Learn how to calculate percentage increase step by step. Formula: ((New−Old)÷Old)×100. With 10 real examples for salaries, prices and investment returns.
Formula: Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100. Example: from $50 to $65 → ((65−50)÷50)×100 = 30% increase. Always divide by the ORIGINAL value.
Percentage increase only applies when the new value is higher. For any direction (up or down), use percentage change. The formula is identical — the sign tells you which it is.
When you know the new value is HIGHER. Salary went up, price increased, population grew.
When you don't know the direction, or want to show both increases and decreases. Stock prices, temperature changes.
A negative result means the value decreased, not increased. That's a percentage decrease. Example: $100 to $80: ((80−100)/100)×100=−20%.
Yes. If something doubles: from $50 to $100 is +100%. From $50 to $200 is +300%. There's no upper limit.
Aim for 10-20 problems per concept, gradually increasing difficulty. Consistent daily practice (even 15 minutes) beats occasional marathon sessions.
1) Re-read the problem. 2) List all given information. 3) Identify what you need to find. 4) Choose the right formula. 5) Calculate step by step.
Writing each step helps you spot errors, earns partial credit on tests, and builds the habit of organized mathematical thinking.
% Increase = (New − Old) / Old × 100. Result is always positive for a real increase.
New = Old × (1 + rate). After 20% increase on $500: $500×1.20 = $600
Old = New ÷ (1 + rate). If price is now $720 after 20% increase: $720÷1.20 = $600
Percentage increase is always calculated on the original, not the final value. Two consecutive increases do NOT add up linearly: 10% then 10% gives 21% total (1.1×1.1=1.21), not 20%. This is why compound interest grows faster than simple interest.
Remember: percentage increase is always relative to the original. Growing from $50 to $100 is a 100% increase (doubled), but growing from $1,000 to $1,050 is only 5% — even though $1,050 is a much larger number.
Formula del Porcentaje de Aumento
% = ((Valor nuevo - Valor original) / Valor original) x 100
Positivo=aumento | Negativo=disminucion
Ejemplo: $80 a $100 = ((100-80)/80)x100 = 25%
TRAMPA — Sube X% y baja X% NO da igual
$100 +20%=$120. $120 -20%=$96. Queda -4%.
Porque la base del segundo calculo cambio.
Percentage increase and decrease are fundamental math skills used in everyday life — from shopping discounts to salary raises, from inflation rates to population growth. Mastering this calculation will help you with math tests, business decisions, and financial planning.
% Increase = ((New Value − Old Value) / Old Value) × 100
% Decrease = ((Old Value − New Value) / Old Value) × 100
Your salary was $2,000. Now it's $2,300. What's the percentage increase?
Step 1: Find the difference: $2,300 − $2,000 = $300
Step 2: Divide by original: $300 ÷ $2,000 = 0.15
Step 3: Multiply by 100: 0.15 × 100 = 15% increase
A jacket was $80, now it's $60. What's the percentage decrease?
Difference = $80 − $60 = $20
$20 ÷ $80 = 0.25 × 100 = 25% decrease
A city had 500,000 people. Now it has 575,000. What's the growth rate?
Increase = 75,000 | 75,000 ÷ 500,000 = 0.15 × 100 = 15% growth
After an increase: New Value = Old Value × (1 + %/100)
Example: $500 after a 20% increase = $500 × 1.20 = $600
After a decrease: New Value = Old Value × (1 − %/100)
Example: $500 after a 20% decrease = $500 × 0.80 = $400
Important: A 20% increase followed by a 20% decrease does NOT return to the original value.
$100 → +20% → $120 → -20% → $120 × 0.80 = $96 (not $100!)
This is because the 20% decrease is applied to a larger number ($120) than the original ($100).
Inflation: If inflation is 5% per year, $100 today will have the purchasing power of $100 × 1.05 = $105 worth of goods next year — meaning you need $105 to buy what $100 bought today.
