Statistics

Learning tasks

A) Numbers 1 and 0
Applying Number Properties
Numbers 1 and 0	Zero \((0)\) and one \((1)\) are very special numbers that have important properties. Proposition Additive Identity Property Adding \(0\) to any number results in the number itself. For any number \(a\),$$0 + a = a \quad \text{and} \quad a + 0 = a.$$ Ex 1 Proposition Multiplicative Identity Property Multiplying any number by \(1\) results in the number itself. For any number \(a\),$$1 \times a = a \quad \text{and} \quad a \times 1 = a.$$ Ex 2 Discover Multiplying by \(0\): Any number multiplied by \(0\) always results in \(0\). For example, \(5 \times 0 = 0 + 0 + 0 + 0 + 0 = 0\). Dividing by \(0\): Division by \(0\) is undefined in mathematics because it leads to a contradiction. For example, if we assume \(a = 5 \div 0\), then \(a \times 0 = 5\). But this is impossible because \(a \times 0\) is always \(0\), not \(5\). Proposition Multiplying by \(0\) For any number \(a\),$$a \times 0 = 0 \quad \text{and} \quad 0 \times a = 0.$$ Proposition Dividing by \(0\) For any number \(a\), the division \(a \div 0\) is undefined.
Numbers 1 and 0	Ex 3 Ex 4 Ex 5 Ex 6

Lesson Summary
Text book

Exercises Correction
A) Numbers 1 and 0
Applying Number Properties
Numbers 1 and 0

Zero $(0)$ and one $(1)$ are very special numbers that have important properties.

Proposition Additive Identity Property

Adding $0$ to any number results in the number itself.
For any number $a$,$$0 + a = a \quad \text{and} \quad a + 0 = a.$$

Ex 1

Proposition Multiplicative Identity Property

Multiplying any number by $1$ results in the number itself.
For any number $a$,$$1 \times a = a \quad \text{and} \quad a \times 1 = a.$$

Ex 2
Discover

Multiplying by $0$:

Any number multiplied by $0$ always results in $0$.
For example, $5 \times 0 = 0 + 0 + 0 + 0 + 0 = 0$.

Dividing by $0$:

Division by $0$ is undefined in mathematics because it leads to a contradiction.
For example, if we assume $a = 5 \div 0$, then $a \times 0 = 5$. But this is impossible because $a \times 0$ is always $0$, not $5$.

Proposition Multiplying by $0$

For any number $a$,$$a \times 0 = 0 \quad \text{and} \quad 0 \times a = 0.$$

Proposition Dividing by $0$

For any number $a$, the division $a \div 0$ is undefined.

Numbers 1 and 0 Ex 3 Ex 4 Ex 5 Ex 6