Learn on PengiPengi Math (Grade 6)Chapter 3: Ratios, Rates, and Percent

Lesson 2: Equivalent Ratios and Scaling

In this Grade 6 Pengi Math lesson from Chapter 3: Ratios, Rates, and Percent, students learn how to generate equivalent ratios using multiplication and division and represent them in tables. The lesson explains why additive changes do not preserve ratios and teaches students to verify ratio equivalence using cross products.

Section 1

Generating Equivalent Ratios

Property

To find a ratio equivalent to $a:b$ , multiply or divide both terms by the same non-zero number, $c$ .

a:b = (a \times c):(b \times c)

a:b = (a \div c):(b \div c)

Examples

Section 2

Verifying Ratio Equivalence

Property

Two ratios, represented as fractions $\frac{a}{b}$ and $\frac{c}{d}$ , are equivalent if and only if their cross-products are equal.

a \times d = b \times c

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Generating Equivalent Ratios

Property

To find a ratio equivalent to $a:b$ , multiply or divide both terms by the same non-zero number, $c$ .

a:b = (a \times c):(b \times c)

a:b = (a \div c):(b \div c)

Examples

Section 2

Verifying Ratio Equivalence

Property

Two ratios, represented as fractions $\frac{a}{b}$ and $\frac{c}{d}$ , are equivalent if and only if their cross-products are equal.

a \times d = b \times c