Explain why different fractions can name the same number. Scale the numerator and denominator together and connect the calculation to equal parts of one whole.
Recognize equivalent fractions using a model or calculation.
Scale numerator and denominator by the same nonzero factor.
Explain why the whole must stay consistent when comparing models.
Change the pieces, preserve the amount
Dividing each fractional piece into smaller equal pieces changes how many pieces you count and the size of each piece together. The amount represented can stay the same.
Scale both parts of the notation
Multiplying numerator and denominator by the same nonzero number preserves a fraction’s value. Dividing both by a shared nonzero factor works in the reverse direction and can simplify the fraction.
A mistake to avoid
Adding the same number to the numerator and denominator does not generally preserve the value. Also check that two pictures represent the same whole before using their shaded areas to compare fractions.
Worked example
Show why 2/3 = 8/12
Split each third into 4 equal pieces. The whole now contains 12 pieces, and the 2 selected thirds contain 8 of them. In symbols, (2 × 4)/(3 × 4) = 8/12, so the represented amount is unchanged.
Learning paths that include this skill
Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.