Equivalent Fraction Bars
Same amount, different denominators
Stacked bars all show the same proportional amount. Change the denominator and slide the numerator — green dots mark exact equivalents, pink bars show close-but-not-equal approximations.
What this game shows · Equivalent Fractions
Equivalent fractions are different names for the same amount. Stack bars of different denominators and the same proportional length appears at green dots: 1/2 = 2/4 = 3/6 = 5/10 = 6/12. Same length, different ticks.
- Equivalent
- two fractions with the same value: a/b = (a × k)/(b × k).
- Denominator
- how many ticks divide the bar — does not change its length.
- Numerator
- how many ticks are filled — moves with the denominator.
Aligned with CCSS 4.NF.A.1 (explain why a/b = (a × n)/(b × n) using visual fraction models).
Equivalent Fraction Bars
All bars below show the same amount: 1/2 = 50.0%
1/2 is equivalent to: 2/43/64/85/106/12
Equivalent fractions, proven.
01 Why is 1/2 = 2/4 = 3/6 the same? Same length
Each is the same proportional length. Multiplying numerator and denominator by the same number cuts each piece smaller and counts more pieces — the total length is unchanged.
02 How do you check two fractions are equivalent? a · d = b · c
Cross-multiply: a/b = c/d when a × d = b × c. For 2/3 and 8/12: 2 × 12 = 24 and 3 × 8 = 24, so yes.
03 Why do some denominators have no exact equivalent? Multiples only
Because the new denominator must share the prime factors of the original. 2/3 has equivalents only at multiples of 3 (4/6, 6/9, 8/12, …) — never at 4, 5, or 7.
04 Which grade is this game for? Grades 3–4
Grades 3–4, aligned with CCSS 4.NF.A.1. Sets up addition and comparison of fractions in Grade 5.