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Important Questions: Arithmetic Expressions | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Q1: Fill in the blanks to make the expressions equal on both sides of the = sign:
a) 19 + 7 = ____ + 9
b) 5 × 6 = 36 - ____

Sol:
a) 19 + 7 = 26, 
so 17 + 9 = 26. 
The blank is 17.
b) 5 × 6 = 30, 
so 36 - 6 = 30. 
The blank is 6.

Q2: Which is greater: 345 + 128 or 344 + 130? Explain your reasoning without calculating the exact sums.

Sol: Let's compare the two expressions logically:

  • 345 + 128

  • 344 + 130

Now, observe:

  • 345 is 1 more than 344

  • 128 is 2 less than 130

So overall, the first expression increases by 1 but decreases by 2.

That means:
345 + 128 = (344 + 1) + (130 - 2) = 344 + 130 - 1

So, 345 + 128 is 1 less than 344 + 130

Q3: Compare the expressions 156 - 42 and 155 - 41 using ‘>’, ‘<’, or ‘=’. Explain your reasoning.

Sol: Let's compare the two expressions without solving them directly:

  • 156 - 42

  • 155 - 41

Now observe:

  • 156 is 1 more than 155

  • But 42 is also 1 more than 41

So both the increase and the decrease are equal — they cancel each other out.
Therefore, 156 - 42 = 155 - 41

Q4: Identify the terms in the expression 45 - 3 × 8 + 12. Rewrite the expression using the inverse of subtraction and evaluate it.

Sol: Terms: 45, -3 × 8, 12.
Rewrite subtraction as adding the inverse: 45 + (-3 × 8) + 12.
Evaluate: 45 + (-24) + 12 = 45 - 24 + 12 = 21 + 12 = 33.
Ans: 33.

Q5: Add brackets to the expression 28 - 6 + 4 to get a value of 26. Evaluate to confirm.

Sol: To get 26, group the subtraction first: (28 - 6) + 4.
Evaluate: (28 - 6) + 4 = 22 + 4 = 26.

Q6: Remove brackets from the expression 19 + (7 - 3) to get an equivalent expression without changing the value.

Sol: 19 + (7 - 3) = 19 + 7 - 3.

Q7: A school organizes a picnic where each student pays ₹50 for food and ₹20 for transport. Write an expression for the total cost for 5 students, find the value.

Sol: Expression: 5 × (50 + 20).
Value: 5 × (50 + 20) = 5 × 70 = 350. Total cost is ₹350.

Q8: In a game, 28 students form groups of 6. Write an expression to represent the number of students in full groups and those left out. Identify the terms and find the value.

Sol: 28 ÷ 6 = 4 groups with 4 left (28 - 24 = 4).
Expression: 4 × 6 + 4.
Terms: 4 × 6, 4.
Value: 4 × 6 + 4 = 24 + 4 = 28 students.

Q9: Given 42 × 15 = 630, find 52 × 15 using the distributive property.

Sol: Write 52 as (42 + 10):
52 × 15 = (42 + 10) × 15 = 42 × 15 + 10 × 15 = 630 + 150 = 780.
So, 52 × 15 = 780.

Q10: Fill in the blank to make the expressions equal: 7 × (4 + 9) = 7 × 4 + ____.

Sol: Using the distributive property: 7 × (4 + 9) = 7 × 4 + 7 × 9.
The blank is 7 × 9.

Q11: Compare the expressions 64 × (12 - 5) and 64 × 12 - 64 × 5 using ‘=’, ‘>’, or ‘<’. Explain using the distributive property.

Sol: Left side: 64 × (12 - 5) = 64 × 7.
Right side: 64 × 12 - 64 × 5 = 64 × (12 - 5) = 64 × 7 (distributive property).
So, 64 × (12 - 5) = 64 × 12 - 64 × 5.

Q12: Compare 72 + 19 × 25 and (72 + 19) × 25 using ‘<’, ‘>’, or ‘=’. Explain without full computation.
Sol: Left side: 72 + 19 × 25 (multiplication first, then addition).
Right side: (72 + 19) × 25 = 91 × 25 (addition first, then multiplication).
Since 19 × 25 is multiplied by 1 in the left side but by 91 in the right side, the right side is much larger.
So, 72 + 19 × 25 < (72 + 19) × 25.

Q13: Using the numbers 3, 4, and 6, and the operators ‘+’ and ‘-’, with brackets as necessary, generate expressions to produce at least five different values.

Sol: Using 3, 4, 6 with + and -:

  1. 3 + 4 + 6 = 13

  2. 3 + 4 - 6 = 1

  3. 6 - (3 + 4) = -1

  4. 4 + 6 - 3 = 7

  5. (6 + 4) - 3 = 7

Q14: A shop sells 3 pens for ₹10 each and 2 notebooks for ₹15 each. Write two different expressions for the total cost, identify their terms, and find the value.

Sol: First way: 3 × 10 + 2 × 15.
Terms: 3 × 10, 2 × 15.
Value: 30 + 30 = 60.
Second way: (3 × 10 + 15) + 15.
Terms: (3 × 10 + 15), 15.
Value: (30 + 15) + 15 = 45 + 15 = 60.
Total cost is ₹60.

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FAQs on Important Questions: Arithmetic Expressions - Mathematics (Ganita Prakash) Class 7 - New NCERT

1. What are arithmetic expressions and how are they used in mathematics?
Ans. Arithmetic expressions are combinations of numbers, variables, and operators (such as +, -, *, /) that represent a value. They are fundamental in mathematics as they allow us to perform calculations and solve problems. For example, the expression 3 + 5 represents the sum of 3 and 5, which equals 8.
2. How do you evaluate an arithmetic expression step by step?
Ans. To evaluate an arithmetic expression, follow these steps: 1. Identify the numbers and operators in the expression. 2. Follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 3. Perform the calculations in the correct order. For example, in the expression 2 + 3 * 4, you first multiply 3 and 4 to get 12, then add 2 to get 14.
3. What is the difference between an expression and an equation in mathematics?
Ans. An expression is a combination of numbers, variables, and operators that represents a value, while an equation is a statement that two expressions are equal, indicated by the equal sign (=). For example, 2 + 3 is an expression, whereas 2 + 3 = 5 is an equation that states that the expression on the left equals the expression on the right.
4. Can you give an example of a simple arithmetic expression and its solution?
Ans. Yes, a simple arithmetic expression is 7 - 2 + 5. To solve it, first subtract 2 from 7, which gives you 5. Then add 5 to that result: 5 + 5 equals 10. Therefore, the solution to the expression 7 - 2 + 5 is 10.
5. Why is it important to understand arithmetic expressions in everyday life?
Ans. Understanding arithmetic expressions is crucial in everyday life as they help us perform basic calculations such as budgeting, cooking measurements, and shopping discounts. For instance, if you want to calculate the total cost of items or how much money you save from a discount, you rely on arithmetic expressions to find accurate answers quickly and efficiently.
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