Fraction Operations: Adding, Subtracting, Multiplying, and Dividing Fractions

A fraction shows a part of a whole.

Example:

3/4

● 3 is the numerator (how many parts we have)

● 4 is the denominator (how many equal parts make the whole)

Educational standards from the National Council of Teachers of Mathematics recommend teaching fraction operations using visual models like pizza slices or pie charts.

Fractions can be added when the denominators are the same.

Example:

1/5 + 2/5

Add the numerators:

1 + 2 = 3

Answer:

3/5

This means 3 parts out of 5.

Subtract fractions the same way when the denominators match.

Example:

4/6 − 2/6

Subtract the numerators:

4 − 2 = 2

Answer:

2/6

When multiplying fractions, multiply the numerators and multiply the denominators.

Example:

2/3 × 3/4

Multiply the top numbers and the bottom numbers.

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Example calculation:

2 × 3 = 6

3 × 4 = 12

Answer:

6/12

To divide fractions, multiply by the reciprocal of the second fraction.

The reciprocal means flipping the numerator and denominator.

Example:

2/3 ÷ 1/4

Flip the second fraction:

1/4 → 4/1

Then multiply:

2/3 × 4/1 = 8/3

Imagine a cake cut into 8 slices.

You eat 3 slices.

That means you ate:

3/8 of the cake.

If your friend eats 2/8, together you ate:

3/8 + 2/8 = 5/8

So five slices of the cake were eaten.

Problem 1

1/6 + 3/6 = ___

Answer:

4/6

Problem 2

5/7 − 2/7 = ___

Answer:

3/7

Problem 3

1/2 × 3/5 = ___

Answer:

3/10

Fraction operations help children:

● Solve sharing and measurement problems

● Understand parts of a whole

● Prepare for ratios, percentages, and algebra

Fraction operations help children combine, compare, and divide parts of a whole. By practicing addition, subtraction, multiplication, and division with fractions, students gain stronger math skills and a deeper understanding of numbers.