Writing Numerical Expressions
Basics on the topic Writing Numerical Expressions
Writing Numerical Expressions – Introduction
Math enthusiasts and curious learners, you're about to embark on an exciting journey to understand numerical expressions. Picture this: Each numerical expression is a math puzzle waiting for you to solve. It's not just about numbers; it's about the language of mathematics that helps us solve realworld problems. So, let's dive in and discover the world of numerical expressions together!
Understanding Numerical Expressions – Definition
A numerical expression is a mathematical phrase that combines numbers and operation symbols without an equals sign. Unlike equations, numerical expressions don't show the result of the calculation.
Numerical expressions are combinations of numbers and mathematical operations (e.g., addition, subtraction, multiplication, and division) that represent a specific calculation to be performed.
They're the backbone of algebra and help us simplify complex problems into manageable steps.
Operation  Keywords 

Addition  sum, total, add, increase, plus, combined, together, more than 
Subtraction  difference, subtract, decrease, minus, less, fewer, remain, take away 
Multiplication  product, multiply, times, of, double, triple, groups of 
Division  quotient, divide, per, ratio, out of, split, shared equally 
Writing Numerical Expressions – Example
Consider the following scenario: You have 3 baskets, and each basket contains 4 apples and 2 oranges. To express this mathematically, you could write a numerical expression like: $3 \times (4 + 2)$.
Here's how it breaks down:
Step  Description  Mathematical Expression 

1  Identify the quantities  3 baskets, 4 apples/basket, 2 oranges/basket 
2  Choose the operation for the apples and oranges  Add the number of apples and oranges per basket: $4 + 2$ 
3  Express the multiplication of baskets  Multiply the sum by the number of baskets: $3 \times (4 + 2)$ 
Writing Numerical Expressions – Summary
Key Learnings from this Text:
Numerical expressions are mathematical phrases that combine numbers and operators.
They help us represent and solve realworld problems in a simplified way.
It's important to understand the order of operations when writing numerical expressions.
Practice is key to becoming confident in writing and interpreting numerical expressions.
Keep exploring mathematical concepts, and don't hesitate to reach out with questions or for more examples to further your understanding!
Writing Numerical Expressions – Frequently Asked Questions
Transcript Writing Numerical Expressions
You're relaxing on the couch, minding your own business, scrolling away when you see it. Someone has posted a riddle, and everyone is commenting with a different answer, and it is challenging you to solve it! What starts out seeming like a daunting task becomes a piece of cake when you know about writing numerical expressions. A numerical expression is a sentence with a minimum of two numbers or variables and at least one math operation. We use these number sentences to break down more complex ideas into easier manageable parts. An expression does not solve the problem directly, but rather guides you in the order of operations needed to obtain a solution. Remember, the order of operations is gems. G stands for groupings, E for exponents, M is mulitply and its opposite, divide, S is subtract and add. Let's write an expression for multiply the sum of two and six by nine. First, let's look at the digits in this statement. We have two, six, and nine. It says to multiply the sum of two and six. This tells us that the two and six are grouped together and added, so we can use a parenthesis and addition sign to show this. Based on the statement, what operation would we put between the parentheses and the nine? A multiplication sign. Note, that just because the word multiply was first doesn't always mean it comes first in the expression. These are the two ways to express this sentence. Write the expression for this example. The difference between thirtysix and N, divided by two. Here, thirtysix minus N is inside parenthesis, and then we have divide by two. Let's apply what we've learned to some more complex problems. Read each statement carefully, and apply the order of operations. Which of the following number sentences shows the statement, the product of thirtyfive and five, times five. Pause the video whenever you need extended time. The correct numerical expression is C. Which of the following number sentences shows the statement two to the fourth power, divided by the product of six and three. The correct numerical expression is D. So, let's apply what we now know about numerical expressions to that challenging online post. Which statement shows six plus fifteen plus the product of three and twentyfour, divided by three to the second power. The correct numerical expression is B. To summarize, by writing and interpreting numerical expressions, we can improve our math fluency and become more comfortable working with numbers and mathematical symbols.
Writing Numerical Expressions exercise

What is the purpose of writing numerical expressions in mathematics?
HintsThink about how numerical expressions help break down complicated problems into smaller, more manageable parts.
Consider the purpose of using mathematical symbols and operations to represent realworld scenarios or abstract concepts.
SolutionThe purpose of writing numerical expressions in mathematics is to represent complex ideas in simpler terms.

Which acronym helps in remembering the order of operations in numerical expressions?
HintsEach letter represents a step in the order of operations.
Pay attention to what each letter stands for.
A useful mnemonic for remembering the order of operations is: Go Eat My Sandwich.
SolutionThe acronym which helps in remembering the order of operations in numerical expressions is GEMS.
The acronym GEMS stands for:
G  Groupings
E  Exponents
M  Multiply and its opposite, Divide
S  Subtract and Add

Find the order of operations to find a solution to a numerical expression.
HintsIdentify the operation inside the parentheses and evaluate it first.
Once the expression inside the parentheses is simplified, proceed with the remaining operations according to the order of operations, which in this case is addition.
SolutionThe order of operations is:
 Perform the multiplication operation inside the parentheses.
 Replace the expression inside the parentheses with its result.
 Perform the addition operation.
 The final result is 19.

Use order of operations to evaluate the expression.
HintsApply the order of operations acronym GEMS to determine the correct sequence of operations.
Remember to perform multiplication and division before addition and subtraction, and follow the lefttoright rule when operations have the same precedence.
Solution8 $\div$ 2 + 3 x 4 = 16
 Start with Division: Perform the division operation first. 8÷2=4
 Then Multiplication: Perform the multiplication operation next. 3×4=12
 Finally, Addition: Add the results of the previous operations. 4+12=16

Write a numerical expression to represent a situation.
HintsWe know there are 7 days in a week and Zuri is spending $3 a day.
How would we find the total of what she spends for the week?
How would we find out how much she had left from $25?
SolutionThe correct answer is 25 − (7 × 3).
To write the expression, we need to calculate how much money Zuri spends during the week (7 x 3).
Then we need to subtract that amount of money from the total amount or money Zuri has to spend.

Read the statement carefully, and apply the order of operations.
HintsRemember the meaning of these keywords.
Identify the operations mentioned in the statement: addition and multiplication.
According to the order of operations, you must perform the addition inside the parentheses first.
Solution First, we add twenty and ten to find the sum.
 Then, we multiply the sum by three.
 We write this process as a number sentence ( 20 + 10 ) × 3.
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