Percentage Increase and Decrease

The increase and decrease of values and quantities are constant in our everyday lives. One way to measure this change is in form of a percentage.

Explore our app and discover over 50 million learning materials for free.

- Applied Mathematics
- Calculus
- Decision Maths
- Discrete Mathematics
- Geometry
- Logic and Functions
- Mechanics Maths
- Probability and Statistics
- Pure Maths
- ASA Theorem
- Absolute Convergence
- Absolute Value Equations and Inequalities
- Abstract algebra
- Addition and Multiplication of series
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebra of limits
- Algebra over a field
- Algebraic Fractions
- Algebraic K-theory
- Algebraic Notation
- Algebraic Representation
- Algebraic curves
- Algebraic geometry
- Algebraic number theory
- Algebraic topology
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Argand Diagram
- Arithmetic Sequences
- Associative algebra
- Average Rate of Change
- Banach algebras
- Basis
- Bijective Functions
- Bilinear forms
- Binomial Expansion
- Binomial Theorem
- Bounded Sequence
- C*-algebras
- Category theory
- Cauchy Sequence
- Cayley Hamilton Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Clifford algebras
- Cohomology theory
- Combinatorics
- Common Factors
- Common Multiples
- Commutative algebra
- Compact Set
- Completing the Square
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Congruence Equations
- Conic Sections
- Connected Set
- Construction and Loci
- Continuity and Uniform convergence
- Continuity of derivative
- Continuity of real valued functions
- Continuous Function
- Convergent Sequence
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Coupled First-order Differential Equations
- Cubic Function Graph
- Data Transformations
- De Moivre's Theorem
- Deductive Reasoning
- Definite Integrals
- Derivative of a real function
- Deriving Equations
- Determinant Of Inverse Matrix
- Determinant of Matrix
- Determinants
- Diagonalising Matrix
- Differentiability of real valued functions
- Differential Equations
- Differential algebra
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Dimension
- Direct and Inverse proportions
- Discontinuity
- Disjoint and Overlapping Events
- Disproof By Counterexample
- Distance from a Point to a Line
- Divergent Sequence
- Divisibility Tests
- Division algebras
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Eigenvalues and Eigenvectors
- Ellipse
- Elliptic curves
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Equicontinuous families of functions
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Fermat's Little Theorem
- Field theory
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding The Area
- First Fundamental Theorem
- First-order Differential Equations
- Forms of Quadratic Functions
- Fourier analysis
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Gram-Schmidt Process
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs And Differentiation
- Graphs Of Exponents And Logarithms
- Graphs of Common Functions
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Grothendieck topologies
- Group Mathematics
- Group representations
- Growth and Decay
- Growth of Functions
- Gröbner bases
- Harmonic Motion
- Hermitian algebra
- Higher Derivatives
- Highest Common Factor
- Homogeneous System of Equations
- Homological algebra
- Homotopy theory
- Hopf algebras
- Hyperbolas
- Ideal theory
- Imaginary Unit And Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Injective linear transformation
- Instantaneous Rate of Change
- Integers
- Integrating Ex And 1x
- Integrating Polynomials
- Integrating Trigonometric Functions
- Integration
- Integration By Parts
- Integration By Substitution
- Integration Using Partial Fractions
- Integration of Hyperbolic Functions
- Interest
- Invariant Points
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Inverse of a Matrix and System of Linear equation
- Invertible linear transformation
- Iterative Methods
- Jordan algebras
- Knot theory
- L'hopitals Rule
- Lattice theory
- Law Of Cosines In Algebra
- Law Of Sines In Algebra
- Laws of Logs
- Leibnitz's Theorem
- Lie algebras
- Lie groups
- Limits of Accuracy
- Linear Algebra
- Linear Combination
- Linear Expressions
- Linear Independence
- Linear Systems
- Linear Transformation
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition And Subtraction
- Matrix Calculations
- Matrix Determinant
- Matrix Multiplication
- Matrix operations
- Mean value theorem
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modelling with First-order Differential Equations
- Modular Arithmetic
- Module theory
- Modulus Functions
- Modulus and Phase
- Monoidal categories
- Monotonic Function
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplicative ideal theory
- Multiplying And Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Non-associative algebra
- Normed spaces
- Notation
- Number
- Number Line
- Number Systems
- Number Theory
- Number e
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations With Matrices
- Operations with Decimals
- Operations with Polynomials
- Operator algebras
- Order of Operations
- Orthogonal groups
- Orthogonality
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Hyperbolas
- Parametric Integration
- Parametric Parabolas
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Pointwise convergence
- Poisson algebras
- Polynomial Graphs
- Polynomial rings
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Determinants
- Properties of Exponents
- Properties of Riemann Integral
- Properties of dimension
- Properties of eigenvalues and eigenvectors
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic forms
- Quadratic functions
- Quadrilaterals
- Quantum groups
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Ratio and Root test
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Rearrangement
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Reduced Row Echelon Form
- Reducible Differential Equations
- Remainder and Factor Theorems
- Representation Of Complex Numbers
- Representation theory
- Rewriting Formulas and Equations
- Riemann integral for step function
- Riemann surfaces
- Riemannian geometry
- Ring theory
- Roots Of Unity
- Roots of Complex Numbers
- Roots of Polynomials
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Products
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Fundamental Theorem
- Second Order Recurrence Relation
- Second-order Differential Equations
- Sector of a Circle
- Segment of a Circle
- Sequence and series of real valued functions
- Sequence of Real Numbers
- Sequences
- Sequences and Series
- Series Maths
- Series of non negative terms
- Series of real numbers
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Similarity and diagonalisation
- Simple Interest
- Simple algebras
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Spanning Set
- Special Products
- Special Sequences
- Standard Form
- Standard Integrals
- Standard Unit
- Stone Weierstrass theorem
- Straight Line Graphs
- Subgroup
- Subsequence
- Subspace
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Summation by Parts
- Supremum and Infimum
- Surds
- Surjective functions
- Surjective linear transformation
- System of Linear Equations
- Tables and Graphs
- Tangent of a Circle
- Taylor theorem
- The Quadratic Formula and the Discriminant
- Topological groups
- Torsion theories
- Transformations
- Transformations of Graphs
- Transformations of Roots
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Uniform convergence
- Unit Circle
- Units
- Universal algebra
- Upper and Lower Bounds
- Valuation theory
- Variables in Algebra
- Vector Notation
- Vector Space
- Vector spaces
- Vectors
- Verifying Trigonometric Identities
- Volumes of Revolution
- Von Neumann algebras
- Writing Equations
- Writing Linear Equations
- Zariski topology
- Statistics
- Theoretical and Mathematical Physics

