s) to make the columns align, which can help prevent errors.
- Add or Subtract: Perform the addition or subtraction as you would with whole numbers, starting from the rightmost column.
- Place the Decimal Point: The decimal point in the answer should be directly below the decimal points in the numbers being added or subtracted.
Remember to always simplify your final answer whenever possible, whether it’s a fraction or a decimal.
Pay attention to the signs of the rational numbers when performing the operations. The rules for adding and subtracting integers (same signs add and keep the sign, different signs subtract and keep the sign of the larger absolute value) apply to the numerators of fractions and to decimal numbers as well.
How to add and subtract rational numbers?
When we add or subtract rational numbers that have the same denominator, we add or subtract only the numerators. The denominators stay the same.
When we add or subtract rational numbers with unlike denominators, we need to change the rational numbers to equivalent rational numbers that have the same denominators, before we find the sum or difference.
Adding & Subtraction Rational Numbers
Addition of Rational Numbers
Subtraction of Rational Numbers
Add Rational Numbers
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
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