Calculator inputs
Formula used
Let a/b ≤ c/d and multiply both sides by the signed fraction m/n.
New left side: (a/b) × (m/n) = am / bn
New right side: (c/d) × (m/n) = cm / dn
If m/n > 0, the inequality sign stays the same.
If m/n < 0, the inequality sign reverses. Multiplying by zero is not allowed because it does not keep an equivalent inequality statement.
How to use this calculator
- Enter the left fraction using its numerator and denominator.
- Choose the inequality sign between both fractions.
- Enter the right fraction values.
- Enter the signed multiplier fraction you want to apply.
- Choose how many decimal places you want for previews.
- Keep step display and decimal display checked if you want a fuller explanation.
- Press Calculate to see the transformed inequality above the form.
- Use the CSV or PDF buttons to export the result summary.
Example data table
| Original inequality | Multiplier | Rule | Transformed inequality |
|---|---|---|---|
| -3/4 ≤ 5/6 | -2/3 | Negative multiplier reverses sign | 1/2 ≥ -5/9 |
| 2/5 > -1/2 | 3/4 | Positive multiplier keeps sign | 3/10 > -3/8 |
| -7/8 < 1/4 | -5/2 | Negative multiplier reverses sign | 35/16 > -5/8 |
| 4/9 ≥ -2/3 | 1/6 | Positive multiplier keeps sign | 2/27 ≥ -1/9 |
FAQs
1. What happens when the multiplier fraction is negative?
A negative multiplier reverses the inequality symbol. For example, < becomes >, and ≤ becomes ≥. The calculator applies that rule automatically after multiplying both sides.
2. Can I multiply an inequality by zero?
No. Multiplying by zero collapses both sides to zero and does not preserve an equivalent inequality. That is why this calculator rejects a zero multiplier.
3. Why must denominators be nonzero?
A denominator of zero makes a fraction undefined. Since undefined values cannot be compared reliably, the calculator requires every denominator to be a nonzero integer.
4. Does simplification change the answer?
No. Simplifying only rewrites equivalent fractions in lower terms. It makes the transformed inequality easier to read, but it does not change the mathematical relationship.
5. Can I use improper fractions and negative fractions?
Yes. Improper fractions, mixed-sign fractions, and negative numerators are all acceptable. The calculator normalizes the sign and then simplifies the results.
6. When does the inequality sign stay the same?
The sign stays the same whenever you multiply both sides by a positive fraction. Positive scaling preserves order on the number line.
7. Why does the calculator also show decimals?
Decimal values give a quick visual check of the fraction comparison. They are helpful for graphs and for confirming the transformed inequality numerically.
8. Is multiplying by a signed fraction similar to dividing?
Yes. Dividing by a fraction is the same as multiplying by its reciprocal. The same sign rule applies: if the effective multiplier is negative, reverse the inequality.