Learn on PengiThe Art of Problem Solving: Prealgebra (AMC 8)Chapter 4: Fractions

Lesson 7: Adding and Subtracting Fractions

In this Grade 4 lesson from The Art of Problem Solving: Prealgebra (AMC 8), students learn how to add and subtract fractions by applying the distributive property of division over addition and subtraction to combine fractions with like denominators. The lesson emphasizes a common misconception — that adding numerators and denominators separately is incorrect — and builds toward finding common denominators for fractions with unlike denominators. Students practice simplifying results and interpreting fraction addition and subtraction on the number line.

Section 1

Add Fractions with a Common Denominator

Property

If aa, bb, and cc are numbers where c0c \neq 0, then

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

To add fractions with a common denominator, add the numerators and place the sum over the common denominator.

Section 2

Subtract Fractions with a Common Denominator

Property

If aa, bb, and cc are numbers where c0c \neq 0, then

acbc=abc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

To subtract fractions with a common denominator, we subtract the numerators and place the difference over the common denominator.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Fractions

  1. Lesson 1

    Lesson 1: What is a Fraction?

  2. Lesson 2

    Lesson 2: Multiplying Fractions

  3. Lesson 3

    Lesson 3: Dividing by a Fraction

  4. Lesson 4

    Lesson 4: Raising Fractions to Powers

  5. Lesson 5

    Lesson 5: Simplest Form of a Fraction

  6. Lesson 6

    Lesson 6: Comparing Fractions

  7. Lesson 7Current

    Lesson 7: Adding and Subtracting Fractions

  8. Lesson 8

    Lesson 8: Mixed Numbers

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Add Fractions with a Common Denominator

Property

If aa, bb, and cc are numbers where c0c \neq 0, then

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

To add fractions with a common denominator, add the numerators and place the sum over the common denominator.

Section 2

Subtract Fractions with a Common Denominator

Property

If aa, bb, and cc are numbers where c0c \neq 0, then

acbc=abc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

To subtract fractions with a common denominator, we subtract the numerators and place the difference over the common denominator.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Fractions

  1. Lesson 1

    Lesson 1: What is a Fraction?

  2. Lesson 2

    Lesson 2: Multiplying Fractions

  3. Lesson 3

    Lesson 3: Dividing by a Fraction

  4. Lesson 4

    Lesson 4: Raising Fractions to Powers

  5. Lesson 5

    Lesson 5: Simplest Form of a Fraction

  6. Lesson 6

    Lesson 6: Comparing Fractions

  7. Lesson 7Current

    Lesson 7: Adding and Subtracting Fractions

  8. Lesson 8

    Lesson 8: Mixed Numbers