Solved Exercises on Adding Fractions with Like Denominators in Grade 4

Master adding fractions with like denominators: proper fractions, mixed numbers, and simplification through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic addition
Exercise 1
Add:
\(\frac{2}{7} + \frac{3}{7}\)
Definition:

Like denominators: Fractions with the same bottom number (denominator)

Addition method:
  1. Add the numerators together
  2. Keep the same denominator
  3. Simplify if possible
Expression
\(\frac{2}{7} + \frac{3}{7}\)
Add Numerators
\(\frac{2+3}{7}\)
Result
\(\frac{5}{7}\)
Step 1: Confirm denominators are the same

Both fractions have denominator 7, so we can add directly

Step 2: Add the numerators

\(2 + 3 = 5\)

Step 3: Keep the same denominator

The denominator stays 7

Step 4: Write the result

\(\frac{2}{7} + \frac{3}{7} = \frac{5}{7}\)

\(\frac{2}{7} + \frac{3}{7} = \frac{5}{7}\)
Final answer:

\(\frac{2}{7} + \frac{3}{7} = \frac{5}{7}\)

Applied rules:

• Like denominators: When denominators are the same, add numerators only

• Keep denominator: The denominator remains unchanged

• Simplification: Check if fraction can be reduced to lowest terms

2 Addition with simplification
Exercise 2
Add:
\(\frac{3}{8} + \frac{1}{8}\)
Definition:

Simplification: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their GCD

Expression
\(\frac{3}{8} + \frac{1}{8}\)
Add Numerators
\(\frac{4}{8}\)
Simplify
\(\frac{1}{2}\)
Step 1: Add the numerators

\(3 + 1 = 4\)

Step 2: Keep the same denominator

The denominator stays 8

Step 3: Write the result

\(\frac{3}{8} + \frac{1}{8} = \frac{4}{8}\)

Step 4: Simplify the fraction

\(\frac{4}{8} = \frac{4 ÷ 4}{8 ÷ 4} = \frac{1}{2}\)

\(\frac{3}{8} + \frac{1}{8} = \frac{1}{2}\)
Final answer:

\(\frac{3}{8} + \frac{1}{8} = \frac{1}{2}\)

Applied rules:

• Like denominators: Add numerators only, keep denominator

• Simplification: Divide both numerator and denominator by their GCD

• GCD: Greatest Common Divisor of 4 and 8 is 4

3 Mixed numbers addition
Exercise 3
Add:
\(2\frac{1}{5} + 1\frac{2}{5}\)
Definition:

Mixed number: A whole number combined with a fraction, like \(2\frac{1}{5}\)

Expression
\(2\frac{1}{5} + 1\frac{2}{5}\)
Add Parts Separately
\(3 + \frac{3}{5}\)
Result
\(3\frac{3}{5}\)
Step 1: Add the whole numbers

\(2 + 1 = 3\)

Step 2: Add the fractions

\(\frac{1}{5} + \frac{2}{5} = \frac{3}{5}\)

Step 3: Combine results

\(3 + \frac{3}{5} = 3\frac{3}{5}\)

Step 4: Check if simplification is needed

\(\frac{3}{5}\) is already in lowest terms

\(2\frac{1}{5} + 1\frac{2}{5} = 3\frac{3}{5}\)
Final answer:

\(2\frac{1}{5} + 1\frac{2}{5} = 3\frac{3}{5}\)

Applied rules:

• Separate addition: Add whole numbers and fractions separately

• Like denominators: Add numerators of fractions, keep denominator

• Simplification: Reduce fractions to lowest terms if possible

Key Concepts and Methods
\(\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}\)
Adding Fractions with Like Denominators
Key definitions:

Fraction: A number representing part of a whole, with a numerator (top) and denominator (bottom)

Like Denominators: Fractions that have the same denominator (bottom number)

Numerator: The top number in a fraction, representing how many parts are taken

Denominator: The bottom number in a fraction, representing the total number of equal parts

