Meaning of the equal sign Knowledge-Based Study

Study notes

1. A common misconception is that the equal sign (=) means "here comes the answer" or "compute now". In mathematics, the equal sign actually represents a relationship of equivalence.

   Think of an equation as a balanced scale:

   • The quantity on the left side of the symbol has the exact same value as the quantity on the right side.
   • It states: "the value here is the same as the value there."

   For example, writing 7 = 7 is a true statement because both sides represent the identical quantity.

   Because the equal sign indicates balance, mathematical expressions can appear on either or both sides of the sign:

   • Standard form: 4 + 5 = 9
   • Reversed form: 9 = 4 + 5
   • Operations on both sides: 6 + 2 = 5 + 3

   To check if 6 + 2 = 5 + 3 is true, evaluate each side separately:

   • Left side: 6 + 2 = 8
   • Right side: 5 + 3 = 8

   Since 8 equals 8, the balance holds and the equation is correct.

   When solving an equation with a missing value, your goal is to find the number that keeps both sides equal in value.

   Consider the problem:

   8 + 4 = ___ + 5

   Follow these steps to solve it:

   1. Calculate the known side: 8 + 4 = 12.
   2. Identify the requirement for the other side: the right side must also equal 12.
   3. Determine the missing number: ___ + 5 = 12.
   4. Since 7 + 5 = 12, the missing number is 7.

   Notice that the answer is not 12. Writing 12 in the blank would create an untrue statement: 8 + 4 = 12 + 5, which simplifies to 12 = 17.

   You can test whether any number sentence is true or false by evaluating both sides independently.

   Example 1

   10 - 3 = 4 + 3

   • Left side: 10 - 3 = 7
   • Right side: 4 + 3 = 7
   • Both sides equal 7, so the statement is True.

   Example 2

   9 - 2 = 3 + 5

   • Left side: 9 - 2 = 7
   • Right side: 3 + 5 = 8
   • Because 7 does not equal 8, the statement is False.