Multiplying & Dividing Fractions

Multiplying fractions

Multiply straight across: numerator times numerator, denominator times denominator. Then simplify. For example, 2/3 × 4/5 = 8/15.

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.

Dividing fractions - keep, change, flip

To divide by a fraction, you multiply by its reciprocal (the fraction flipped upside down).

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. 1Keep the first fraction as it is.
2. 2Change the ÷ sign to ×.
3. 3Flip the second fraction (its reciprocal).
4. 4Multiply across and simplify.

Why this matters

Multiplying & Dividing Fractions shows up constantly in multiply straight across. To divide, keep-change-flip. 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. Multiplying fractions
2. Dividing fractions - keep, change, flip
3. Keep the first fraction as it is.
4. Change the ÷ sign to ×.
5. Flip the second fraction (its reciprocal).
6. Multiply across and simplify.