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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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.
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Simplify the value first, then list every applicable set. On this worksheet natural numbers start at 1; whole numbers include 0.
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A number can belong to several sets
The natural numbers sit inside the whole numbers, which sit inside the integers. Every integer is rational, and every rational number is real. Irrational numbers are real too, but cannot be written as a ratio of integers.
Every worksheet has fourteen values. The worksheet defines N as 1, 2, 3, … and W as 0, 1, 2, 3, … . List all applicable sets using the legend; simplify fractions and roots before deciding.
Learning objective
What this activity builds
Classify a value as natural, whole, integer, rational or irrational, and recognize that all values on this worksheet are real.
Worked example
Which sets contain −18 / −3?
Natural, whole, integer, rational and real: N, W, Z, Q, R.
The quotient is 6. Its written fraction form does not prevent it from being an integer. Six belongs to each of the larger sets containing the natural numbers.
Teaching notes
Make the practice count
- Use the set legend before starting the first question.
- Ask for all applicable sets, not just the smallest one.
- Simplify an unreduced fraction and compare its value with the original form.
- Compare √49 with √50 to separate rational and irrational roots.
- Keep zero visible as the boundary between our natural and whole number conventions.
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Use an original printable reference to set notation, unions, intersections, complements, subset relations and number sets, with clear definitions and examples.
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