Fraction: worked example
| First numerator | 3 |
|---|---|
| First denominator | 4 |
| Operation | Add (+) |
| Second numerator | 5 |
| Second denominator | 6 |
| Simplified numerator | 19 |
| Simplified denominator | 12 |
| Decimal value | 1.6 |
Fraction: formula
Enter the numerator and denominator of each fraction and pick the operation: add, subtract, multiply or divide. Denominators must not be zero. To add or subtract, the calculator finds a common denominator, multiplies for multiplication, and inverts the second fraction for division.
The answer is reduced to lowest terms and also shown as a decimal. Mixed numbers should be converted to improper fractions first.
Fraction: changing First numerator
| First numerator | Simplified numerator | Simplified denominator | Decimal value |
|---|---|---|---|
| 1 | 13 | 12 | 1.1 |
| 2 | 4 | 3 | 1.3 |
| 3 (example) | 19 | 12 | 1.6 |
| 4 | 11 | 6 | 1.8 |
| 5 | 25 | 12 | 2.1 |
Fraction: compare input ranges
| Input | Tested from | To | Simplified numerator: low input | Simplified numerator: high input | Swing |
|---|---|---|---|---|---|
| Operation | Add (+) | Divide (÷) | 19 | 9 | 10 (105%) |
| Second denominator | 4 | 8 | 2 | 11 | 9 (47%) |
| First denominator | 3 | 5 | 11 | 43 | 32 (168%) |
| First numerator | 2 | 4 | 4 | 11 | 7 (37%) |
| Second numerator | 4 | 6 | 17 | 7 | 10 (53%) |
Fraction: individual input comparisons
| Input | Value | Simplified numerator | Simplified denominator | Decimal value |
|---|---|---|---|---|
| First numerator | 1 | 13 | 12 | 1.1 |
| 2 | 4 | 3 | 1.3 | |
| 3 | 19 | 12 | 1.6 | |
| 4 | 11 | 6 | 1.8 | |
| 5 | 25 | 12 | 2.1 | |
| First denominator | 2 | 7 | 3 | 2.3 |
| 3 | 11 | 6 | 1.8 | |
| 4 | 19 | 12 | 1.6 | |
| 5 | 43 | 30 | 1.4 | |
| 6 | 4 | 3 | 1.3 | |
| Operation | Add (+) | 19 | 12 | 1.6 |
| Subtract (−) | -1 | 12 | -0.083 | |
| Multiply (×) | 5 | 8 | 0.625 | |
| Divide (÷) | 9 | 10 | 0.9 | |
| Second numerator | 3 | 5 | 4 | 1.3 |
| 4 | 17 | 12 | 1.4 | |
| 5 | 19 | 12 | 1.6 | |
| 6 | 7 | 4 | 1.8 | |
| 7 | 23 | 12 | 1.9 | |
| Second denominator | 2 | 13 | 4 | 3.3 |
| 4 | 2 | 1 | 2 | |
| 6 | 19 | 12 | 1.6 | |
| 8 | 11 | 8 | 1.4 | |
| 10 | 5 | 4 | 1.3 |
Fraction: combined input changes
| First numerator / First denominator | 2 | 4 | 6 |
|---|---|---|---|
| 1 | 4 | 13 | 1 |
| 2 | 11 | 4 | 7 |
| 3 | 7 | 19 | 4 |
| 4 | 17 | 11 | 3 |
| 5 | 10 | 25 | 5 |
Fraction: which assumptions move the result?
Fraction: values and definitions
| Quantity and definition | Value used |
|---|---|
| First numerator — The top number of the first fraction. | 3 |
| First denominator — The bottom number of the first fraction. It cannot be zero. | 4 |
| Operation — Choose add, subtract, multiply or divide. | Add (+) |
| Second numerator — The top number of the second fraction. | 5 |
| Second denominator — The bottom number of the second fraction. It cannot be zero. | 6 |
| Simplified numerator | 19 |
| Simplified denominator | 12 |
| Decimal value | 1.6 |
Common error: Adding tops and bottoms separately. It feels natural and gives an answer smaller than one of the inputs, which can never be right for a sum of positive fractions.
Dividing by a fraction with a zero numerator is undefined. The decimal is an approximation for fractions that repeat, such as one third. Very large numerators and denominators may lose precision.
Negative fractions follow the usual sign rules, and the tool keeps the minus sign in the numerator.
Algebra & Arithmetic calculators: Decimal to Fraction Calculator, Arithmetic Sequence Calculator, Geometric Sequence Calculator, Percent Difference Calculator, Proportion Calculator, Roman Numeral Calculator.
Two fractions with different bottoms cannot be added until they share one. That is the whole reason 3/4 + 5/6 does not equal 8/10. The calculator finds the shared bottom, adds, then divides top and bottom by whatever they have in common, so 38/24 arrives as 19/12.
Seeing the decimal beside it, 1.583, tells you whether a recipe or a cut list is in the right neighborhood before you trust the reduced form.
Estimate first. Three quarters plus five sixths must land a little under two, so 19/12 passes and 8/10 fails on sight.
Reduce a result on the fraction simplifier calculator, convert a mixed number on the mixed number page, and turn decimals into fractions on the decimal to fraction calculator. The GCF and LCM calculator finds common denominators, and the ratio and proportion pages solve related problems.
How do I add fractions with different denominators?
Rewrite them with a common denominator, add the numerators and keep the denominator, then simplify the result.
How do I divide by a fraction?
Multiply by its reciprocal. Dividing by five sixths is the same as multiplying by six fifths.
What is an improper fraction?
A fraction whose numerator is larger than its denominator, so it represents more than one whole, such as 19 over 12.