Identity Elements Math Example 2

Follow the full solution, then compare it with the other examples linked below.

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Show that multiplying any number by 1 doesn't change it. Use \(23 \times 1\) and \(1 \times 23\). Also show what happens with \(23 \times 0\).

1
\(23 \times 1 = 23\). One group of 23 is still 23.
2
\(1 \times 23 = 23\). Same result.
3
\(23 \times 0 = 0\). Zero groups of anything is 0.
4
Identity for multiplication: \(a \times 1 = a\). Zero property: \(a \times 0 = 0\).

Answer

\(23 \times 1 = 23\); \(23 \times 0 = 0\)

1 is the multiplicative identity. Multiplying by 1 leaves a number unchanged. Multiplying by 0 always gives 0.

About Identity Elements

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

Show that adding 0 to any number doesn't change it. Verify with (14 + 0) and (0 + 14).

What is (387 + 0)? What property does this demonstrate?

Fill in the blank and name the property: (456 times square = 456) and (456 times square = 0).