Practice Identity Elements in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Special numbers that leave any other number unchanged under a given operation: 0 for addition, 1 for multiplication.

Adding 0 leaves any number unchanged; multiplying by 1 also leaves it unchanged. Both are 'do-nothing' values.

Showing a random 20 of 50 problems.

Example 1

challenge
Does the operation a⋆b=aba\star b=a^b on positive reals have an identity? Explain.

Example 2

hard
For the operation a⋆b=a+b+aba \star b = a + b + ab, find the identity element.

Example 3

medium
Rewrite 58\frac{5}{8} with denominator 24 by multiplying by a form of 1.

Example 4

hard
What is the identity element of the operation 'string concatenation' on the set of strings?

Example 5

medium
To convert 23\frac{2}{3} to a fraction with denominator 15, multiply by what form of 1?

Example 6

medium
What is the identity for the operation a⋆b=min⁡(a,b)a \star b = \min(a,b) on positive integers up to 100?

Example 7

medium
Simplify (x+0)⋅1−0(x+0)\cdot 1 - 0.

Example 8

medium
For a⋆b=a+b−5a \star b = a + b - 5, find the identity element.

Example 9

medium
Simplify 88⋅23+0\frac{8}{8}\cdot 23 + 0.

Example 10

medium
Why does multiplying a fraction by 33\frac{3}{3} not change its value?

Example 11

easy
What is 1×1561 \times 156?

Example 12

hard
Show that a⋆b=a+b−aba \star b = a + b - ab has identity e=0e=0, and find the inverse of aa.

Example 13

easy
True or false: 0×999=00 \times 999 = 0.

Example 14

hard
For the operation a⋆b=2aba \star b = 2ab, does an identity element exist?

Example 15

easy
What is 14+014 + 0?

Example 16

challenge
For the operation a⋆b=ab+a+ba\star b = ab + a + b, find the identity element ee.

Example 17

hard
Why is the identity element in a group always unique?

Example 18

easy
Fill the blank: 42+□=4242 + \square = 42.

Example 19

easy
Does 5+15 + 1 equal 5?

Example 20

easy
Fill the blank: □×73=73\square \times 73 = 73.
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