Real numbers
Classifying real numbers worksheets
Classify fourteen values into every applicable number set. Compare integers, reducible and irreducible signed fractions, square roots and pi with a separate answer key.
Preview and downloadUnderstand the value. Read the sign.
Real numbers worksheets
Build a clear picture of the number sets, then practice calculating with signed numbers. Choose a focused worksheet and print the same questions with a separate key.
Choose a practice sheetBuild the next skill
Understand the number sets
Classify the value, even when a fraction or root disguises it.
Build the next skill
Calculate with signed numbers
Choose sums and differences, integer notation practice, or mixed rational multiplication and division.
Real numbers
Adding and subtracting rational numbers worksheets
Create fourteen signed sums and differences with integers, decimals, fractions or a mixture. Each question has two or three operands and an exact answer.
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Real numbers
Multiplying and dividing integers worksheets
Practice fourteen signed integer products and exact quotients. Choose fraction-bar division, ÷, × or parentheses, with factor magnitudes from 2 to 20.
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Real numbers
Multiplying and dividing rational numbers worksheets
Create fourteen signed products and quotients with any combination of integers, decimal tenths and fractions. Exact answers use terminating decimals or simplest fractions.
Preview and downloadChoose a starting point
Isolate one skill, then combine settings when the learner is ready. These links configure the same worksheets without creating a new activity.
Look past the fraction bar
Compare signed fractions that simplify to integers with fractions that remain nonintegers, alongside roots and pi.
Open this practice →Start with integers
Practice positive and negative sums and differences before introducing fractions.
Open this practice →Keep the tenths aligned
Work with signed decimal operands and preserve place value.
Open this practice →Find a common denominator
Combine signed fractions and write the result in simplest form.
Open this practice →Two ways to write division
Connect a fraction bar with the division sign using familiar fact magnitudes.
Open this practice →Read multiplication notation
Compare the multiplication sign with adjacent parentheses using larger factors.
Open this practice →Mix rational number types
Practice signed integer, decimal and fraction products and quotients on one sheet.
Open this practice →Simplify first. Classify second.
A fraction does not always represent a noninteger. The value −18/−3 is 6, so it is natural, whole, integer, rational and real. In contrast, 5/3 is rational and real but is not an integer.
A square-root symbol does not automatically mean irrational. The principal square root √36 is 6; √37 is irrational because 37 is not a perfect square.
The classification worksheet asks for every applicable set. Its legend defines natural numbers as 1, 2, 3, … and whole numbers as 0, 1, 2, 3, … .
Separate number signs from operation signs
Add or subtract
In −4 − (−7), the middle minus sign means subtraction and the other signs belong to the numbers. Adding the opposite gives −4 + 7 = 3.
Multiply
Both (−4) × (−7) and (−4)(−7) mean multiplication. Their product is 28. Parentheses also keep each negative factor together.
Divide
28 ÷ (−7) = −4. Writing 28 over −7 as a stacked fraction represents the same calculation. Multiply the quotient by the divisor to check.
Teaching questions
Is zero a natural number?
Conventions differ. These worksheets define natural numbers as starting at 1 and whole numbers as starting at 0. The printed legend states that convention, so zero belongs to W, Z, Q and R.
Why can an integer have several labels?
The number sets overlap. Every natural number is whole, every whole number is an integer, and every integer is rational and real. Listing only N leaves out the larger sets.
Do mixed rational questions combine decimals and fractions?
You can include integers, decimal tenths and fractions on one sheet. Each individual sum or difference uses one number type, which keeps the focus on signed arithmetic.
What does the multiplication range control?
It controls the magnitudes of factors and divisors, along with the constructed quotient. A dividend is built from two factors, so it can be larger than the selected range.
Can I practice multiplying noninteger fractions?
Yes. The rational-number multiplication and division sheet can combine signed fractions with integer and decimal questions, while the focused multiplication and division worksheets provide fraction-only practice.
Which paper sizes and languages are available?
All real-number activities support Letter and A4. The new mixed rational multiplication and division activity is English-only; the three earlier activities continue to support English, German, Albanian, Spanish, Italian, French, Turkish and Norwegian Bokmål. Ready-made PDFs are English.
Connect this practice with algebra
Order of operations
Apply the sign rules while deciding which calculation comes first.
Practice order of operations →Evaluate an expression
Substitute known values and calculate carefully with the resulting signed numbers.
Practice substitution →Continue into Algebra 2
Review the basic skills before moving to complex numbers.
Explore Algebra 2 practice →