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Rational Numbers and Fractions

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Area Between Two Curves
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits at Infinity and Asymptotes
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Radius of Convergence
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Separation of Variables
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Vectors in Space
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
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- 3-Dimensional Figures
- Altitude
- Angles in Circles
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- Area and Volume
- Area of Circles
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- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
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- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
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- Rotations
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- Segment Length
- Similarity
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- Special quadrilaterals
- Squares
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- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
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- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Conservation of Mechanical Energy
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Elastic Strings and Springs
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Power
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Work Done by a Constant Force
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Argand Diagram
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- De Moivre's Theorem
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- 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
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- 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
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- 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 Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- 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 Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- 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
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- 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
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Distribution Function
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Degrees of Freedom
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test for Regression Slope
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Paired T-Test
- Point Estimation
- Probability
- Probability Calculations
- Probability Density Function
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- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
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- Types of Data in Statistics
- Variance for Binomial Distribution
- Venn Diagrams

You are studying with your friend Max for the examination and both of you started to discuss how long you guys studied. Max said both of you studied for \(3.5\) hours, but you believe that you both studied for \(3\) and half an hour \((3\frac{1}{2})\). But which one of you is correct about the time? If both of you studied for the same amount then why the difference in the number? Well, both \(3.5\) and \(3\frac{1}{2}\) are the same. They are different forms of numbers. One is in the **rational number** form and the other is in the **fraction** form.

In this section, we will understand the concept of rational numbers and fractions and how they are different.

Rational numbers and fractional numbers are two mathematical concepts that seem very closely related and most often are used interchangeably. However, this section will introduce the meaning of rational numbers and fractions, and how different they are described.

**Rational numbers** are a type of real number that can be written as the ratio of two integers. They are expressed in the form \(\frac{p}{q}\).

Note that \(p\) and \(q\) are both integers and \(q\) is non-zero. Examples of rational numbers are \(12, 10/12, 3/10,\) and \(0.5\). The set of rational numbers is always denoted by \(\mathbb{Q}\).

**Integers** are the set of all positive, negative numbers, and zero. They do not contain any decimal or fraction form.

**Fractions** are numbers that define a part or portion of any whole quantity written as the ratio of whole numbers. They are in the form \(a / b\) where \(a\) is the numerator and \(b\) is the denominator.

Note that, both the numerator and denominator are whole numbers and the denominator cannot be zero. Examples of fractions are \(10/32, 12/10, 4/23,\) and \(6/7\).

**Whole numbers** are a collection of natural numbers and zero. That is all the positive integers with zero without any decimal, fraction, or negative part.

Though both fractions and rational numbers look alike, they are not the same every time. As rational numbers have integers and contain negative numbers, they cannot be considered fractions. As fractions do not include negative numbers.

As defined above, a **rational number** is a type of real number that is expressed in the form \(p / q\), where \(p\) and \(q\) are integers and not equal to \(0\). Simply, it can be said that any fraction with a non-zero denominator is a rational number.

The standard form of rational numbers is expressed as when it has **no common factors** aside from one between the dividend and divisor and therefore the divisor is positive. So, the standard form of fractions is achieved by simplifying fractions. For example, \(3/9\) is an example of a rational number, but it can be divisible furthermore to have \(1/3\). In the form \(1/3\), it is considered the standard form since the number is no longer divisible by any number other than \(1\) and itself.

Remember that the number which you divide is called the **dividend**, and the number by which you perform the division is called the **divisor**.

The mathematical concept of **fractions** is used to describe parts of a **whole**. When we take a slice of pizza from the whole, for example, we say that we have a fraction of it. Fractions are numbers given in the form \(\frac{a}{b}\) where \(a\) and \(b\) are whole numbers and \(b\) is not equal to \(0\).

The fraction with numerator \(0\) is \(0\), but the fraction with \(0\) as denominator is undefined. A fraction is denoted by the simple "/" in the form \(a/b\) where \(a\), the upper number is called a numerator, and \(b\), the lower number is called the denominator. Examples of fractions are \(12/20, 5/6,\) and \(50/100\).

There are significant differences between rational numbers and fractions, and they are as follows:

Rational Numbers | Fraction |

1. Rational numbers are in the form \(p/q\), where \(p\) and \(q\) are integers. | 1. Rational numbers are in the form \(a/b\), where \(a\) and \(b\) are whole numbers. |

2. Rational number have the positive and negative form of numbers. | 2. Fraction only have the positive form of numbers. |

3. Rational numbers cannot be considered as fractions. | 3. Fraction can be considered as rational number. |

4. Examples - \(-3/7, 1/3, 12\) | 4. Examples - \(4/5, 1\frac{2}{5}, 23/6\) |

There are several types of rational numbers, and they are as follows;

Integers, for example, \(-3, 5,\) and \(4\).

Fractions of the form \(p / q\) where \(p\) and \(q\) are integers, For Example, \(1/2\).

Numbers that do not have infinite decimals, for example, \(1/4\) of \(0.25\). They are also called

**terminating decimals**.Numbers that have infinite decimals, for example, \(1/3\) of \(0.333....., 1.222.....\), etc. They are known as

**non-terminating decimals**.Whole numbers.

There are quite a number of types of fractions. If we want to use the numerator and denominator as a basis, they can be considered as three; a proper fraction, mixed fraction, and improper fraction. However, these are further subdivided into different types.

Proper fractions are ones where the numerators are smaller than the denominator (numerator < denominator). For example, \(3/4\) is a proper fraction.

