Mathematics
Grade 4
15 min
Write numerical expressions
Write numerical expressions
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate word phrases with addition and subtraction into numerical expressions.
Translate word phrases with multiplication and division into numerical expressions.
Write a single numerical expression for a problem involving two or more operations.
Use parentheses `( )` to show which part of an expression should be calculated first.
Identify the correct numerical expression that matches a multi-step word problem.
Differentiate between expressions where order matters, such as 'subtract 4 from 20' versus 'subtract 20 from 4'.
Ever wanted to write a math secret code? 🤫 That's what writing numerical expressions is like!
In this lesson, you will learn how to turn word problems into math phrases called numerical expressions. This is a...
2
Key Concepts & Vocabulary
TermDefinitionExample
Numerical ExpressionA math phrase made up of numbers and operation symbols. It does not have an equal sign.8 + (3 × 4)
OperationA mathematical action. The four basic operations are addition (+), subtraction (-), multiplication (×), and division (÷).In the expression 10 - 2, subtraction is the operation.
SumThe result of an addition problem.The sum of 7 and 5 is 12.
DifferenceThe result of a subtraction problem.The difference between 9 and 2 is 7.
ProductThe result of a multiplication problem.The product of 6 and 4 is 24.
QuotientThe result of a division problem.The quotient of 15 divided by 3 is 5.
Parentheses ( )Symbols used to group parts of an expression. The operation inside the parentheses is always done first.In (2 + 8) × 3, you solve 2 + 8 first.
3
Core Formulas
Translating Key Words
Sum/Plus/More than -> `+` | Difference/Minus/Less than -> `-` | Product/Times/Of -> `×` | Quotient/Divided by -> `÷`
Look for these signal words in a word problem to know which operation symbol to use. They are clues for building your expression.
Grouping with Parentheses
Use `( )` to group the part of the expression that must be done first.
When a phrase says 'the sum of 4 and 5, then multiply by 2,' the addition must happen first. We write this as `(4 + 5) × 2` to show the correct order.
Order in Subtraction and Division
`a - b` is not `b - a`. `a ÷ b` is not `b ÷ a`.
The order of numbers matters for subtraction and division. 'Subtract 3 from 10' means `10 - 3`. 'Divide 12 by 4' means `12 ÷ 4`.
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Consider the expressions: (A) `(24 ÷ 4) + 2` and (B) `24 ÷ (4 + 2)`. Which statement is true?
A.Expression (A) means 'the sum of the quotient of 24 and 4, and 2'.
B.Expression (B) means 'divide 24 by 4, then add 2'.
C.Both expressions have the same value.
D.Expression (A) means 'divide 24 by the sum of 4 and 2'.
Challenging
A student was asked to write an expression for "6 plus the product of 4 and 2". They wrote `(6 + 4) × 2`. What is the student's mistake?
A.They should have used division instead of multiplication.
B.They grouped the addition (6 + 4) first, instead of the multiplication.
C.They should have written 4 × 2 + 6.
D.They subtracted instead of adding.
Challenging
A farmer has 3 rows of corn with 10 plants in each row. He also has 2 rows of tomatoes with 10 plants in each row. He wants to combine all the plants and divide them into 5 new, equal sections. Which expression represents the number of plants in each new section?
A.(3 × 10) + (2 × 10 ÷ 5)
B.3 × 10 + 2 × 10 ÷ 5
C.(3 + 2) × 10 ÷ 5
D.((3 × 10) + (2 × 10)) ÷ 5
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free