Complete methodology:
  1. Identify like denominators: Check that all fractions have the same denominator
  2. Add numerators: Sum all the numerators together
  3. Keep denominator: The denominator remains the same
  4. Simplify if needed: Reduce the fraction to lowest terms
Tip 1: Only add fractions when they have the same denominator. If denominators differ, find a common denominator first.
Tip 2: The denominator never changes when adding fractions with like denominators.
Tip 3: Always check if your final fraction can be simplified by finding the GCD of numerator and denominator.
Tip 4: You can visualize adding fractions by imagining pie slices with the same size pieces.
Common errors: Adding denominators instead of keeping them, forgetting to simplify, or trying to add fractions with different denominators directly.
Practice tips: Work with visual models like fraction bars, practice converting between mixed numbers and improper fractions, check answers by estimation.
Key formulas and rules:

• Addition with like denominators: \(\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}\)

• Simplification: Divide numerator and denominator by their GCD

• Mixed number addition: Add whole numbers and fractions separately

• GCD: Greatest Common Divisor is the largest number that divides both numerator and denominator evenly

Detailed Summary
Core Concepts:

• Fraction: A number expressing parts of a whole (numerator/denominator)

• Like Denominators: Fractions sharing the same denominator

• Simplification: Reducing fractions to lowest terms using GCD

Step-by-Step Process:
  1. Confirm all fractions have the same denominator
  2. Add all numerators together
  3. Keep the denominator unchanged
  4. Simplify the result if possible
Examples: Simple: \(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\), Advanced: \(3\frac{1}{6} + 2\frac{3}{6} = 5\frac{4}{6} = 5\frac{2}{3}\)
Common Mistakes: Adding denominators, forgetting to simplify, adding fractions with different denominators directly
Memory Tip: Think "Same Bottom, Add Top" - when denominators are the same, only add the numerators!
Visual Examples and Properties
\(\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}\)
Addition Formula
Example 1
\(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\)
Add numerators, keep denominator
Example 2
\(\frac{2}{5} + \frac{1}{5} = \frac{3}{5}\)
Same denominator stays
Simplification
\(\frac{4}{8} = \frac{1}{2}\)
Divide by GCD
Addition Process
📊
Step 1: Check denominators

Confirm all fractions have the same denominator

\(\frac{2}{7} + \frac{3}{7}\) ✓ same denominator
Step 2: Add numerators

Sum all numerators, keep denominator

\(\frac{2+3}{7} = \frac{5}{7}\)
Step 3: Simplify

Reduce fraction to lowest terms if possible

\(\frac{4}{8} = \frac{1}{2}\)
Visual Process
1
Check Denominators
2
Add Numerators
3
Keep Denominator
4
Simplify
Fraction Visualization
Visual representation showing how like denominators allow direct addition of numerators
Practice Makes Perfect!
Frequently Asked Questions

Question: Why do we only add the numerators when fractions have the same denominator? Why don't we add the denominators too?

Answer: The denominator tells us the size of the pieces we're working with. When we have fractions like \(\frac{2}{7}\) and \(\frac{3}{7}\), both refer to pieces of the same size (sevenths). So we're just counting how many pieces we have in total: 2 pieces plus 3 pieces equals 5 pieces. The pieces stay the same size (sevenths), so the denominator doesn't change.

Think of it like adding apples: 2 apples + 3 apples = 5 apples. The "apples" part doesn't change, only the count changes. Similarly, \(\frac{2}{7} + \frac{3}{7} = \frac{5}{7}\), the "sevenths" part doesn't change, only the count changes.

Question: When do I need to simplify my answer after adding fractions?

Answer: You should always check if your answer can be simplified after adding fractions. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify:

  • Find the Greatest Common Divisor (GCD) of the numerator and denominator
  • Divide both the numerator and denominator by the GCD
  • Repeat until no common factors remain

For example, if you get \(\frac{6}{8}\) as your answer, since 6 and 8 share a common factor of 2, you divide both by 2 to get \(\frac{3}{4}\), which is the simplified form.

Question: What happens if I try to add fractions that don't have the same denominator?

Answer: You cannot add fractions directly if they have different denominators. You must first find a common denominator. The easiest way is to find the Least Common Denominator (LCD), which is the smallest number that both denominators divide into evenly.

For example, to add \(\frac{1}{3} + \frac{1}{4}\), you would find the LCD of 3 and 4, which is 12. Then convert each fraction: \(\frac{1}{3} = \frac{4}{12}\) and \(\frac{1}{4} = \frac{3}{12}\). Now you can add: \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\).