Hello Champions!
Today, we are going to learn about "Arithmetic Expressions".
What is an Arithmetic Expression?
An arithmetic expression is just a math sentence that uses:
- Numbers \((1, 2, 3 ...)\) and
- Operations like addition \((+)\), subtraction \((-)\), multiplication \((\times)\) or division \((\div)\).
Let's Try Together!
I'll say a situation, and you tell me the expression!
1. You have \(7\) chocolates and get \(5\) more. What is the expression?
Ans: \(7 + 5\)
2. You share \(24\) pencils with \(4\) friends. What is the expression?
Ans: \(24 \div 4\)
Let's compare arithmetic expressions!
The signs used to compare two expressions:
- \(=\) if both sides are the same.
- \(>\) if the left side value is bigger.
- \(<\) if the right side value is bigger.
Example:
Compare \(4 + 7\) _______ \(5 \times 2\).
Solution: \(4 + 7 = 11\) and \(5 \times 2 = 10\)
Since \(11 > 10\), we get \(4 + 7 > 5 \times 2\).
Solution: \(4 + 7 = 11\) and \(5 \times 2 = 10\)
Since \(11 > 10\), we get \(4 + 7 > 5 \times 2\).
Terms in Expressions
Terms are parts of the expression separated by both ‘\(+\)’ and '\(-\)' signs.
In the expression \(10 + 7\), there are two terms present.
One is \(10\) and the other is \(7\).
What if there’s a minus sign?
Suppose the expression is \(30 - 8\).
Subtracting \(8\) from \(30\) is same as adding the opposite of \(8\).
So, \(30 - 8 = 30 + (-8)\).
Now, the terms are \(30\) and \(-8\).
What if there's a multiplication or division sign?
Suppose the expression is \(30 \times 2 + 5\).
The terms are \(30 \times 2\) and \(5\).
Note that \(30 \times 2\) is a single term as they do not have any '\(+\)' sign.
Removing Brackets
Let's look at this expression \(100 - (54 + 5)\).
Normally, we do this:
(i) Add inside the bracket: \(54 + 5 = 59\)
(ii) Then subtract: \(100 - 59 = 41\)
There is a another way to solve this.
You can remove the bracket by breaking it into two subtractions.
\(100 - (54 + 5) = 100 - 54 - 5 = 46 - 5 = 41\)
Answer is the same.
Important!
Magic Rule:
When there's a minus sign before a bracket "\(- (A + B)\)" turns into "\(- A - B\)" and "\(- (A - B)\)" turns into "\(- A + B\)".