7th Grade Math Problems

In 7th grade math problems you will get all types of examples on different topics along with the solutions.

Keeping in mind the mental level of child in Grade 7, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily.

The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts.

If student follow math-only-math they can improve their knowledge by practicing the solutions step by step which will help you to score in your exam.

7th Grade Math Problems

● Set Theory

Sets: An introduction to sets, methods for defining sets, element of set and use of set notations.

Objects Form a Set: State, whether the following objects form a set or not by giving reasons.

Elements of a Set: Learn how to find the elements of a set with the help of various types of problems on the basic concepts of sets.

Properties of Sets: Using the basic properties to represent a set learn to solve various basic types of problems on sets.

Representation of a Set: Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Different Notations in Sets: Some of the familiar notations used in sets which are generally required to solve various types of problems on sets.

Standard Sets of Numbers: Learn to represent the standard sets of numbers using the three methods i.e. statement form, roster form and set builder form.

Types of Sets: Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Pairs of Sets: Definition with examples of equal set, equivalent set, disjoint sets and overlapping set.

Subset: Definition with examples of subset and its types, super set, proper subset, power set and universal set.

Subsets of a Given Set: How to find the number of subsets of a given set and number of proper subsets of a given set.

Operations on Sets: Learn the meaning. What are the four basic operations on sets? How the operations are carried out in union of sets and intersection of sets?

Union of Sets: Definition of union of sets with examples. Learn how to find the union of two sets and worked-out examples.

Intersection of Sets: Definition of intersection of sets with examples. Learn how to find the intersection of two sets and worked-out examples.

Difference of two Sets: Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set: Definition of complement of a set and their properties with some worked-out examples.

Cardinal number of a set: Definition of a cardinal number of a set, the symbol used for showing the cardinal number, worked-out examples.

Cardinal Properties of Sets: Learn how to solve the real-life word problems on set using the cardinal properties.

Venn Diagrams: Learn to represent the basic concepts of sets using Venn-diagram in different situations.

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Relation

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Numbers - Integers

Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

● Fractions

Fractions

Types of Fractions

Equivalent Fractions

Like and Unlike Fractions

Conversion of Fractions

Fraction in Lowest Terms

Addition and Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

● Fractions - Worksheets

Worksheet on Fractions

Worksheet on Multiplication of Fractions

Worksheet on Division of Fractions

● Story about the Decimal Number

Decimals: Concept for decimals in derails.

Decimal Numbers: Learn reading decimal numbers, writing decimal numbers etc,.

Decimal Fractions: Learn reading decimal fractions, writing decimal fractions.

Decimal Places: Learn reading and writing the place values of a decimal number in words.

Decimal and Fractional Expansion: Learn how to expand the decimal numbers and the decimal numbers in fractions

Like and Unlike Decimals: Learn to identify like decimals and unlike decimals.

Conversion of Unlike Decimals to Like Decimals: Learn to convert unlike decimals in like decimals

Comparing Decimals: Learn to order and compare decimal numbers, arranging decimals in ascending order and arranging decimals in descending order

Adding Decimals: Learn to add decimals in the correct order, word problems.

Subtracting Decimals: Learn to subtract decimals in the correct order, word problems

Simplify Decimals Involving Addition and Subtraction Decimals: Examples for simplifying decimals for adding and subtracting.

Multiplying Decimal by a Whole Number: Learn to multiply decimals by a whole number in the correct order, word problems

Multiplying Decimal by a Decimal Number: Learn to multiply decimals by a decimal number in the correct order, word problems

Dividing Decimal by a Whole Number: Learn to divide decimals by a whole number in the correct order, word problems

Dividing Decimal by a Decimal Number: Learn to divide decimals by a decimal number in the correct order, word problems

Simplification of Decimal: Examples for simplifying decimals, operation on decimals.

Converting Decimals to Fractions: Learn to express decimal number into fraction

Converting Fractions to Decimals: Learn to express fraction into decimal number

Rounding Decimals: Learn to round off decimals

Rounding Decimals to the Nearest Whole Number: Learn to round off decimals to the nearest whole number

Rounding Decimals to the Nearest Tenths: Learn to round off decimals to the nearest tenths

Rounding Decimals to the Nearest Hundredths: Learn to round off decimals to the nearest hundredths

Round a Decimal: Problems for rounding off decimals

H.C.F. and L.C.M. of Decimals: Learn to find the highest common factor, lowest common multiple of more than two decimal numbers

Terminating Decimal: Definition of terminating decimals, examples to identify terminating decimals

Non-Terminating Decimal: Definition of non-terminating decimal, examples to identify non-terminating decimals

Repeating or Recurring Decimal: Definition of recurring decimals, examples to identify recurring decimals

Pure Recurring Decimal: Definition of pure recurring decimal, examples to pure recurring decimal

Mixed Recurring Decimal: Definition of mixed recurring decimal, examples to identify mixed recurring decimal

Conversion of Pure Recurring Decimal into Vulgar Fraction: Learn to express pure recurring decimals to vulgar fractions with examples.

