Uvero — STEM Learning

Equivalent Ratios

Multiplying or dividing every ratio part by the same non-zero number preserves the comparison. Simplify ratios using a common factor and keep quantities in the same units. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Multiply both parts by 4.
$3:5=12:20$ .

Which ratio is equivalent to $3:5$ ?

$12:20$

$6:15$

$9:10$

$15:3$

Which statement best captures the central mathematical idea in Equivalent Ratios?

Simplify ratios using a common factor and keep quantities in the same units.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Equivalent Ratios, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for equivalent ratios.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Equivalent Ratios?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

Simplify ratios using a common factor and keep quantities in the same units.

Represent the given information clearly and identify the operation or relationship required for equivalent ratios.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.