Equal 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.
Equal amounts match one to one, and equal numbers land on the same point of the number line even when they are written differently.
Formal definition and notation
Two quantities a and b are equal, written a = b, when they have the same value; on the number line they mark the same point. For any two real numbers exactly one of a < b, a = b, a > b is true (the trichotomy property). Two groups of objects are equal in number when their objects can be matched one to one with none left over.
Symbol
Read it as
Meaning
a = b
a is equal to b
a and b have the same value
a ≠ b
a is not equal to b
a and b have different values
a ≤ b
a is less than or equal to b
a is smaller than b or equal to it
Key facts
When comparing two numbers, exactly one is true: the first is greater than, less than, or equal to the second.
Equal numbers sit at the same point on a number line.
One number can have many names: 6, 3 + 3, 122 and 6.0 are all equal to each other.
Two groups are equal in number when you can pair every object in one with an object in the other and none are left.
Equal is symmetric: if a is equal to b, then b is equal to a.
Try it: when are two numbers equal?
Interactive
Drag the two points. The readout says which number is greater, and it says “they are equal” only when both points land on the same spot.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Equal To examples, step by step
Example 1: Comparing two groups
Warm-up
A plate has 7 crackers and another has 4 + 3 crackers. Are the amounts equal?
Find each amount: the first plate has 7.
The second plate has 4 + 3 = 7.
Answer: Yes, 7 is equal to 4 + 3, so the amounts are equal.
Example 2: Equal fractions and decimals
Core
Which of these are equal to 34: 0.75, 68, 0.34, 75%?
Answer: A.35 = 3 ÷ 5 = 0.6, so they are equal. Choosing > or < treats different-looking numbers as different, and ≠ says they are not equal.
Question 3 of 3
Group A has 9 stars. Group B has 6 stars. How many stars must be added to Group B to make the groups equal?
Show answer and explanation
Answer: C.9 − 6 = 3, and 6 + 3 = 9. 15 is the total, and 9 or 6 would make Group B larger than Group A or leave it smaller.
Equal To: frequently asked questions
What does equal to mean for kids?
It means the same amount. If you have 4 crayons and your friend has 4 crayons, you have an equal number. You can check by pairing your crayons with your friend’s: if every crayon has a partner and none are left over, the amounts are equal. We write it with the equal sign: 4 = 4.
What is the symbol for equal to and not equal to?
“Equal to” is written =, as in 2 + 2 = 4. “Not equal to” is the equal sign with a slash through it, ≠, as in 2 + 2 ≠ 5. There are also combined symbols: ≤ means less than or equal to, and ≥ means greater than or equal to.
Can two different-looking numbers be equal?
Yes, and it happens all the time. 14, 0.25, 25% and 28 all name the same amount, so they are equal to each other. Whole numbers have many names too: 10 equals 7 + 3, 2 × 5 and 303. To check, find the value of each and compare.
Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6Real NumberA real number is any number that can be placed on the number line. The real numbers are all the rational numbers (fractions, integers, terminating and repeating decimals) together with all the irrational numbers (such as √2 and π). Square roots of negative numbers, like √−4, are not real.Number System · Grade 8, Algebra 1NumberA 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 2HundredthsHundredths are the parts you get when one whole is split into 100 equal parts; one hundredth is 1100 or 0.01. The hundredths place is the second digit to the right of the decimal point, so in 3.47 the 7 means 7 hundredths. One cent is one hundredth of a dollar.Number System · Grade 4, Grade 5, Grade 6TenthsTenths are the parts you get when one whole is split into 10 equal parts; each part is one tenth, written 110 or 0.1. The tenths place is the first digit to the right of the decimal point, so in 4.7 the 7 means 7 tenths, or 0.7.Number System · Grade 3, Grade 4, Grade 5Equal SignThe 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.Symbols and Notation · Kindergarten, Grade 1, Grade 2Equivalent FractionsEquivalent fractions are fractions that name the same value, like 12, 24 and 36. To make one, multiply or divide the numerator and denominator by the same nonzero number. That multiplies the fraction by 1, so its value does not change, and the fractions land on the same point of a number line.Number System · Grade 3, Grade 4, Grade 5Equivalent ExpressionsEquivalent expressions are expressions that have the same value for every value of the variable, even though they look different. For example, 3(x + 2) and 3x + 6 are equivalent: both equal 15 when x = 3 and 0 when x = −2. You build them with the properties of operations, such as the distributive property.Algebra · Grade 6, Grade 7, Algebra 1Less Than or Equal ToLess than or equal to is a comparison meaning one value is smaller than another or exactly equal to it, written with the symbol ≤. The statement x ≤ 5 is true for 5 itself and for every number below 5, such as 4.9, 0 and −3. In words, ≤ means at most or no more than.Symbols and Notation · Grade 6, Grade 7, Algebra 1Greater Than or Equal ToGreater than or equal to means a value is either bigger than a number or exactly equal to it, and its symbol is ≥. The inequality x ≥ 3 is true for 3 and every number above it. It means “at least 3”. On a number line it is graphed with a filled dot, because the endpoint is included.Symbols and Notation · Grade 6, Grade 7, Algebra 1Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5EquationAn 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 8Greater 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 3Less 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