Conversion of Mixed Recurring Decimals into Vulgar Fractions: Learn to express mixed recurring decimals to vulgar fractions with examples.

BODMAS/PEMDAS rule:

BODMAS Rule: Learn how to follow the BODMAS rules to simply the order of operations.

BODMAS Rules - Involving Integers: Learn how to follow the BODMAS rules to simply the order of operations involving integers.

BODMAS/PEMDAS Rules - Involving Decimals: Learn how to follow the BODMAS rules to simply the order of operations involving decimals

PEMDAS Rule: Learn how to follow the PEMDAS rules to simply the order of operations.

PEMDAS Rules - Involving Integers: Learn how to follow the PEMDAS rules to simply the order of operations involving integers.

PEMDAS Rules - Involving Decimals: Learn how to follow the PEMDAS rules to simply the order of operations involving decimals.

● Profit, Loss and Discount

Concept of Profit and Loss

Calculate Profit and Profit Percent

Calculate Loss and Loss Percent

Calculate Cost Price using Sell Price and Loss Percent

Calculate Cost Price using Sell Price and Profit Percent

Calculate Selling Price using Cost and Loss Percent

Calculate Selling Price using Cost and Profit Percent

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Discount

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Ratios and Proportions

What is a Ratio?

What is a Proportion?

● Ratios and Proportions - Worksheets

Worksheet on Ratios

Worksheet on Proportions

● Time and Work

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Time and Work

Pipes and Water Tank

Problems on Pipes and Water Tank

● Time and Work - Worksheets

Worksheet on Work Done in a Given Period of Time

Worksheet on Time Required to Complete a Piece of Work

Worksheet on Pipes and Water Tank

● Unitary Method

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method

● Unitary Method - Worksheets

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Algebraic Expressions

Division of Polynomial by Monomial

● Algebraic Expressions - Worksheets

Worksheet on Dividing Polynomial by Monomial

● Formula

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Algebraic Identities

Square of The Sum of Two Binomials: Using the formula of (a + b)\(^{2}\) = a\(^{2}\) + b\(^{2}\) + 2ab, learn to evaluate the square of the sum of two terms.

Square of The Difference of Two Binomials: Using the formula of (a - b)\(^{2}\)
 = a\(^{2}\) + b\(^{2}\) - 2ab, learn to evaluate the square of the difference of two terms.

Product of Sum and Difference of Two Binomials: Using the formula of a\(^{2}\) - b\(^{2}\) = (a + b) (a - b), learn to evaluate the product of sum and difference of two terms.

Product of Two Binomials whose First Terms are Same and Second Terms are Different: Learn to use the given formulas to evaluate the product of the two terms whose 1\(^{st}\) terms are same and 2\(^{nd}\) terms are different.

• (x + a) (x + b) = x\(^{2}\) + x(a + b) + ab

• (x + a) (x - b) = x\(^{2}\) + x (a – b) – ab

• (x - a) (x - b) = x\(^{2}\) – x (a + b) + ab

• (x - a) (x + b) = x\(^{2}\) + x (b – a) – ab

Square of a Trinomial: Learn to use the formula for the expansion of the square of a trinomial.

• (a + b + c)\(^{2}\) = a\(^{2}\) + b\(^{2}\) + c\(^{2}\) + 2ab + 2bc + 2ca

• (a + b - c)\(^{2}\) = a\(^{2}\) + b\(^{2}\) + c\(^{2}\) + 2ab – 2bc - 2ca

• (a - b + c)\(^{2}\) = a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – 2ab – 2bc + 2ca

• (a - b - c)\(^{2}\) = a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – 2ab + 2bc – 2ca

Cube of The Sum of Two Binomials: Learn the formula to determine the cube of the sum of two terms.

(a + b)\(^{3}\) = a\(^{3}\)  + 3a\(^{2}\)b + 3ab\(^{2}\)  + b\(^{3}\)

             = a\(^{3}\) + b\(^{3}\) + 3ab (a + b)

Cube of The Difference of Two Binomials: Learn the formula to determine the cube of the difference of two terms.

