NCERT Class 7 Ganita Prakash 1 Chapter 02 Arithmetic Expressions PDF Download

Chapter 2: Arithmetic Expressions

2.1 Simple Expressions

You may have seen mathematical phrases like \( 13 + 2 \), \( 20 - 4 \), \( 12 \times 5 \), and \( 18 \div 3 \). Such phrases are called arithmetic expressions.

Every arithmetic expression has a value which is the number it evaluates to. For example, the value of the expression \( 13 + 2 \) is 15. This expression can be read as '13 plus 2' or 'the sum of 13 and 2'.

We use the equality sign '=' to denote the relationship between an arithmetic expression and its value. For example:

\[ 13 + 2 = 15 \]

Mallika spends Rs. 25 every day for lunch at school. Write the expression for the total amount she spends on lunch in a week from Monday to Friday.

The expression for the total amount is \( 5 \times 25 \).

\( 5 \times 25 \) is "5 times 25" or "the product of 5 and 25".

Teacher's Note

Notice that the expression \( 5 \times 25 \) directly answers the problem: 5 days times 25 rupees per day. When you write an expression from a word problem, make sure each part of the expression represents something real from the situation. This helps you check if your expression makes sense before you even calculate its value.

Different expressions can have the same value. Here are multiple ways to express the number 12, using two numbers and any of the four operations \( + \), \( - \), \( \times \) and \( \div \):

\( 10 + 2 \), \( 15 - 3 \), \( 3 \times 4 \), \( 24 \div 2 \).

Choose your favourite number and write as many expressions as you can having that value.

Comparing Expressions

As we compare numbers using '=', '<' and '>' signs, we can also compare expressions. We compare expressions based on their values and write the 'equal to', 'greater than' or 'less than' sign accordingly. For example,

\[ 10 + 2 > 7 + 1 \]

because the value of \( 10 + 2 = 12 \) is greater than the value of \( 7 + 1 = 8 \). Similarly,

\[ 13 - 2 < 4 \times 3 \]

Figure it Out

1. Fill in the blanks to make the expressions equal on both sides of the = sign:
   1. \( 13 + 4 = \) ____ \( + 6 \)
   2. \( 22 + \) ____ \( = 6 \times 5 \)
   3. \( 8 \times \) ____ \( = 64 \div 2 \)
   4. \( 34 - \) ____ \( = 25 \)
2. Arrange the following expressions in ascending (increasing) order of their values.
   1. \( 67 - 19 \)
   2. \( 67 - 20 \)
   3. \( 35 + 25 \)
   4. \( 5 \times 11 \)
   5. \( 120 \div 3 \)

Which is greater? \( 1023 + 125 \) or \( 1022 + 128 \)?

Imagining a situation could help us answer this without finding the values. Raja had 1023 marbles and got 125 more today. Now he has \( 1023 + 125 \) marbles. Joy had 1022 marbles and got 128 more today. Now he has \( 1022 + 128 \) marbles. Who has more?

This situation can be represented as shown in the picture on the right. To begin with, Raja had 1 more marble than Joy. But Joy got 3 more marbles than Raja today. We can see that Joy has (two) more marbles than Raja now.

That is,

\[ 1023 + 125 < 1022 + 128 \]

Which is greater? \( 113 - 25 \) or \( 112 - 24 \)?

Imagine a situation, Raja had 113 marbles and lost 25 of them. He has \( 113 - 25 \) marbles. Joy had 112 marbles and lost 24 today. He has \( 112 - 24 \) marbles. Who has more marbles left with them?

Raja had 1 marble more than Joy. But he also lost 1 marble more than Joy did. Therefore, they have an equal number of marbles now.

That is,

\[ 113 - 25 = 112 - 24 \]

Teacher's Note

When comparing expressions, you do not always need to calculate the exact values. Look at what changes from one expression to the other. In Example 2, one person started with 1 less but received 3 more, so the net change is +2. This reasoning is faster and less error-prone than computing both sums separately, especially with large numbers.

Use '>' or '<' or '=' in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case.

1. \( 245 + 289 \) ____ \( 246 + 285 \)
2. \( 273 - 145 \) ____ \( 272 - 144 \)
3. \( 364 + 587 \) ____ \( 363 + 589 \)
4. \( 124 + 245 \) ____ \( 129 + 245 \)
5. \( 213 - 77 \) ____ \( 214 - 76 \)

2.2 Reading and Evaluating Complex Expressions

Sometimes, when an expression is not accompanied by a context, there can be more than one way of evaluating its value. In such cases, we need some tools and rules to specify how exactly the expression has to be evaluated.

To give an example with language, look at the following sentences:

1. Sentence: "Shalini sat next to a friend with toys".
   Meaning: The friend has toys and Shalini sat next to her.
2. Sentence: "Shalini sat next to a friend, with toys".
   Meaning: Shalini has the toys and she sat with them next to her friend.

This sentence without the punctuation could have been interpreted in two different ways. The appropriate use of a comma specifies how the sentence has to be understood.

Let us see an expression that can be evaluated in more than one way.

Mallesh brought 30 marbles to the playground. Arun brought 5 bags of marbles with 4 marbles in each bag. How many marbles did Mallesh and Arun bring to the playground?

Mallesh summarized this by writing the mathematical expression - \( 30 + 5 \times 4 \).

Key Points

• An arithmetic expression is a mathematical phrase using numbers and operations like addition, subtraction, multiplication and division. Each expression has a value that we can find by evaluating it.
• We compare expressions by finding their values first, then using the symbols =, > or < to show which is greater, equal or less.
• Different expressions can have the same value. When comparing two expressions, you can sometimes avoid calculating the exact values by thinking about how the numbers change from one expression to the other.
• When an expression could be understood in more than one way, we need rules to specify exactly how to evaluate it, just as punctuation clarifies the meaning of a sentence.

This is a preview of the first 3 pages. To get the complete chapter, click below.