Learn on PengiEureka Math, Grade 4Chapter 22: Fraction Equivalence Using Multiplication and Division

Lesson 2: Use the area model and multiplication to show the equivalence of two fractions.

In this Grade 4 Eureka Math lesson from Chapter 22, students learn how to use area models and multiplication to prove that two fractions are equivalent, such as showing that 2/3 equals 8/12 by multiplying both the numerator and denominator by the same number. The lesson builds understanding of fraction equivalence through visual models, number sentences, and counting exercises with equivalent fractions like thirds and sixths. Students practice applying this concept to both unit and non-unit fractions, connecting area model drawings to the multiplication rule for generating equivalent fractions.

Section 1

Decomposing Area Models for Equivalent Fractions

Property

Decomposing a fraction's area model by partitioning it into nn equal horizontal sections multiplies both the number of shaded parts (numerator) and the total number of parts (denominator) by nn, creating an equivalent fraction.

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 2

Verify Fraction Equivalence Using Multiplication

Property

To determine if two fractions are equivalent, such as ab=cd\frac{a}{b} = \frac{c}{d}, you must find a single whole number, nn, that satisfies both equations:

c=a×nandd=b×nc = a \times n \quad \text{and} \quad d = b \times n

If the same multiplier nn works for both the numerator and the denominator, the fractions are equivalent.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Decomposing Area Models for Equivalent Fractions

Property

Decomposing a fraction's area model by partitioning it into nn equal horizontal sections multiplies both the number of shaded parts (numerator) and the total number of parts (denominator) by nn, creating an equivalent fraction.

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 2

Verify Fraction Equivalence Using Multiplication

Property

To determine if two fractions are equivalent, such as ab=cd\frac{a}{b} = \frac{c}{d}, you must find a single whole number, nn, that satisfies both equations:

c=a×nandd=b×nc = a \times n \quad \text{and} \quad d = b \times n

If the same multiplier nn works for both the numerator and the denominator, the fractions are equivalent.

Examples