(a - b)\(^{3}\) = a\(^{3}\)  – 3a\(^{2}\)b + 3ab\(^{2}\)  – b\(^{3}\)

           = a\(^{3}\) – b\(^{3}\) – 3ab (a - b)

Cube of a Binomial:

Square of a Binomial:

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Inequations - Worksheets

Worksheet on Linear Inequations

7th Grade Math Problems

Geometry

● Lines and Angles

Fundamental Geometrical Concepts

Angles

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Congruence

Congruent Shapes:

Congruent Line-segments:

Congruent Angles:

Congruent Triangles:

Conditions for the Congruence of Triangles:

Side Side Side Congruence:

Side Angle Side Congruence: 

Angle Side Angle Congruence:

Angle Angle Side Congruence:

Right Angle Hypotenuse Side congruence:

Pythagorean Theorem:

Proof of Pythagorean Theorem:

Converse of Pythagorean Theorem:

Word problems on Pythagorean Theorem:

● Polygons

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

● Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon

● Quadrilateral

Quadrilateral:

Perimeter of Quadrilateral:

Angle Sum Property of a Quadrilateral:

Missing angle of a Quadrilateral:

Angles of a Quadrilateral are in Ratio:

● Symmetrical Figure

Linear Symmetry: Identify symmetric and non-symmetric figures and also identify shapes having horizontal line of symmetry, vertical line of symmetry, both horizontal and vertical lines of symmetry, infinite lines of symmetry and no line of symmetry.

Lines of Symmetry: Identify the geometrical shapes having 1, 2, 3, 4, 0 and so on or infinite lines of symmetry.

Point Symmetry: How to find the point symmetry of letters of the English alphabet and the different geometrical figures. Learn the important points to find the conditions that satisfy centre of symmetry.

Reflection Symmetry:

Reflection and Symmetry:

Nets of a Solids:

Rotational Symmetry: Learn what is rotational symmetry and types of rotation i.e. clockwise rotation and anticlockwise rotation. 

Order of Rotational Symmetry: Learn the different orders of rotation of the shapes through 360° in clockwise direction and anticlockwise direction.

Types of Symmetry: Learn the various symmetries i.e. linear symmetry, point symmetry and rotational symmetry of the geometrical shapes. 

Reflection: Learn how reflection is related to math, define reflection using an image and worked-out examples on math reflection. 

Reflection of a Point in x-axis: Learn how to draw the image on the graph paper to find the reflection of a point in x-axis.

Reflection of a Point in y-axis: Learn how to draw the image on the graph paper to find the reflection of a point in y-axis.

Reflection of a point in origin: Learn how to draw the image on the graph paper to find the reflection of a point in origin. 

Rotation: Explanation of rotation using an image.

90 Degree Clockwise Rotation: Learn with the help of solved examples to rotate a figure 90 degrees clockwise direction around the origin on a graph paper.

90 Degree Anticlockwise Rotation: Learn with the help of solved examples to rotate a figure 90 degrees anticlockwise direction around the origin on a graph paper.

180 Degree Rotation: Learn with the help of solved examples to rotate a figure 180 degrees clockwise direction and anticlockwise direction around the origin on a graph paper.

● Practical Geometry

• Practical Geometry
• Construction of a Circle

● Coordinate System

• Coordinate Graph
• Ordered pair of a Coordinate System
• Plot Ordered Pairs
• Coordinates of a Point
• All Four Quadrants
• Signs of Coordinates
• Find the Coordinates of a Point
• Coordinates of a Point in a Plane
• Plot Points on Coordinate Graph
• Graph of Linear Equation
• Simultaneous Equations Graphically
• Graphs of Simple Function
• Graph of Perimeter vs. Length of the Side of a Square
• Graph of Area vs. Side of a Square
• Graph of Simple Interest vs. Number of Years
• Graph of Distance vs. Time

● Mensuration

• Area and Perimeter
• Perimeter and Area of Rectangle
• Perimeter and Area of Square
• Area of the Path
• Area and Perimeter of the Triangle
• Area and Perimeter of the Parallelogram
• Area and Perimeter of Rhombus
• Area of Trapezium
• Circumference and Area of Circle
• Units of Area Conversion
• Practice Test on Area and Perimeter of Rectangle
• Practice Test on Area and Perimeter of Square

● Mensuration - Worksheets

• Worksheet on Area and Perimeter of Rectangles
• Worksheet on Area and Perimeter of Squares
• Worksheet on Area of the Path
• Worksheet on Circumference and Area of Circle
• Worksheet on Area and Perimeter of Triangle

● Volume and Surface Area of Solids

• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid

● Statistics

• Real Life Statistics
• Terms Related to Statistics
• Frequency Distribution of Ungrouped and Grouped Data
• Use of Tally Marks
• Class Limits in Exclusive and Inclusive Form
• Construction of Bar Graphs
• Mean
• Mean of the Tabulated Data
• Mode
• Median
• Construction of Pie Chart
• How to Construct a Line Graph?

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