What is a number sentence? It is a math statement made of numbers and symbols that expresses a complete idea, such as 8 + 5 = 13 or 12 > 7. Just as an English sentence needs a verb, a number sentence needs a relation symbol such as =, < or >, and that symbol is what lets you judge the statement true or false. This guide explains the parts of a number sentence, the difference between open and closed sentences, how to write one from a word problem and why the idea matters for algebra. It is written for students reviewing the basics, parents helping with homework and education majors preparing to teach elementary math.
A number sentence is a mathematical statement that uses numbers, operation symbols and a relation symbol to show how quantities compare. In elementary math it is often used as a friendlier name for an equation, but it also covers inequalities. The key test is that a number sentence can be judged true or false, at least once any unknown has been filled in.
Compare these three lines:
| Symbol | Read As | Example |
|---|---|---|
| = | is equal to | 4 × 3 = 12 |
| ≠ | is not equal to | 10 ÷ 2 ≠ 4 |
| < | is less than | 7 − 5 < 3 |
| > | is greater than | 6 + 6 > 11 |
| ≤ | is less than or equal to | n + 1 ≤ 5 |
| ≥ | is greater than or equal to | 2 × 5 ≥ 10 |
A quick way to remember < and >: the narrow, pointed end always points to the smaller number.
A number sentence is true when the two sides relate the way the symbol says, and false when they do not. 8 + 5 = 13 is true; 12 − 4 = 9 is false because 12 − 4 = 8. A false number sentence is still a number sentence, in the same way that "The sky is green" is still a grammatical English sentence.
A closed number sentence has no unknowns, so it is already true or false: 16 + 34 = 50 is true, and 2 × 9 = 19 is false. An open number sentence contains an unknown, so it is neither true nor false until you choose a value. For example, n + 7 = 12 is true when n = 5 and false for any other number. Solving an open number sentence means finding the value or values that make it true.
Some open sentences have many solutions. The inequality x + 2 < 5 is true for every number less than 3, and n + 3 = 3 + n is true for every value of n.
A number sentence with an equal sign is an equation. One that uses <, >, ≤, ≥ or ≠ is an inequality. Both count as number sentences.
| Number Sentence | Open or Closed? | True or False? |
|---|---|---|
| 8 + 5 = 13 | Closed | True |
| 12 − 4 = 9 | Closed | False |
| 15 ÷ 3 > 4 | Closed | True, because 5 > 4 |
| 6 × n = 42 | Open | True only when n = 7 |
| x + 2 < 5 | Open | True whenever x is less than 3 |
Related sentences form fact families that show how operations undo each other. The numbers 3, 5 and 8 give 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5 and 8 − 5 = 3. The numbers 4, 6 and 24 give 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
Here are four worked examples:
Work out each side separately using the order of operations: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Then compare the two results using the relation symbol.
Many students read = as "the answer comes next." In a well-known study, researchers asked elementary students to solve 8 + 4 = __ + 5, and many answered 12 or 17 instead of 7. The equal sign really means "has the same value as," so both sides must balance: 8 + 4 is 12, and 7 + 5 is also 12.
Practicing sentences with operations on both sides, such as 6 + 3 = 4 + 5 or 10 − 2 = 2 × 4, builds this balance view of the equal sign, which students need when they reach algebra.
Open number sentences are early equations. The blank in 4 × __ = 20 becomes the x in 4x = 20, and the strategy is the same: use the inverse operation, then check. Properties of operations are number sentences that are true for every value: a + b = b + a (commutative property), (a + b) + c = a + (b + c) (associative property) and a × (b + c) = a × b + a × c (distributive property). Our guide to understanding algebra and these quick algebra tricks pick up where number sentences leave off.
If number sentences or the algebra that follows feel shaky, practice and feedback help. Our math homework help connects you with tutors: you post your question with instructions and a deadline, compare tutor bids and profiles, and chat with your tutor about each step. Use worked solutions to check your understanding, and follow your school's academic integrity policy. For more ways to build skills, see our tips for mastering math homework, or ask a math question to get started.
A number sentence is a math statement that uses numbers, operation symbols and a relation symbol, such as =, < or >, to express a complete idea. Because it makes a claim, it can be judged true or false. For example, 7 + 3 = 10 is a true number sentence, while 7 + 3 > 12 is a false one. Expressions without a relation symbol, like 7 + 3, are not sentences.
An equation is one kind of number sentence: a statement that two expressions are equal, such as 5 × 4 = 20. Number sentences also include inequalities, which use symbols such as <, >, ≤, ≥ or ≠, for example 5 × 4 > 18. In elementary classrooms, "number sentence" is often used as a simpler name for equations, but the broader term covers both.
An open number sentence contains an unknown, shown as a blank, box or letter, so it is neither true nor false until you choose a value for it. For example, n + 4 = 9 is open; it becomes true when n = 5 and false for any other number. A closed number sentence, such as 5 + 4 = 9, has no unknowns and is already true or false.
No. On its own, 5 + 3 is an expression, a math phrase with a value of 8, because it lacks a relation symbol and does not claim anything. Adding a relation symbol and another side turns it into a number sentence: 5 + 3 = 8 is a true number sentence, and 5 + 3 < 6 is a false one. The relation symbol works like the verb in an English sentence.
Yes. A number sentence only needs to make a claim that can be checked, so 6 + 2 = 9 and 10 < 4 are both number sentences, even though both are false. Deciding whether a sentence is true or false is a common exercise, because it makes students compute each side and think about what the equal sign or inequality symbol actually means.
Identify what the question asks, pick out the numbers that matter and decide what action the story describes: joining, separating, comparing, equal groups or sharing. Choose the matching operation, use a letter or blank for the unknown and write the sentence. For example, "Sam had some stickers, got 9 more and now has 23" becomes n + 9 = 23, so n = 14.
Common examples include 12 + 8 = 20 for addition, 15 − 6 = 9 for subtraction, 3 × 7 = 21 for multiplication and 36 ÷ 4 = 9 for division. Inequalities such as 9 > 2 + 5 are number sentences too. Open examples include n − 4 = 10 and 6 × __ = 30, which become true when n = 14 and the blank is 5.
Post your assignment, compare tutor bids and work with an expert who explains each step.
Math Homework Help from Tutors Who Show Every Step
Get affordable and top-notch help for your essays and homework services from our expert tutors. Ace your homework, boost your grades, and shine in online classes—all with just a click away!
Fast, secure, and handled by vetted experts.
These details about the ⭐BEST WORDS TO START A CONCLUSION⭐ highlight the dos and don'ts to consider when winding up on your essay or speech.
Read More
Are you learning ⭐ HOW TO CALCULATE FINANCE CHARGE ⭐ Don't worry! Learn the best ways to get your correct finance charge from financial experts.
Read More
Arguments can be divided into two main categories: Inductive and deductive. use this post to get insight on inductive vs deductive argument and examples for each type.
Read More