Multiply fractions, mixed numbers, and whole integers with instant step-by-step solutions. Features automatic cross-cancellation, lowest terms GCD reduction, mixed number conversions, and visual 2D area models.
Multiplying fractions is straightforward because you do not need to find a common denominator. Follow these essential steps:
Enter the numerator and denominator for each fraction. If multiplying mixed numbers (e.g. 1 1/2), enter the whole integer in the designated field.
Review the cross-cancellation diagnostic to see how opposite terms are simplified before multiplying to keep numbers manageable.
Examine the simplified irreducible fraction, mixed number equivalent, floating-point decimal, and step-by-step arithmetic proof.
Bakers needing half or two-thirds of a recipe (such as 3/4 cup of sugar multiplied by 1/2 = 3/8 cup) avoid messy decimal conversions.
Multiplying mixed numbers like 2 1/3 by 3 1/4 directly requires four-term polynomial expansion; this tool handles seamless improper conversion.
Calculating joint independent probabilities (such as P(A and B) = 3/10 * 5/12 = 1/8) with instant cross-cancellation verification.
Contractors computing rectangular floor or fabric areas with fractional dimensions (such as 8 1/2 ft by 10 3/4 ft = 91 3/8 sq ft).
Identifies and cancels shared factors between opposite numerators and denominators prior to multiplication.
Seamlessly add a third fraction with a single click to multiply multi-factor chain problems without manual recalculation.
Accepts mixed numbers with whole parts, converts them to improper form, and provides the final product in both mixed and improper formats.
Shows both the unreduced product (straight multiplication) and the simplified lowest terms result with greatest common divisor steps.
To multiply two fractions, multiply the numerators together and multiply the denominators together:
Where \(b \neq 0\) and \(d \neq 0\). If common factors exist between \(a\) and \(d\) or between \(c\) and \(b\), divide them out before multiplying.
Multiply straight across, but cross-cancel shared factors first. Divide 3 and 9 by 3, and divide 4 and 8 by 4:
Convert each mixed number to an improper fraction before multiplying straight across:
| Multiplication Problem | Unreduced Product | Simplified Lowest Terms | Decimal Equivalent |
|---|---|---|---|
| 1/2 × 1/3 | 1/6 | 1/6 | 0.1667 |
| 2/3 × 3/4 | 6/12 | 1/2 | 0.5 |
| 3/5 × 5/6 | 15/30 | 1/2 | 0.5 |
| 3/4 × 4/5 | 12/20 | 3/5 | 0.6 |
| 1 1/2 × 2/3 | 6/6 | 1 | 1.0 |
Never waste time finding a common denominator when multiplying fractions. Multiply straight across (numerator by numerator, denominator by denominator). Always cross-cancel factors beforehand to keep calculations fast and simple.
When resizing batches in a kitchen or shop, multiplying fractions preserves standard physical measuring units. For instance, halving 3/4 cup produces 3/8 cup (which converts directly to 6 level tablespoons) without decimal rounding error.
No. Unlike fraction addition and subtraction, multiplying fractions does not require a common denominator. You simply multiply the numerators straight across to obtain the new numerator, and multiply the denominators straight across to obtain the new denominator.
Cross-cancellation is a technique where you simplify common factors between any numerator and any opposite denominator before multiplying. This keeps the intermediate numbers much smaller and prevents the need for tedious simplification of large numbers at the final step.
You must always convert mixed numbers into improper fractions first. For example, to multiply 1 1/2 by 2 2/3: convert 1 1/2 to 3/2 and 2 2/3 to 8/3. Next, cross-cancel the 3s and simplify 8/2 to 4/1. Multiplying across yields 4, which is far simpler than direct polynomial expansion.
Rewrite the whole integer as a fraction with a denominator of 1 (for example, 4 becomes 4/1). Then multiply the numerators straight across and the denominators straight across: (3/5) * (4/1) = 12/5 = 2 2/5.
A proper fraction represents a quantity strictly between 0 and 1 (a part of a whole). When you multiply by a fraction like 1/2, you are calculating a fraction of that quantity (such as half of a third, which is 1/6). Taking a fraction of a portion always yields an even smaller subdivision.
