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Interactive toolkit

Fraction Toolkit

Four ways to see the same idea. Change the numerator and denominator and watch each model respond.

Fraction Bar

See equal parts of a length, and fractions beyond one whole.

1/41/41/41/4
Fraction bar showing 3 quarters: 1 whole bar, each split into 4 equal parts, with 3 shaded.
Numerator3
Denominator4

Number Line

Locate fractions as distances from zero.

01/42/43/415/46/47/42
Number line from 0 to 2, each whole split into 4 equal parts. A point marks 5 quarters, 5 jumps of one 4th from zero.
Numerator5
Denominator4

Fraction Circle

Compare slices of the same whole.

Fraction circles showing 2 thirds: 1 circle, each cut into 3 equal slices, with 2 shaded.
Numerator2
Denominator3

Area Model

Multiply fractions by finding the overlap.

Area model of 3 quarters times 2 thirds: 3 of 4 columns and 2 of 3 rows are shaded. They overlap in 6 of 12 equal cells, which is 6 twelfths.

Columns fraction

Numerator3
Denominator4

Rows fraction

Numerator2
Denominator3

Numerators are kept at or below their denominators in this model.