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenThe increase and decrease of values and quantities are constant in our everyday lives. One way to measure this change is in form of a percentage.

In this article, we will learn more about Percentage increases and decreases and how this will lead to the comparison of different values and quantities.

The percentage is denoted by the symbol %.

$3\%$ is $\frac{3}{100}$ which is equal to $0.03$.

With this knowledge, we are now ready to define the percentage increase and decrease of a number.

Percentage increase is the increase of a number, amount, or quantity expressed in percentage.

Percentage decrease is the decrease of a number, amount, or quantity expressed in percentage.

The difference between percentage increase and percentage decrease is that one has to do with increase and the other has to do with decrease. What to note here is that whether increase or decrease, there is a change in value.

Let's take a look at different percentage increase and decrease formulas and how we can use them in our calculations.

To find the percentage increase, we find the difference between the numbers that are being compared and then change the result to a percentage by dividing the result by the original number and multiplying by $100$.

The following steps will guide you on how to calculate a percentage increase.

- First, find the increase by subtracting the original number from the new number.
- Divide the result by the original number and multiply by $100$ to get the percentage increase.

The formulae of the increase and the percentage increase are as follows,

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}\%Increase=\frac{Increase}{Originalnumber}\times 100$

To find the percentage decrease, you will first find the difference between the numbers or quantities to be compared and then divide the result by the original number and multiply by $100$. Below are the steps to follow.

- Find the decrease by subtracting the new number from the original number
- Then find the percentage decrease by dividing the decrease by the original number and multiplying by $100$.

The formula to use is below.

$Decrease=Originalnumber-Newnumber\phantom{\rule{0ex}{0ex}}\%Decrease=\frac{Decrease}{Originalnumber}\times 100$

When increasing or decreasing a number by a percentage, you first find the percentage of the number and add or subtract it from the original number. We will see some examples hereafter.

You may come across questions where you will be asked to find the percentage change, either increase or decrease over time. These types of questions aim to analyze growth or reduction over time. In this case, you will use the following formula.

$\%Changeovertime=\frac{\left[\left(\frac{newnumber}{originalnumber}-1\right)\times 100\right]}{time}\phantom{\rule{0ex}{0ex}}$

The same formula is used to calculate the percentage increase and decrease over time.

