Subtracting Fractions with Like Denominators Worksheets for Grade 4

Master subtracting fractions with like denominators: subtracting numerators, simplifying, through these 5 detailed exercises designed for worksheets.

Worksheet Problems 1 to 3 with Solutions
1 Basic subtraction without simplification
Problem 1
Subtract:
\(\frac{5}{8} - \frac{3}{8}\)
Definition:

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

Numerator: The top number in a fraction (represents the parts taken)

Denominator: The bottom number in a fraction (represents the total number of equal parts)

Subtraction method:
  1. Check that denominators are the same
  2. Subtract the numerators
  3. Keep the denominator the same
  4. Simplify the fraction if needed
Original Expression
\(\frac{5}{8} - \frac{3}{8}\)
Subtract Numerators
\(\frac{5-3}{8}\)
Result
\(\frac{2}{8}\)
Step 1: Check denominators

Both fractions have denominator 8, so they are like fractions.

Step 2: Subtract the numerators

\(5 - 3 = 2\)

Step 3: Keep the denominator

The denominator stays 8: \(\frac{2}{8}\)

Step 4: Simplify the fraction

\(\frac{2}{8} = \frac{1}{4}\) (divide numerator and denominator by 2)

\(\frac{5}{8} - \frac{3}{8} = \frac{1}{4}\)
Final answer:

\(\frac{5}{8} - \frac{3}{8} = \frac{1}{4}\)

Applied rules:

• Like denominators: Only subtract numerators, keep denominator

• Simplification: Divide numerator and denominator by their greatest common divisor (GCD)

• Rule: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

5/8
-
3/8
=
2/8
→
1/4
2 Subtraction with simplification
Problem 2
Subtract:
\(\frac{7}{12} - \frac{5}{12}\)
Definition:

Simplification: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).

Original Expression
\(\frac{7}{12} - \frac{5}{12}\)
Subtract Numerators
\(\frac{7-5}{12}\)
Simplify
\(\frac{1}{6}\)
Step 1: Check denominators

Both fractions have denominator 12, so they are like fractions.

Step 2: Subtract the numerators

\(7 - 5 = 2\)

Step 3: Keep the denominator

The denominator stays 12: \(\frac{2}{12}\)

Step 4: Simplify the fraction

Find GCD of 2 and 12: GCD(2, 12) = 2

Divide both by 2: \(\frac{2 ÷ 2}{12 ÷ 2} = \frac{1}{6}\)

\(\frac{7}{12} - \frac{5}{12} = \frac{1}{6}\)
Final answer:

\(\frac{7}{12} - \frac{5}{12} = \frac{1}{6}\)

Applied rules:

• Like denominators: Only subtract numerators, keep denominator

• Simplification: Divide by GCD to reduce to lowest terms

• Rule: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

7/12
-
5/12
=
2/12
→
1/6
3 Subtraction resulting in zero
Problem 3
Subtract:
\(\frac{4}{7} - \frac{4}{7}\)
Definition:

Identity property: Any number minus itself equals zero.

Original Expression
\(\frac{4}{7} - \frac{4}{7}\)
Subtract Numerators
\(\frac{4-4}{7}\)
Result
\(\frac{0}{7} = 0\)
Step 1: Check denominators

Both fractions have denominator 7, so they are like fractions.

Step 2: Subtract the numerators

\(4 - 4 = 0\)

Step 3: Keep the denominator

The denominator stays 7: \(\frac{0}{7}\)

Step 4: Simplify

\(\frac{0}{7} = 0\) (zero divided by any non-zero number is zero)

\(\frac{4}{7} - \frac{4}{7} = 0\)
Final answer:

\(\frac{4}{7} - \frac{4}{7} = 0\)

Applied rules:

• Identity property: \(a - a = 0\)

• Zero fraction: \(\frac{0}{a} = 0\) (where a ≠ 0)

• Rule: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

4/7
-
4/7
=
0/7
→
0
Rules and Methods for Subtracting Like Denominators
\(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)
Subtracting Fractions with Like Denominators
Rule 1
\(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)
Like Denominator Subtraction
Rule 2
\(\frac{0}{a} = 0\)
Zero Property
Rule 3
\(\frac{a}{a} = 1\)
Identity Property
Key Steps: 1) Check denominators are the same, 2) Subtract numerators, 3) Keep denominator, 4) Simplify if needed
Visual Model: Use fraction bars or circles to represent fractions
Worksheet Problems 4 to 5 with Solutions
4 Subtraction with larger numerator difference
Problem 4
Subtract:
\(\frac{9}{10} - \frac{3}{10}\)
Definition:

Greatest Common Divisor (GCD): The largest positive integer that divides both numerator and denominator without remainder.

Original Expression
\(\frac{9}{10} - \frac{3}{10}\)
Subtract Numerators
\(\frac{9-3}{10}\)
Simplify
\(\frac{3}{5}\)
Step 1: Check denominators

Both fractions have denominator 10, so they are like fractions.

Step 2: Subtract the numerators

\(9 - 3 = 6\)

Step 3: Keep the denominator

The denominator stays 10: \(\frac{6}{10}\)

Step 4: Simplify the fraction

Find GCD of 6 and 10: GCD(6, 10) = 2

Divide both by 2: \(\frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5}\)

\(\frac{9}{10} - \frac{3}{10} = \frac{3}{5}\)
Final answer:

\(\frac{9}{10} - \frac{3}{10} = \frac{3}{5}\)

Applied rules:

• Like denominators: Only subtract numerators, keep denominator

• Simplification: Divide by GCD to reduce to lowest terms

• Rule: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

9/10
-
3/10
=
6/10
→
3/5
5 Word problem with like denominators
Problem 5
Sarah ate \(\frac{5}{6}\) of a pizza. Her brother ate \(\frac{2}{6}\) of the same pizza. How much more pizza did Sarah eat?
Definition:

Word problems: Real-world scenarios that require mathematical operations to solve.

