Different pieces. Same amount.
Different fractions can name the same amount.
One printable page with the original image and complete lesson.
Question
How can one-half, two-fourths, and four-eighths all be equal?
Answer
They are equivalent fractions: different ways to describe the same amount when we start with the same-sized whole.
History
Long before calculators, people used fractions to share food, measure land, and solve practical problems. The ancient Egyptian Rhind Mathematical Papyrus includes problems involving fractions.
Example
Divide a rectangle into two equal pieces and shade one. Divide an identical rectangle into four equal pieces and shade two. Each picture shows half of the whole.
Insight
Multiplying a fraction's numerator and denominator by the same positive whole number preserves its value: 1/2 = 2/4 = 4/8. More, smaller pieces can represent the same amount.
Connection
Equivalent fractions help us compare quantities, adjust recipes, and measure accurately. Always check the whole: half of a small pizza is not the same amount of food as half of a large pizza!
Challenge
Cut three equal paper strips. Fold them into halves, fourths, and eighths. Shade half of each and label the fractions. Line them up to check the shaded lengths. Explain why the amounts match. Can you also show 3/6?