All Labs

Fraction Operations & Equivalents Lab

Visualize fraction arithmetic with colored fraction bars. Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step solutions. Discover equivalent fractions and learn to simplify to lowest terms.

Guided Experiment: Adding Fractions with Unlike Denominators

What happens when you add two fractions that have different denominators? Why can't you simply add the numerators and denominators separately?

Write your hypothesis in the Lab Report panel, then click Next.

Fraction Bars

A1/2+B1/3==5/6
Fraction AFraction BResult

Controls

Fraction A
Fraction B

Results

Final Answer
56\frac{5}{6}
Common Denominator (LCD)
6
Step-by-Step Solution
1Convert to improper fractions: 12+13\text{Convert to improper fractions: } \frac{1}{2} + \frac{1}{3}
2LCD=6\text{LCD} = 6
31×32×3+1×23×2=36+26\frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} = \frac{3}{6} + \frac{2}{6}
43+26=56\frac{3 + 2}{6} = \frac{5}{6}

Data Table

(0 rows)
#OperationFraction AFraction BResultSimplifiedCommon Denominator
0 / 500
0 / 500
0 / 500

Reference Guide

Adding & Subtracting Fractions

To add or subtract fractions, first find a common denominator (the LCD). Then add or subtract the numerators and keep the common denominator.

ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

Always simplify the result by dividing both numerator and denominator by their greatest common divisor (GCD).

Multiplying & Dividing Fractions

To multiply fractions, multiply the numerators together and the denominators together. No common denominator is needed.

ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

To divide fractions, multiply by the reciprocal of the second fraction. Flip the second fraction and multiply.

Equivalent Fractions

Two fractions are equivalent if they simplify to the same value. Multiply or divide both numerator and denominator by the same non-zero number.

12=24=36=48\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}

To check equivalence, cross-multiply. If ad = bc, then a/b = c/d.

Mixed Numbers & Improper Fractions

A mixed number like 2 3/4 can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator.

234=2×4+34=1142\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}

To convert back, divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator.