The equal sign (=) is the symbol that shows two expressions have the same value. In 3 + 5 = 2 + 6, both sides equal 8, so the statement is true. The equal sign does not mean “the answer comes next”; it works like a balanced scale, and a number sentence with = is called an equation.
An equal sign says the two sides balance. Check a number sentence by finding the value of each side, not by looking for an answer after the sign.
Formal definition and notation
The equal sign is a relation symbol placed between two expressions to form an equationA = B, which asserts that A and B name the same number. The statement is true when both sides have the same value and false otherwise; an equation with a variable is true only for certain values, its solutions. Equality is reflexive (a = a), symmetric (if a = b then b = a) and transitive (if a = b and b = c then a = c).
Symbol
Read it as
Meaning
=
equals, or is equal to
the two sides have the same value
≠
is not equal to
the two sides have different values: 4 + 1 ≠ 5 + 2
≈
is approximately equal to
close but not exactly equal: π ≈ 3.14
Key facts
An equal sign can have one number on either side: 9 = 4 + 5 is just as correct as 4 + 5 = 9.
Both sides can be expressions: 6 + 2 = 10 − 2.
Do not chain steps with equal signs that are not true: write 3 + 4 = 7, then 7 + 2 = 9 on a new line.
An equation with a missing number asks which number makes it true: in 8 + □ = 11, the box is 3.
Use = only for exact equality; use ≈ for estimates and rounded answers.
Where the name comes from. Robert Recorde introduced the equal sign in The Whetstone of Witte in 1557, according to Wolfram MathWorld.
Keeping an equation balanced
Keeping an equation balanced
if a = b, then a + c = b + c and a × c = b × c
a, b
the two equal sides
c
any number added to (or multiplied on) both sides
Doing the same thing to both sides keeps the scale balanced. This is how equations are solved.
Try it: keep it balanced
Interactive
The scale shows 2x + 3 = 11. Do the same step to both sides until x is alone, and watch the scale stay level.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Equal Sign examples, step by step
Example 1: True or false?
Warm-up
Is 9 + 6 = 20 − 5 true or false?
Left side: 9 + 6 = 15.
Right side: 20 − 5 = 15.
Both sides are 15.
Answer: True: both sides equal 15.
Example 2: Find the missing number
Core
What number makes 7 + 5 = □ + 8 true?
The left side is 7 + 5 = 12.
The right side must also be 12: □ + 8 = 12.
12 − 8 = 4.
Answer: The missing number is 4.
Example 3: Spot the misuse
Test-style
To share 15 + 5 stickers among 4 friends, a student wrote 15 + 5 = 20 ÷ 4 = 5. What is wrong, and how should it be written?
Read the first sign: 15 + 5 = 20 is true.
The second sign claims 15 + 5 = 5, because every = says all linked parts are equal, and 20 is not 5.
Write two separate equations: 15 + 5 = 20, then 20 ÷ 4 = 5.
Answer: The chain says 20 equals 5, which is false; write 15 + 5 = 20 and 20 ÷ 4 = 5 as separate lines.
Common mistakes
✗ MistakeFilling the box with the sum so far: in 8 + 4 = □ + 5, writing 12.
✓ InsteadThe right side must equal 12: □ = 7.
The equal sign means “same value as”, not “write the answer here”. 12 + 5 = 17, which is not 12.
> says the left side is bigger: 9 > 4. = says the sides are the same size.
Quick check: 3 questions
Question 1 of 3
Which equation is true?
Show answer and explanation
Answer: B.5 × 2 = 10 and 7 + 3 = 10. The others compare 9 with 8, 12 with 13, and 7 with −7.
Question 2 of 3
What number goes in the box? 9 + 6 = □ + 10
Show answer and explanation
Answer: C. The left side is 15, so □ + 10 = 15 and the box is 5. 15 is the left side’s value, 25 adds 10 more, and 16 is a slip.
Question 3 of 3
Which use of the equal sign is correct?
Show answer and explanation
Answer: C.3 × 4 and 6 × 2 both equal 12. A and D chain unequal values, and B needs ≈ because 0.33 is rounded.
Equal Sign: frequently asked questions
What does the equal sign really mean?
It means “is the same amount as”. The values on its left and right must match, like the two pans of a balanced scale. Many young students read it as “and the answer is”, which leads to errors such as filling 12 into 8 + 4 = □ + 5. Reading = as “is the same as” fixes that.
Who invented the equal sign?
The Welsh mathematician Robert Recorde introduced the equal sign in his book The Whetstone of Witte, published in 1557. Before that, writers spelled out “is equal to” in words. The two parallel lines are now used everywhere in mathematics, science and computing.
Can a number go on the left of the equal sign?
Yes. 7 = 3 + 4 is a correct, true equation, exactly the same statement as 3 + 4 = 7. Equations in algebra often have the variable on the right, such as 20 = 4x, and teachers deliberately show forms like 10 = □ + 6 so students see that = is not a one-way arrow.
RelationA relation is any set of ordered pairs that links inputs to outputs, such as {(1, 4), (2, 5), (2, 7)}. It can be shown as a list, table, mapping diagram or graph. A relation in which every input has exactly one output is a function; this one is not, because 2 has two outputs.Functions · Grade 8, Algebra 1EquationAn equation is a statement that two expressions are equal. It always has an equal sign, such as x + 5 = 12 or 3a = 18. Solving an equation means finding the value of the variable that makes it true: here x = 7 and a = 6. An expression like 4x + 7 has no equal sign, so it is not an equation.Algebra · Grade 6, Grade 7, Grade 8NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2VariableA variable is a letter or symbol that represents a number or value, usually one that can change or is not yet known. In n + 5 = 12, the variable n is an unknown that equals 7. In A = lw, the variables l and w can take many values. Any letter can be a variable, not just x.Algebra · Grade 6, Grade 7, Grade 8SolutionA solution is a value that makes an equation or inequality true. To test a value, substitute it for the variable and check that the statement holds: x = 4 solves x + 2 = 6 because 4 + 2 = 6. A solution can also be an ordered pair, a point on a graph that satisfies the relationship.Algebra · Grade 6, Grade 7, Grade 8Equal ToEqual to means having exactly the same value or amount, and it is written with the symbol =. Numbers that look different can still be equal to each other: 12 is equal to 0.5. When two amounts are not the same, one is greater than or less than the other.Symbols and Notation · Kindergarten, Grade 1, Grade 2Greater ThanGreater than means that one number is bigger than another, and its symbol is >. The statement 7 > 3 reads “seven is greater than three”. The open side of the symbol faces the bigger number and the point aims at the smaller one. On a number line, the greater number is always farther to the right.Symbols and Notation · Grade 1, Grade 2, Grade 3Parallel LinesParallel lines are lines in the same plane that never intersect. They stay the same distance apart and point in the same direction, like the rails of a straight railroad track. On a coordinate plane, parallel lines have the same slope but different y-intercepts. The symbol ∥ means is parallel to.Geometry · Grade 4, Grade 5, Grade 6AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3ExpressionAn expression is a number, variable, or combination of numbers and variables joined by operations, without an equal sign. Examples are 7, 4x + 9 and 3(a − 2). Expressions can be simplified, but they are not solved unless they are part of an equation. You evaluate one by replacing each variable with a number.Algebra · Grade 6, Grade 7, Grade 8Less ThanLess than means smaller in value, and its symbol is <. The statement 4 < 9 reads “4 is less than 9.” The pointed end of the symbol always faces the smaller number. On a number line, the smaller number is farther left, so −3 < 2 even though 3 is bigger than 2. Less than does not include equal.Symbols and Notation · Grade 1, Grade 2, Grade 6