If you are using the formula to calculate the percentage decrease, you will get a negative answer. In this case, we remove the negative sign and say that the quantities being compared decreased by that number.

The formula looks a little complex and may not be easy to remember. So, let’s break it down in the following steps.

- Divide the new number by the original number and subtract 1 from the result.
- Multiply the result of the first step by 100
- Divide the result by the time given.

The unit of percentage increase or decrease over time is percentage per time, that is, $\%/time$. The time can be in seconds, minutes, years or in any other way the time can be measured.

We've looked at the various formulas that are associated with percentage increase and decrease. Now, let's take some percentage increase and decrease examples.

The first set of examples will show how to calculate a percentage increase.

The price of a bag of rice went up from £20 to £35. What is the percentage increase?

**Solution**

The formula to be used here is the following,

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}\%Increase=\frac{Increase}{Originalnumber}\times 100$

The first thing is to identify the values that are given. The question says that the price went up from $\pounds 20$ to $\pounds 35$. This means that,

$Originalnumber=20\phantom{\rule{0ex}{0ex}}Newnumber=35$

We will first find the increase.

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}Increase=35-20\phantom{\rule{0ex}{0ex}}=15$

We will now find the percentage increase.

$\%Increase=\frac{Increase}{Originalnumber}\times 100\phantom{\rule{0ex}{0ex}}=\frac{15}{20}\times 100\phantom{\rule{0ex}{0ex}}=75\%$

This means the price increased by $75\%$.

Let's take another example.

A bag contains 15 balls. After some time, the number of balls increased to 35. What is the percentage increase?

**Solution**

From the question, the original number is $15$ and the new number is $35$.

We will first find the increase as shown below.

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}=35-15\phantom{\rule{0ex}{0ex}}=20$

We will now find the percentage increase.

$\%Increase=\frac{Increase}{Originalnumber}\times 100\phantom{\rule{0ex}{0ex}}\%Increase=\frac{20}{15}\times 100\phantom{\rule{0ex}{0ex}}=133.33\%$

This means the number of balls increased by $133.33\%$.

The next set of percentage increase and decrease examples will show how to calculate percentage decrease.

Harry had £2000 in his bank account last week but now he has £800. What is the percentage decrease?

**Solution**

From the question, the original amount or number is $2000$ and the new amount or number is$800$.

We will first find the decrease using the formula below.

$Decrease=Originalnumber-Newnumber\phantom{\rule{0ex}{0ex}}=2000-800\phantom{\rule{0ex}{0ex}}=1200$

We will now use the decrease to find the percentage decrease using the formula below.

$\%Decrease=\frac{Decrease}{Originalnumber}\times 100\phantom{\rule{0ex}{0ex}}=\frac{1200}{2000}\times 100\phantom{\rule{0ex}{0ex}}=60\%$

This means the money in Harry’s bank account decreased by $60\%$.

Let's take another example.

A factory went from producing 200 packs of its product to producing 180. What is the percentage decrease?

**Solution**

The formula to be used is the following,

$Decrease=Originalnumber-Newnumber\phantom{\rule{0ex}{0ex}}\%Decrease=\frac{Decrease}{Originalnumber}\times 100$

From the question, the original number is $200$ and the new number is $180$. So we will first find the decrease and then find the percentage decrease as shown below.

$Decrease=Originalnumber-newnumber\phantom{\rule{0ex}{0ex}}=200-180\phantom{\rule{0ex}{0ex}}=20\phantom{\rule{0ex}{0ex}}\%Decrease=\frac{Decrease}{Originalnumber}\times 100\phantom{\rule{0ex}{0ex}}=\frac{20}{200}\times 100\phantom{\rule{0ex}{0ex}}=10\%$

The percentage decrease is $10\%$.

The next set of examples shows how to increase and decrease a number by a percentage.

Increase £80 by 5%.

**Solution**

The first thing to do here is to find $5\%$ of $\pounds 80$. We will do this by multiplying $5\%$ by $\pounds 80$.

$5\%\times 80=\frac{5}{100}\times 80=4$.

Now, we will add $4$ to $\pounds 80$ since we are looking for an increase. If it were to be a decrease, we would be subtracting.

$\pounds 80+4=\pounds 84$

Therefore, $\pounds 80$ increased by $5\%$ is $\pounds 84$.

Let's take another example.

The length of a 70 cm wood was decreased by 3%. What is the new length?

**Solution**

We want to know the new length after $3\%$decrease. To find this we will solve for $3\%$ of the original wood length which is $3\%of70$.