Investment returns: A stock that goes from $50 to $75 has increased by 50%. From $75 back to $50 is a 33.3% decrease (not 50%).
Discounts: A 30% discount on a $200 item: $200 × 0.70 = $140 sale price.
Tax calculation: Price + 16% IVA: $100 × 1.16 = $116 total.
1. 50 → 75: increase = (25/50)×100 = 50%
2. 80 → 60: decrease = (20/80)×100 = 25%
3. $1,000 after 15% increase = $1,000 × 1.15 = $1,150
4. $200 after 25% discount = $200 × 0.75 = $150
5. Population: 10,000 → 12,500 = 25% increase
6. Price with 16% tax: $300 × 1.16 = $348
7. Score: 45/60 → percentage = (45/60)×100 = 75%
8. Grade dropped from 90 to 81 = (9/90)×100 = 10% decrease
9. $500 → +10% → -10%: 500×1.1=550, 550×0.9 = $495 (not $500!)
10. What is a 40% increase of 250? 250 × 1.40 = 350
Los mejores matemáticos del mundo no memorizan fórmulas — entienden los conceptos detrás de ellas. Cuando entiendes POR QUÉ funciona una fórmula, nunca la olvidas. En cambio, si solo la memorizas sin entender, la olvidarás pronto.
Para cada problema de matemáticas, sigue este método: lee el problema completo, identifica qué datos tienes, identifica qué te piden encontrar, selecciona la fórmula o método adecuado, resuelve paso a paso, y verifica tu respuesta.
Este tema matemático aparece constantemente en situaciones cotidianas. Las matemáticas no son un tema abstracto que solo existe en los libros — son el lenguaje con el que describimos el mundo. Desde calcular el cambio en una tienda hasta diseñar un puente, desde predecir el clima hasta programar una aplicación, las matemáticas están en todo.
En México, las materias donde más necesitas estas habilidades son: física, química, economía, geografía y estadística. En el COMIPEMS, los temas de matemáticas representan una gran parte del examen.
El COMIPEMS incluye aproximadamente 128 preguntas de matemáticas distribuidas en aritmética, álgebra, geometría y estadística. Para maximizar tu puntaje:
Aritmética (40% del examen): Fracciones, decimales, porcentajes, potencias, raíces. Practica operaciones sin calculadora.
Álgebra (25%): Ecuaciones lineales, factorización, sistemas de ecuaciones. Practica despejar variables.
Geometría (20%): Áreas, perímetros, volúmenes, ángulos, triángulos. Memoriza las fórmulas más importantes.
Estadística (15%): Media, mediana, moda, probabilidad básica. Practica con conjuntos de datos reales.
Error 1 — Saltarse pasos: Los errores de matemáticas suelen ocurrir cuando se saltan pasos para ir más rápido. Escribe cada paso, aunque te parezca obvio.
Error 2 — No verificar: Siempre sustituye tu respuesta en la ecuación original para verificar que es correcta. Toma solo 30 segundos y puede salvarte de perder puntos.
Error 3 — Confundir fórmulas similares: El área del triángulo (base×altura÷2) se confunde con el perímetro (suma de los tres lados). Entiende qué mide cada fórmula.
Error 4 — Operaciones con fracciones: Para sumar fracciones necesitas denominador común. Para multiplicar, no. Para dividir, invierte la segunda fracción y multiplica.
Semana 1: Repasa aritmética básica — fracciones, decimales, porcentajes, potencias y raíces.
Semana 2: Álgebra — ecuaciones lineales, factorización, sistemas de ecuaciones.
Semana 3: Geometría — áreas, perímetros, volúmenes, triángulos, ángulos.
Semana 4: Simulacros completos en tiempo real y repaso de temas débiles.
🧮 Herramientas de práctica gratuitas
Khan Academy: khanacademy.org — videos y ejercicios gratuitos de todos los temas. Desmos: desmos.com — graficadora gratuita para visualizar funciones. Wolfram Alpha: wolframalpha.com — resuelve y explica cualquier problema matemático.