Find Whole Number from Fraction Calculator
Calculate the total value (X) when you know that a specific fraction of it equals a certain number. Features Reciprocal Method visualization and instant verification.
If
of a number is, what is the number?
The number is:18
Reciprocal Method:
X = 12 × 32
About
A common algebraic puzzle asks: "If 23 of a number is 12, what is the number?" This requires reverse thinking. Instead of finding a part of a whole, you are rebuilding the whole from a part.
This tool solves the equation ab X = Y by utilizing the multiplicative inverse (reciprocal). By multiplying the known value Y by the reciprocal of the fraction (ba), we isolate X efficiently.
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Formulas
The equation is defined as:
ab × X = Y
To solve for X, multiply both sides by the reciprocal ba:
X = Y × ba = Y × ba
Reference Data
| If Fraction... | Is Equal To... | Operation | Total (X) |
|---|---|---|---|
| 12 | 10 | 10 × 2 | 20 |
| 23 | 12 | 12 × 3 ÷ 2 | 18 |
| 34 | 9 | 9 × 4 ÷ 3 | 12 |
| 15 | 5 | 5 × 5 | 25 |
Frequently Asked Questions
The reciprocal of a fraction is found by flipping it upside down (numerator becomes denominator). Dividing by a fraction is mathematically identical to multiplying by its reciprocal.
Flip 3/5 to get 5/3. Multiply 60 by 5/3. (60 × 5 = 300) ÷ 3 = 100.