Fractions as equal parts
The idea
A fraction compares selected equal parts with the total equal parts in a whole. The denominator names the size of the parts; the numerator counts them. Always identify the whole before comparing fractions. Equal-looking numerators do not mean equal quantities.
Worked example
Three quarters of a pizza means three of four equal pieces. Three eighths of the same-sized pizza is smaller because eighths are smaller pieces. Multiplying numerator and denominator by two gives 3/4 = 6/8.
Another application
To compare 1/2 and 3/8, rename 1/2 as 4/8. Four eighths exceeds three eighths. A drawing of the same-sized whole shows why the equivalent fraction preserves the quantity.
A common misunderstanding
A larger denominator means smaller parts when the whole is fixed. Compare equal-sized wholes before deciding which fraction is greater.
Try it yourself
Draw a rectangle partitioned into fourths, then split every fourth in half. Shade three fourths and count the shaded eighths.
Check your understanding
What fraction equals 2/3 when the denominator is 12?
Reveal the explained answer
8/12. Multiply numerator and denominator by four.