Fraction Fundamentals and Operations

Name:

Date:

📚 Part 1: Understanding Fractions

A fraction shows equal parts of a whole. The denominator is the bottom number. It tells us how many equal parts make the whole. The numerator is the top number. It tells us how many parts we have.

For example, in 3/4, the denominator is 4 and the numerator is 3. The whole is divided into four equal parts, and three parts are being described.

One half is written as 1/2. One quarter is written as 1/4. Two quarters are equivalent to one half: 2/4 = 1/2.

1. A cake is cut into 4 equal pieces. Mia eats 1 piece. What fraction of the cake does she eat?

1/2

1/3

1/4

2. In the fraction 5/8, which number is the numerator?

3. Complete the equivalent fraction: 1/2 = ____/4.

4. Write the fraction shown by 3 shaded parts out of 5 equal parts.

✏️ Part 2: Adding and Subtracting Fractions

When fractions have the same denominator, keep the denominator and add or subtract the numerators.

Example: 2/7 + 3/7 = 5/7. The denominator stays 7.

Example: 6/9 − 2/9 = 4/9.

When denominators are different, rename the fractions so they have a common denominator. For example, 1/2 = 2/4, so 1/2 + 1/4 = 2/4 + 1/4 = 3/4.

5. Add: 3/8 + 2/8 =

6. Subtract: 7/10 − 3/10 =

7. Add: 1/2 + 1/4 =

8. A bottle is 5/6 full. Sam drinks 2/6 of the bottle. What fraction is left?

🔢 Part 3: Improper Fractions and Mixed Numbers

A proper fraction has a numerator smaller than its denominator, such as 3/5.

An improper fraction has a numerator equal to or greater than its denominator, such as 7/4. It can be written as a mixed number: 7/4 = 1 3/4.

To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the numerator.

9. Change 9/4 into a mixed number.

10. Change 2 1/3 into an improper fraction.

11. Add: 1 1/2 + 1/2 =

12. Explain why 2/4 and 1/2 are equivalent fractions.