Operations with Rational Numbers

The rules don't change

Negative fractions and decimals follow the same sign rules as integers. First handle the sign, then do the arithmetic you already know.

Adding & subtracting fractions

The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.

Always ask: "What is the whole?" In 3/4 of a pizza, the whole is one pizza. In 3/4 of 20 students, the whole is 20 students.

1. 1Rewrite subtraction as adding the opposite if it helps.
2. 2Find a common denominator.
3. 3Add or subtract the numerators and apply the sign rule.

Why this matters

Apply the sign rules to fractions and decimals, not just whole numbers.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Adding numerators and denominators separately (2/3 + 1/4 is not 3/7). Match denominators first, or use a clear model.

Forgetting to simplify the final answer when a smaller equivalent fraction is possible.

Key ideas from this lesson

1. The rules don't change
2. Adding & subtracting fractions
3. Rewrite subtraction as adding the opposite if it helps.
4. Find a common denominator.
5. Add or subtract the numerators and apply the sign rule.