Understanding Fractions

📚 Grade 3
📂 Number & Operations - Fractions (NF)
⏱️ 15 minutes
❓ 10 Questions
Common Core Standards:
3.NF.A.1: Understand a fraction 1/b as one part when a whole is partitioned into b equal parts
3.NF.A.2: Understand a fraction as a number on the number line
3.NF.A.3: Explain equivalence of fractions
Name: _______________________ Date: _______________________ Score: _______ / 10

📖 What are Fractions?

A fraction represents part of a whole. When we cut a pizza into equal slices,
each slice is a fraction of the whole pizza.

Fractions have two numbers. The top number is called the numerator (it tells us how
many parts we have). The bottom number is called the denominator (it tells us how
many equal parts make up the whole).

For example, in the fraction 1/4 (one-fourth), the 1 is the numerator and 4 is the
denominator. This means we have 1 part out of 4 equal parts total.

Common fractions you'll see: 1/2 (one-half), 1/3 (one-third), 1/4 (one-fourth),
3/4 (three-fourths), and more!

💡 Worked Examples

Study these examples carefully before starting the practice questions.

Example 1

Problem: What fraction of the circle is shaded? [Circle divided into 4 parts, 1 shaded]

◔ (1 out of 4 parts shaded)

Finding a fraction from a visual

  1. Count the total equal parts: 4 parts
  2. Count the shaded parts: 1 part
  3. Write as a fraction: 1 (shaded) / 4 (total)
  4. The fraction is 1/4

Answer: 1/4

Example 2

Problem: Sarah ate 3 slices of pizza. The whole pizza had 8 equal slices. What fraction of the pizza did Sarah eat?

🍕 (8 slices, 3 eaten)

Writing a fraction from a word problem

  1. Total slices (denominator): 8
  2. Slices Sarah ate (numerator): 3
  3. Write the fraction: 3/8
  4. We read this as 'three-eighths'

Answer: 3/8

Example 3

Problem: Show 2/3 on a number line from 0 to 1

0 ——|——|——• 1 (divided into 3 parts, mark at 2nd)

Placing fractions on a number line

  1. The denominator is 3, so divide the line into 3 equal parts
  2. The numerator is 2, so count 2 parts from 0
  3. Mark the point at the 2nd division
  4. This point represents 2/3

Answer: Point marked at 2/3

✏️ Practice Questions

Solve each problem. Show your work in the space provided.

1. What fraction of the circle is shaded? [circle divided into 2 equal parts, 1 shaded]
2. What fraction of the square is shaded? [square divided into 3 equal parts, 1 shaded]
3. What fraction of the square is shaded? [square divided into 3 equal parts, 2 shaded]
4. What fraction of the rectangle is shaded? [rectangle divided into 4 equal parts, 1 shaded]
5. What fraction of the square is shaded? [square divided into 4 equal parts, 3 shaded]
6. Write the fraction: one-half
7. Write the fraction: three-fourths
8. Write the fraction: two-thirds
9. Write the fraction: one-fourth
10. Write the fraction: five-sixths
Generated on November 17, 2025 | Math Practice Curriculum - Grade 3
Created by Naveen Ede