Pourcentage Inverse

Trouver la valeur originale avant l'application d'un changement en pourcentage.

Apprendre

Trouver la valeur originale avant l'application d'un changement en pourcentage.

Reverse percentage problems ask you to work backwards from a final value to find the original. If something increased by X%, the final value equals the original times (1 + X/100). To find the original, divide the final value by this multiplier. This is trickier than forward percentages because you can't simply subtract the percentage.

If Final = Original × (1 + X/100), then Original = Final ÷ (1 + X/100)

After a 20% increase, a price is $120. Original = $120 ÷ 1.20 = $100
After a 25% discount, a price is $60. Original = $60 ÷ 0.75 = $80
After a 10% raise, salary is $55,000. Original = $55,000 ÷ 1.10 = $50,000

Comment le reconnaître

You're given the final value after a percentage change
You need to find what the value was before the change
Keywords: 'original price', 'was before', 'started at'

Erreurs fréquentes

Subtracting the percentage from the final (e.g., $120 - 20% = $96, wrong!)
Using the wrong multiplier (1.20 for increase, 0.80 for 20% decrease)
Confusing increase (multiply by >1) with decrease (multiply by <1)

Résolution étape par étape

Après une augmentation de 25 %, un prix est de 150 $. Quel était le prix original ?

Identifiez le multiplicateur pour 25 % d'augmentation : 1 + 25/100 = 1,25
Posez l'équation : Original x 1,25 = 150 $
Divisez la valeur finale par le multiplicateur : 150 $ / 1,25
Calculez : 150 $ / 1,25 = 120 $

Réponse: $120

Conseils de pratique

Raisonnement Numérique