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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%

/21/2 /3≈— /42/4 /5≈— /63/6 /84/8 /105/10 /126/12
11/22

1/2 is equivalent to: 2/43/64/85/106/12

Fraction visualizer

Who this demo helps, and where to practice next

Equivalent Fraction Bars is built for students who need fractions as visible equal parts and number-line positions. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.

Equivalent Fraction Bars helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.

Learning goals

  • Change the denominator from 2 to 4: the same half becomes 2/4. The bar length never changes — only how many ticks divide it.
  • At 1/2, green dots appear on bars 4, 6, 8, 10, and 12 because 2/4, 3/6, 4/8, 5/10, and 6/12 are all exactly one half.
  • At 2/3, green dots only appear on 6 and 12 (4/6 and 8/12). Denominators that are not multiples of the original often have no exact match.

How to play

  1. 1 Start from one whole and change only the denominator.
  2. 2 Shade, compare, or align fractions while keeping the whole fixed.
  3. 3 Use the related topic pages to move from pictures into symbolic comparisons.
FAQ

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.

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