About the Fraction Visualizer
This fraction visualizer draws fractions the way they are taught in class: as fraction circles (pie models), bar models and a point on a number line. Enter a numerator and denominator and you immediately see how many equal parts the whole is cut into and how many are shaded — and a second fraction alongside it so you can compare the two shapes side by side.
Below the pictures you get the numbers that go with them: each fraction in simplest form, as a decimal and a percentage, both fractions rewritten over their least common denominator, which one is larger, and their sum and difference. Improper fractions such as 7/4 are drawn as more than one whole and shown as mixed numbers.
It is meant for students meeting fractions for the first time, parents helping with homework and teachers who want a quick visual for the board. Equivalent fractions become obvious: 2/4, 3/6 and 6/12 all shade exactly half of the circle.
How to use the fraction visualizer
- 1Type the numerator (top number) and denominator (bottom number) of fraction A.
- 2Enter a second fraction B to compare against.
- 3Look at the pies and bars to see which shades more of the whole.
- 4Read the comparison, simplest forms and the common-denominator version below.
- 5Try equivalent fractions such as 2/4 and 4/8 to see that they shade the same amount.
Formula and method
A fraction a/b means the whole is split into b equal parts and a of them are shaded, which is exactly what the pie and bar models draw. To compare two fractions the tool cross-multiplies: a/b is larger than c/d when a × d is larger than c × b, which avoids rounding decimals.
For the common-denominator view it uses the least common multiple of the two denominators, and sums and differences are computed over b × d and then reduced by dividing the top and bottom by their greatest common divisor. Fractions larger than one are also shown as mixed numbers (for example 7/4 = 1 3/4).
- a, c
- Numerators: how many parts are shaded
- b, d
- Denominators: how many equal parts make one whole
- LCM
- Least common multiple, used as the common denominator
- GCD
- Greatest common divisor, used to simplify
Worked examples
Which is bigger, 3/4 or 2/3?
Cross-multiplying gives 3 × 3 = 9 against 2 × 4 = 8, so 3/4 is larger. Over the common denominator 12 they are 9/12 and 8/12, a difference of 1/12. Together they make 17/12, or 1 and 5/12.
Equivalent fractions: 6/8 and 3/4
Dividing 6 and 8 by their greatest common divisor, 2, gives 3/4, so both fractions shade three quarters of the whole. Cross-multiplying confirms it: 6 × 4 = 24 and 3 × 8 = 24.
Improper fractions: 7/4 vs 5/3
7/4 is one whole and three quarters (1.75) and 5/3 is one whole and two thirds (about 1.667). Cross-multiplying gives 21 versus 20, so 7/4 is bigger by 1/12; their sum is 41/12, or 3 and 5/12.
Frequently asked questions
How do you compare fractions with different denominators?+
Either rewrite both fractions over a common denominator (the least common multiple of the two bottoms) and compare the tops, or cross-multiply: for a/b and c/d, compare a × d with c × b. The larger product belongs to the larger fraction.
What is a fraction circle?+
A fraction circle (pie model) is a circle divided into equal slices, one slice per part of the denominator, with the numerator’s number of slices shaded. It helps students see that larger denominators mean smaller pieces.
What is a bar model for fractions?+
A bar model draws one whole as a rectangle split into equal sections. Shading some sections shows the fraction, and lining up two bars of the same length makes it easy to compare fractions or spot equivalent ones.
Why do 2/4 and 1/2 look the same?+
They are equivalent fractions: multiplying or dividing the top and bottom by the same number does not change the amount. 2/4 cuts the whole into more, smaller pieces, but shades the same total area as 1/2.
How are fractions bigger than 1 shown?+
An improper fraction such as 7/4 fills one whole completely and part of another, so the visualizer draws two pies or bars. It is also written as the mixed number 1 3/4.