⚒️ The Fraction Forge

Hammer fractions into equivalent forms, weigh them on the anvil, and compare against benchmarks.

REMEMBER: Two fractions are equivalent when they name the same amount of the same whole. Multiplying (or dividing) the top and the bottom by the same nonzero number cuts the pieces into finer strips or fuses them into bigger ones — the shaded amount does not change. To compare two fractions: line them up with a common denominator, common numerator, or a benchmark like 0, 1/2, or 1. Comparisons are only valid when the wholes are the same size.

Part 1 · The Forge

Start with a fraction. The hammer multiplies top and bottom by the same number: the strip splits into finer pieces but the shaded amount stays put. The tongs fuse pieces back together (dividing top and bottom by the same number, when the fraction can simplify).

Denominators up to 24. Watch the strip as you hammer: the shaded region stays the same size.

Original
?
Current
?
Simplest form
?

The Anvil — compare two fractions

Two fractions on the anvil. Pick a strategy — common denominator, common numerator, or benchmark 1/2. Wrong strategies still work but leave more to think about; the right one makes the comparison land at a glance.

Same fraction, different wholes — a warning

The very same fraction, 1/2, can name different amounts if the wholes are different sizes. Only compare fractions when the wholes match.

Part 2 · Forge Challenges

Predict, then lock in. Some rounds ask which fractions are equivalent; some ask which is bigger; some catch common mistakes.

Part 3 · The Machines

Three step-by-step machines. Each step says what to do and why.

Make an equivalent fraction (grow or shrink)

    Compare using a common denominator

      Compare using benchmarks 0, 1/2, and 1

        Part 4 · Master Blacksmith Quiz

        Ten questions. Each wrong answer tells you which station to revisit.

        Question 1 of 10 Score: 0

        Word Box

        Numerator · Denominator
        The top and bottom of a fraction. In 3/4, 3 is the numerator (how many pieces you have) and 4 is the denominator (pieces the whole is cut into).
        Equivalent fractions
        Different names for the same amount. 1/2, 2/4, 3/6, 5/10 all shade the same portion of the strip.
        Multiply / divide by 1
        Multiplying top and bottom by the same number is really multiplying by 1 in disguise (2/2 = 1, 3/3 = 1). That’s why the value doesn’t change.
        Simplest form
        The equivalent fraction whose numerator and denominator share no common factor larger than 1.
        Common denominator
        A shared bottom number that lets two fractions be compared directly.
        Common numerator
        A shared top number. With the same top, whichever has the SMALLER bottom is bigger (bigger pieces).
        Benchmark fraction
        An anchor value (0, 1/2, 1) to compare a fraction against without computing.
        Same whole
        Fraction comparisons are valid only when both fractions refer to the same-size whole.
        Free lessons, assessments & worksheets at WinElements.com  ·  Unlimited online practice at Sleedu.com