Strengthen your Grade 7 math skills with topic-based worksheets and
practice problems. Choose a learning area to practise calculations,
solve word problems, and check your understanding.
Ratios and Proportions Worksheets
Practise simplifying ratios, comparing ratios, solving proportions,
and answering real-life word problems.
Percent Problems Worksheets
Review percentage calculations through profit, loss, discount,
and related word problems.
Integers and Rational Numbers Worksheets
Practise integer multiplication and division, signs of numbers,
and fundamental operations.
Fractions and Decimals Worksheets
Practise fraction operations and simplifying answers.
A dedicated Grade 7 decimals worksheet can be added to expand this section.
Algebraic Expressions Worksheets
A dedicated worksheet for evaluating expressions, combining like terms,
using the distributive property, and writing expressions from words
is a useful addition to the collection.
Multi-Step Equations Worksheets
Practise solving equations in several steps, including equations
with variables on both sides.
Geometry Worksheets
Review polygons, angle relationships, interior angles,
and exterior angles.
Area, Surface Area, and Volume Worksheets
Practise area and perimeter calculations. Separate printable resources
for surface area and volume would help complete this learning area.
Statistics and Probability Worksheets
Review frequency distributions and data organisation.
A dedicated Grade 7 probability worksheet would broaden the practice.
Mixed 7th Grade Math Review
A printable review worksheet covering integers, fractions,
ratios, percentages, equations, geometry, and data.
For parents and teachers:
Encourage students to show their working, write units where needed,
and check their answers after completing each worksheet.
Grade 7 Math Topics Aligned with U.S. Learning Goals:
This page provides practice in the major areas commonly studied in U.S. seventh-grade mathematics, including ratios and proportional relationships, rational numbers, expressions and equations, geometry, statistics, and probability.
Students can use the worked examples, practice problems, and worksheets to strengthen their mathematical reasoning and prepare for classroom assignments.
Curriculum pacing and specific requirements vary by state, school district, and textbook. Students should follow their school’s assigned curriculum.
Frequently Asked Questions about 7th Grade Math Problems and Practice:
Answer:
Common topics include ratios and proportions, rational numbers, algebraic expressions, equations, geometry, statistics, and probability.
Answer:
Review a lesson, work through the examples, solve practice problems independently, and check your answers. Use a worksheet or interactive quiz to identify topics that need more practice.
Answer:
Important skills include working with rational numbers, solving proportional and percent problems, simplifying expressions, solving equations, understanding geometry, and interpreting data.
Answer:
Students can use the linked worksheets on this page for extra practice. Check each resource for its available format and answer key.
Answer:
Read the problem carefully, identify the known and unknown quantities, choose an appropriate operation or equation, solve step by step, and check whether the answer makes sense.
About Author
Written by Priyanka Ghosh
Mathematics Educator | Founder of Math Only Math
Priyanka Ghosh has been teaching elementary and middle-school mathematics for over 12 years and specializes in creating simple, child-friendly math lessons and worksheets.
Related Grade-Level Math Resources:
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
Domain and Range of a Relation
Domain Co-domain and Range of Function
● Relations and Mapping – Worksheets
Worksheet on Functions or Mapping
● Numbers – Integers
Properties of Multiplication of Integers
Examples on Multiplication of Integers
Properties of Division of Integers
Examples on Division of Integers
Examples on Fundamental Operations
● Numbers – Worksheets
Worksheet on Multiplication of Integers
Worksheet on Division of Integers
Worksheet on Fundamental Operation
● Fractions
Addition and Subtraction of Fractions
● Fractions – Worksheets
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
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
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
● Ratios and Proportions
● Ratios and Proportions – Worksheets
● 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 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
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
Practice Test on Simple Interest
● Simple Interest – Worksheets
● 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)
● Equations
How to Solve Linear Equations?
Problems on Linear Equations in One Variable
Word Problems on Linear Equations in One Variable
Solving Multi-Step Equations with Variables on Both Sides Worksheet PDF
Practice Test on Linear Equations
Practice Test on Word Problems on Linear Equations
● Equations – Worksheets
Worksheet on Word Problems on Linear Equation
● 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
Some Geometric Terms and Results
Complementary and Supplementary Angles
Parallel and Transversal Lines
● Congruence
Conditions for the Congruence of Triangles:
Right Angle Hypotenuse Side congruence:
Converse of Pythagorean Theorem:
Word problems on Pythagorean Theorem:
● Polygons
Polygon and its Classification
Interior and Exterior of the 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
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.
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
● Coordinate System
● Mensuration
● Mensuration – Worksheets
● Volume and Surface Area of Solids
● Statistics
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