Writing Numerical Expressions
Do you want to learn faster and more easily?
Basics on the topic Writing Numerical Expressions
Writing Numerical Expressions – Introduction
Maths enthusiasts and curious learners, you're about to embark on an exciting journey to understand numerical expressions. Picture this: each numerical expression is a maths puzzle waiting for you to solve. It's not just about numbers; it's about the language of mathematics that helps us solve real-world 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 real-world 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 sofa, minding your own business, scrolling away when you see it. Someone has posted a riddle, 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 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. We can use BODMAS to help us remember the order of operations. B stands for brackets. O for orders, D is for division, M is multiplication, A is addition and S is subtraction. 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 brackets and an addition sign to show this. Based on the statement, what operation would we put between the brackets 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 thirty-six and n, divided by two. Here, thirty-six minus n is inside brackets and then we have divide by two. Let's apply what we've learnt 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 thirty-five 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 twenty-four, divided by three to the second power.' The correct numerical expression is B. To summarise, by writing and interpreting numerical expressions, we can improve our mathematical 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?
HintsAn expression does not solve the problem directly, but rather guides you in the order of operations needed to obtain a solution.
Think about how numerical expressions help break down complicated problems into smaller, more manageable parts.
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?
HintsIf we were solving this expression:
(2 x 3) + 4
We would start by solving (2 x 3). What is this part of the expression inside?
We multiply before we subtract or minus.
SolutionThe acronym which helps in remembering the order of operations in numerical expressions is BODMAS.
The acronym BODMAS stands for:
B - Brackets
O - Orders
D - Division
M - Multiplication
A - Addition
S - Subtraction
-
How would we solve this problem?
HintsRemember BODMAS, where do we start solving this expression?
BODMAS tells us to start with what is inside the brackets. Once this operation has been performed, move on the other parts of the expression.
SolutionThe order of operations is:
- Perform the multiplication operation inside the brackets.
- Replace the expression inside the brackets with its result.
- Perform the addition operation.
- The final result is 19. (5 x 3 = 15; 4 + 15 = 19)
-
Use order of operations to evaluate the expression.
HintsApply the order of operations acronym BODMAS to determine the correct sequence of operations.
There are no brackets or orders in this expression so start with division and work from there.
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 spent £3 each day. Therefore, part of the expression will be 7 x 3.
Zuri started with £25 and she spent money, that means an amount was subtracted. Look for an expression with a subtraction symbol in it.
SolutionThe correct answer is 25 − (7 × 3).
To write the expression, we need to calculate how much money Zuri spent during the week (7 x 3). This represents 7 days and 3 pounds spent on each day.
Then we need to subtract that amount of money from the total amount of money Zuri had to spend.
7 x 3 = 21
25 - 21 = 4
Zuri has £4 left.
-
Read the statement carefully, and apply the order of operations.
HintsThe sum of two numbers is the answer once they have been added together.
Identify the operations mentioned in the statement: addition and multiplication.
The statement says "the sum of twenty and ten" which is then multiplied by three so the sum of twenty and ten will be in brackets.
SolutionThe correct answer is (20 + 10) x 3
- First, we add twenty and ten to find the sum.
- Then, we multiply the sum by three.
- We write this process as an expression ( 20 + 10 ) × 3.
