Wayground
Real Number System & Properties - Printable Mathematics Worksheets class 11 - Wayground

Real Number System & Properties

10 questions

11th - 11th Grade

Mathematics

Real Number System & Properties is a Grade 11 mathematics worksheet that helps students classify numbers within the real number system. In six select-all-that-apply questions, students identify whether numbers are irrational, rational, integer, whole, or natural, including an item that requires simplifying before classification. The format reinforces that a number may belong to more than one category. Four multiple-choice questions then assess students’ ability to recognize the commutative, associative, and identity properties of addition and multiplication from symbolic equations and numerical examples. This free printable worksheet is useful for guided practice, independent review, or a quick skills check after instruction. It includes a complete answer key so teachers can review classifications and property-identification errors efficiently.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Real Number System & Properties

Total questions: 10

Name
Class
Date
1.

Select all that apply for this number:

77  

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

2.

Select all that apply for this number:

−3612-\frac{36}{12}  (Simplify first!)

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

3.

Select all that apply for this number:

π\pi  - π\pi

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

4.

Select all that apply for this number:

6.486.48  

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

5.

Select all that apply for this number:

−10-\sqrt{10}  

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

6.

Select all that apply for this number:

00  

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

7.

Commutative Property of Addition

a)

a+b=ab

b)

a+b+c=b+c+a

c)

a+b=b+a

d)

a+1=a

8.

Associative Property of Addition

a)

a+b=b+a

b)

a+(b+c)=(a+b)+c

c)

abc=a(bc)

d)

a+(-1)=-a

9.

Identity Property of Addition

a)

1 X 4 = 4

b)

4 + 0 = 4

c)

4 X 0 = 0

d)

-9 + 9 = 0

10.

Commutative Property of Multiplication

a)

abc=a(bc)

b)

6 + 0 = 6

c)

ab=ba

d)

6 X 0 = 0

Answer Key

Real Number System & Properties

Total questions: 10

1.
b)

Rational

, c)

Integer

, d)

Whole

, e)

Natural

2.
b)

Rational

, c)

Integer

3.
b)

Rational

, c)

Integer

, d)

Whole

4.
b)

Rational

5.
a)

Irrational

6.
b)

Rational

, c)

Integer

, d)

Whole

7.
c)

a+b=b+a

8.
b)

a+(b+c)=(a+b)+c

9.
b)

4 + 0 = 4

10.
c)

ab=ba

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Real Number System & Properties worksheet cover?

This Grade 11 mathematics worksheet combines real-number classification with property identification. Students complete six select-all-that-apply questions classifying numbers as irrational, rational, integer, whole, or natural—including one item that must be simplified first—followed by four multiple-choice questions on the commutative, associative, and identity properties of addition and multiplication.

How can I use this worksheet to teach real-number classification and properties?

Introduce the classification items by having students explain why a number can fit several categories, then model simplifying an expression before deciding which sets contain it. After students complete the six select-all-that-apply questions, use the four property questions to have them compare equations and discuss whether the change involves order, grouping, or an additive or multiplicative identity.

What mistakes should I watch for on this real number system worksheet?

Students may select only one category even when a number belongs to several nested sets, or classify an expression before simplifying it. In the property section, watch for confusion between commutative equations, which change order, and associative equations, which change grouping, as well as confusing the additive identity with zero-product or additive-inverse examples.

How do I assign and grade this Real Number System & Properties worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all 10 items. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital quiz.

How can I differentiate this worksheet for my students?

For the classification and property-identification items, adjust font spacing and font size to make the answer choices and equations easier to scan. Wayground’s Advanced Settings also let you apply a dyslexia-friendly font or translate the worksheet into another language while preserving its select-all-that-apply and multiple-choice formats.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion