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 - 1So, 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 -:
3 + 4 + 6 = 13
3 + 4 - 6 = 1
6 - (3 + 4) = -1
4 + 6 - 3 = 7
(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.
41 videos|316 docs|8 tests
|
1. What are arithmetic expressions and how are they used in mathematics? | ![]() |
2. How do you evaluate an arithmetic expression step by step? | ![]() |
3. What is the difference between an expression and an equation in mathematics? | ![]() |
4. Can you give an example of a simple arithmetic expression and its solution? | ![]() |
5. Why is it important to understand arithmetic expressions in everyday life? | ![]() |