Problem
Sarah: \(\frac{5}{6}\), Brother: \(\frac{2}{6}\)
Subtract
\(\frac{5}{6} - \frac{2}{6}\)
Result
\(\frac{3}{6} = \frac{1}{2}\)
Step 1: Identify the operation

We need to find the difference: Sarah's portion - Brother's portion

Step 2: Set up the subtraction

\(\frac{5}{6} - \frac{2}{6}\)

Step 3: Check denominators

Both fractions have denominator 6, so they are like fractions.

Step 4: Subtract the numerators

\(5 - 2 = 3\)

Step 5: Keep the denominator

The denominator stays 6: \(\frac{3}{6}\)

Step 6: Simplify the fraction

\(\frac{3}{6} = \frac{1}{2}\) (divide numerator and denominator by 3)

Sarah ate \(\frac{1}{2}\) more pizza than her brother.
Final answer:

Sarah ate \(\frac{1}{2}\) more pizza than her brother.

Applied rules:

• Like denominators: Only subtract numerators, keep denominator

• Simplification: Divide by GCD to reduce to lowest terms

• Rule: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

5/6
(Sarah)
-
2/6
(Brother)
=
3/6
→
1/2
Complete Guide to Subtracting Fractions with Like Denominators
\(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)
Subtracting Fractions Rule
Key definitions:

Fraction: A number representing part of a whole, written as \(\frac{a}{b}\) where a is the numerator and b is the denominator.

Like Denominators: Fractions that have the same denominator (e.g., \(\frac{3}{5}\) and \(\frac{2}{5}\)).

Unlike Denominators: Fractions that have different denominators (e.g., \(\frac{3}{5}\) and \(\frac{2}{3}\)).

Simplification: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).

Complete methodology:
  1. Check denominators: Verify that both fractions have the same denominator
  2. Subtract numerators: Subtract the numerators of the fractions
  3. Keep denominator: The denominator remains unchanged
  4. Simplify: Reduce the fraction to its lowest terms if possible
  5. Check answer: Verify the result makes sense in context
Tip 1: Only subtract fractions that have the same denominator.
Tip 2: Remember to keep the denominator the same after subtracting numerators.
Tip 3: Always simplify your answer by finding the GCD of numerator and denominator.
Tip 4: If the numerator is 0 after subtraction, the result is 0.
Common errors: Forgetting to keep the same denominator, subtracting denominators, not simplifying the final answer.
Memory aid: "Bottom stays the same, top gets subtracted!"
Formulas to know by heart:

• Subtraction: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

• Zero property: \(\frac{0}{a} = 0\) (where a ≠ 0)

• Identity property: \(\frac{a}{a} = 1\) (where a ≠ 0)

• Simplification: Divide numerator and denominator by GCD

Worksheet Practice: Visualizing Fraction Subtraction
Visual Method: Fraction Bars
Using fraction bars to visualize:
\(\frac{5}{8} - \frac{2}{8}\)
Visualization: 5/8 - 2/8 = 3/8

Analysis: The visual representation helps understand how fraction subtraction works.

  • Top bar represents the first fraction (5/8)
  • Red part shows what we're subtracting (2/8)
  • Bottom bar shows the result (3/8)

Questions & Answers

Question: Why do I need to keep the denominator the same when subtracting fractions with like denominators?

Answer: Great question! The denominator tells us how many equal parts the whole is divided into. When we subtract fractions with the same denominator, we're working with pieces of the same size.

Example: In \(\frac{5}{8} - \frac{3}{8}\), both fractions are made of eighths - the same size pieces.

We're just counting how many of those same-sized pieces we have left: 5 pieces - 3 pieces = 2 pieces, so \(\frac{2}{8}\).

If we changed the denominator, we'd be talking about different sized pieces, which wouldn't make sense in this context.

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

Answer: You should always simplify your answer to its lowest terms. This means dividing both the numerator and denominator by their greatest common divisor (GCD).

Example: In \(\frac{6}{8}\), the GCD of 6 and 8 is 2.

So: \(\frac{6}{8} = \frac{6 ÷ 2}{8 ÷ 2} = \frac{3}{4}\)

Why simplify? It gives the clearest, most reduced form of the answer, making it easier to work with and compare to other fractions.

Always check if you can simplify your answer by finding common factors!

Question: What if I want to subtract fractions that don't have the same denominator?

Answer: When fractions have different denominators (unlike denominators), you must first find equivalent fractions with the same denominator.

Steps:

  • Find the Least Common Denominator (LCD) of the fractions
  • Convert each fraction to an equivalent fraction with the LCD
  • Now subtract the numerators and keep the common denominator
  • Simplify if needed

Example: To subtract \(\frac{1}{2} - \frac{1}{3}\):

LCD of 2 and 3 is 6, so: \(\frac{1}{2} = \frac{3}{6}\) and \(\frac{1}{3} = \frac{2}{6}\)

Then: \(\frac{3}{6} - \frac{2}{6} = \frac{1}{6}\)