Mixed fractions are combinations of integers and proper fractions. They are written as \(a\frac{m}{n}\) where \(a\) is the integer. An example of a mixed fraction is \(1\frac{2}{5}\).

Improper fractions, in contrast to proper fractions, are ones whose denominator is smaller than the numerators. (denominator < numerator). An example is \(4/3\).

Like fractions are fractions that have the same denominators. An example is \(1/7\) and \(4/7\). Both fractions here have the same denominator as \(7\), hence are considered like fractions.

These types of fractions are in contrast to like fractions. They have different values in their denominator. An example of unlike fraction is \(11/13\) and \(4/9\).

Two fractions can be considered equivalent when after simplifying by performing multiplication or division. they both give the same. For example, \(2/3\) and \(4/6\) are equivalent fractions because \(4/6\) can be further simplified to be \(2/3\).

When a fraction's numerator is equal to \(1\), it is known as a unit fraction. Examples are \(1/2\) (one-half of a whole) and \(1/4\) (one-fourth of a whole).

Denominator plays a major role in adding and multiplying rational numbers and fractions. Let's see how we can perform the operation of adding and subtracting on rational numbers and fractions.

The given steps should be followed to add and subtract fractions:

Check the type of fraction if they are like fractions or not.

Convert the given fraction to a like fraction, if they are not. Skip to step 4 if they are like fractions.

Find the least common multiple for the given denominators. Then multiply with the equivalent number to all the given denominators to obtain the same value of the denominator.

Add/subtract the numerator while keeping the denominator as it is.

If possible, reduce the obtained fractions.

We follow the same process for fractions to add and subtract rational numbers:

Convert all the denominators to positive numbers if anyone of them is negative.

Use LCM to make all the denominators as same, if they are different.

Add/subtract the integers in the numerator by following the rules of integers. And keep the denominator as it is.

Simplify the rational number.

The multiplication and division of rational numbers and fractions follow the same rule with the addition of rules of integers for rational numbers.

The multiplication of Rational numbers and fractions follows the given rules:

Multiply the numerators of all the given numbers with each other.

Multiply the denominators for all numbers with each other.

Simplify the obtained fraction/rational number.

Remember when dealing with rational numbers always follow the positive and negative sign multiplication rules.

The division of rational numbers is as follows:

Take the reciprocal of the second fraction/rational number by interchanging the numerator with the denominator and vice versa.

Change the division sign to multiplication after performing reciprocal.

Follow the rules of multiplying for rational numbers and fractions as above.

Let us see some rational number and fraction examples.

Identify the types of fractions.

1. \(\frac{6}{7}, \frac{4}{7}\)

2. \(2\frac{3}{8}\)

3. \(\frac{12}{9}\)

**Solution:**

1. Like fraction - As both the denominators are the same.

2. Mixed fraction - It has a fraction with a whole number.

3. Improper fraction - Numerator is greater than the denominator.

Divide the rational number \(\frac{-3}{10}\) by \(\frac{7}{5}\).

**Solution:**

Here we need to perform

\[\frac{-3}{10}\div\frac{7}{5}\]

**Step 1**- Take reciprocal of \(\frac{7}{5}\)

\[\Rightarrow \frac{5}{7}\]

**Step 2** - Changing the division sign to multiplication after getting the reciprocal we have,

\[\frac{-3}{10}\times \frac{5}{7}\]

**Step 3** - Now we multiply the numerator of both the numbers to each other and same with the denominators.

\begin{align} \frac{-3}{10}\times \frac{5}{7} &= \frac{-3\times 5}{10\times 7} \\ &=\frac{-15}{70} \\ \end{align}

**Step 4** - Now we reduce the obtained rational number.

\[\Rightarrow \frac{-15}{70} = \frac{-3}{14}\]

Calculate the given fraction.

\[\frac{1}{3}+\frac{4}{5}\]

**Solution: **

**Step 1** - Here both the fractions are not like fractions. So, we convert it to like fractions.

**Step 2** - We consider LCM of denominators \(3\) and \(5\) to convert the given fractions to like fractions.

Hence, the LCM of \(3\) and \(5\) is \(15\).

**Step 3** - Now we multiply \(5\) to \(\frac{1}{3}\) to make the denominator \(15\). Similarly, we multiply \(3\) to \(\frac{4}{5}\) and add both the numerators we get,

\begin{align} \Rightarrow \frac{1\times 5}{3\times 5} + \frac{4\times 3}{5\times 3} &= \frac{5}{15}+\frac{12}{15} \\ &=\frac{5+12}{15} \\ &=\frac{17}{15} \\ \end{align}

Here, \(\frac{17}{15}\) is already in the reduced form.

- A rational number is a type of real number that is expressed in the form \(p / q\), where \(p\) and \(q\) are integers and not equal to \(0\).
- Fractions are numbers given in the form \(a / b\) where \(a\) and \(b\) are whole numbers and \(b\) is not equal to \(0\).
- All fractions are rational numbers while not all rational numbers are fractions.
Rational numbers involve numbers having either terminating or non-terminating decimals.

Different types of fractions are - proper fraction, improper fraction, mixed fraction, like fraction, unlike fraction, equivalent fraction, and unit fraction.

A rational number is a type of real number that is expressed in the form p / q, where p and q are integers and q is not equal to 0.

Fractions are numbers given in the form a / b where a and b are whole numbers and b is not equal to 0.

- Proper fractions
- Improper fractions
- Mixed fraction

- 3/4 is an example of a fraction
- -3/7 is an example of a rational number

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