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.

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.

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.

When you study adding & subtracting fractions, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

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.

A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.

Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.

A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.

Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.

Why this matters

Operations with Rational Numbers shows up constantly in apply the sign rules to fractions and decimals, not just whole numbers. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

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.