How to Use the Number Zero in Math

Zero is a very special and unique number, and some people are confused about how to use it. The number zero is a symbol used to represent the absence of something. This is a basic guide on the properties of zero and how it is used in everyday mathematics.

Method 1
Method 1 of 6:

Understanding the Concept of Zero

  1. It's not the same as other numbers because of this. If you tell someone that there are zero pieces of pie left, that's the same thing as saying that there's no more pie. You cannot count zero or take a fraction of it.
  2. This is because the positive and negative numbers are defined with relation to zero. Positive numbers are larger than zero, while negative numbers are smaller than zero. Zero can't be larger or smaller than itself, so there is no such thing as +0 or -0. The opposite of zero is zero since 0 + 0 = 0.
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  3. This can be proven in a variety of ways:
    • An even number plus an even number yields an even number. 2+0=2. Therefore, zero must be an even number.
    • An even number divided by two yields zero as remainder. Since zero divided by two is zero, with zero as remainder, zero must be an even number.
    • In fact, zero is possibly the most even number. Six is singularly even, because you can divide it by two, one time, whereas twelve is doubly even, because you can divide it by two, and then by two again. So in a sense, twelve is more even than six. Since you can keep dividing zero by two ad infinitum, it is the most even number.
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Method 2
Method 2 of 6:

Using Zero in Addition

  1. That means, when you add 0 to a number, you get the original number back; in equation form, that would be x + 0 = x .
    • 3 + 0 = 3
    • 5 + 0 = 5
    • -2 + 0 = -2
  2. In equation form, that would be x + (-x) = 0 . A number's opposite is called its additive inverse, and two additive inverses always sum to zero.
    • -8 + 8 = 0
    • 10 + -10 = 0
    • -2 + 2 = 0
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Method 3
Method 3 of 6:

Using Zero in Subtraction

  1. When you do so, you will get the same number back. That would mean:
    • 2 - 0 = 2
    • 5 - 0 = 5
    • -16 - 0 = -16
  2. 0 minus any number is the opposite of that number, or its additive inverse. In equation form, that would be 0 - x = (-x) or 0 - (-x) = x .
    • 0 - 1 = (-1)
    • 0 - 2 = (-2)
    • 0 - (-180) = 180
  3. That would be like having five apples on the table and taking away all five. If you do so, you will get zero. The same applies to subtracting a negative number from itself; when you do this, you also get zero.
    • 2 - 2 = 0
    • 5 - 5 = 0
    • -12 - (-12) = 0
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Method 4
Method 4 of 6:

Using Zero in Multiplication and Division

  1. That means, when you multiply any number by zero, the product will always be zero, no matter how big the number. In equation form, that would be a * 0 = 0 . [1]
    • 0 x 1 = 0
    • 0 x 5 = 0
    • 0 x 280 = 0
    • 0 x 1,000 = 0
    • 0 x 3,000 = 0
    • 0 x 10,000,000 = 0
  2. When you have 0 in the dividend of a division problem, you will always get zero.
  3. An expression where a non-zero number is divided by zero is undefined. For example, 28/0 is the same as asking "what number times 0 is equal to 28?" There is no such number, since anything times 0 is 0.
    • 0/0 is a special case of this rule. It can be reformulated as "what number times 0 is equal to zero?", or "0x=0". Since x can be any number, this expression is indeterminate.
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Method 5
Method 5 of 6:

Using Zero in Exponents

  1. That would be like 0 x 0 x 0 x 0, or multiplying nothing by nothing several times. Since multiplying by nothing never gets one anywhere, 0 to any power stays 0 forever.
  2. For example, 2 to the 0 power is 1 and 8 to the 0 power is 1.
    • 0 to the 0 power is indeterminate, since it is "illegal" to divide by zero and, thus, 0 divided by itself is indeterminate. [2]
  3. Taking the square root of zero can be reformulated as "what number times itself is zero". 0*0=0, so the square root of zero is zero.
    • This holds true for any root of zero: the n th root of zero is equal to zero, as long as n is not equal to zero.
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Method 6
Method 6 of 6:

Teaching Elementary Students About Zero

  1. Mention an object that you have none of and tell your students that if you tried to count it, you couldn't. There's nothing to count in the first place.
  3. You'll just have the same value; it's completely pointless.
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      Tips

      • You can also use zero as a placeholder. If they need to distinguish thirty-eight from three hundred eight, you can add a zero in between the 3 and the 8.
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      References

      1. ↑ https://www.splashmath.com/math-vocabulary/multiplication/zero-property-of-multiplication
      2. ↑ https://medium.com/i-math/the-zero-power-rule-explained-449b4bd6934d

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