$3\%\times 70=\frac{3}{100}\times 70\phantom{\rule{0ex}{0ex}}=2.1$

Since we are looking for the **decreased** length, we will subtract 2.1 from the original length of 70.

$70-2.1=67.9$

The new length of the wood is $67.9cm$.

These last set of examples show how to calculate percentage increase or decrease over time.

Over 2 years, it was noticed that the price of petrol went from £199 per liter to £215 per liter. What is the percentage increase over time?

**Solution**

We are asked to find the percentage increase over time. The time given is 2 years. Following the steps above, the first thing we would do is divide the new number by the original number and subtract 1.

$\frac{Newnumber}{Originalnumber}-1=\frac{215}{199}-1\phantom{\rule{0ex}{0ex}}=0.08$

We will now multiply by $100$.

$0.08\times 100=8$

The last step is to divide by the time given which is $2years$.

$\frac{8}{2}=4\%/year$

Therefore, the percentage increase over time is $4\%/year$.

Let's take another example.

Within 30 minutes, the amount of water in a drum went from level 30 to level 15. What is the percentage decrease over 30 minutes?

**Solution**

Let’s use the formula for this. The formula to be used is below.

$\%Changeovertime=\frac{\left[\left(\frac{newnumber}{originalnumber}-1\right)\times 100\right]}{time}$

All we need to do is to insert the values that are given to us. The values given to us are:

$Time=30minutes\phantom{\rule{0ex}{0ex}}Originalnumber=30\phantom{\rule{0ex}{0ex}}Newnumber=15$

We will now insert the values in the formula.

$\%Decreaseovertime=\frac{\left[\left(\frac{15}{30}-1\right)\times 100\right]}{30}\phantom{\rule{0ex}{0ex}}=\frac{\left[\left(0.5-1\right)\times 100\right]}{30}\phantom{\rule{0ex}{0ex}}=-\frac{0.5}{30}\phantom{\rule{0ex}{0ex}}=-0.017\%/min\phantom{\rule{0ex}{0ex}}=0.017\%/min$

Therefore, the percentage decrease over time is $0.017\%/min$

Notice that the negative sign is taken out. If you get a negative value when calculating, it means that there has been a decrease. You should take out the negative sign and say that the quantity or whatever is being measured has decreased by that value.

- Percentage increase is the increase of a number, amount or quantity expressed in percentage.
- Percentage decrease is the decrease of a number, amount or quantity expressed in percentage.
- If you get a negative value when calculating, it means that there has been a decrease. You should take out the negative sign and say that the quantity or whatever is being measured has decreased by that value.
The percentage is denoted by the symbol %.

To find percentage increase, find the difference between the numbers that are being compared and then change the result to a percentage by dividing it by the original number and multiplying by 100. In other words, find the increase and then the percentage of the increase.

Increase = New number - Original number

% Increase = Increase/Original number

To find percentage decrease, find the difference between the numbers or quantities to be compared and then divide the result by the original number and multiply by 100. In other words, find the decrease and then the percentage of the decrease.

Decrease = Original number - New number

% Decrease Decrease/Original number x 100

The percentage increase formula is:

% Increase = Increase/Original number x 100

The percentage decrease formula is:

% Decrease = Decrease/Original number x 100

If the price of an item was £20 and it increased to £35, this means that the price increased by 75%.

If the price of an item was £2000 and it decreased to £800, it means it decreased by 60%.

What is percentage increase?

Percentage increase is the increase of a number, amount or quantity expressed in percentage.

What is percentage decrease?

Percentage decrease is the decrease of a number, amount or quantity expressed in percentage.

What are the steps used in calculating percentage increase and decrease over time?

- Divide the new number by the original number and subtract 1 from the result.
- Multiply the result of the first step by 100
- Divide the result by the time given.

How do you increase or decrease a number by a percentage?

Already have an account? Log in

Open in App
More about Percentage Increase and Decrease

The first learning app that truly has everything you need to ace your exams in one place

- Flashcards & Quizzes
- AI Study Assistant
- Study Planner
- Mock-Exams
- Smart Note-Taking

Sign up to highlight and take notes. It’s 100% free.

Save explanations to your personalised space and access them anytime, anywhere!

Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.

Already have an account? Log in

Already have an account? Log in

The first learning app that truly has everything you need to ace your exams in one place

- Flashcards & Quizzes
- AI Study Assistant
- Study Planner
- Mock-Exams
- Smart Note-Taking

Sign up with Email

Already have an account? Log in