CBSE Class 7 Mathematics Arithmetic Expressions MCQs Set 11

Answer: (c) value

Explanation:
1. When we work out an arithmetic expression we get exactly one number.
2. That number is called the value of the expression.
3. For example, 13 + 2 works out to 15, so the value of 13 + 2 is 15.

Teacher's Note:
1. Expression = the recipe; value = the final dish.
2. Every expression has just one value.

Answer: (d) the product of 5 and 25

Explanation:
1. The sign × means multiplication.
2. So 5 × 25 is read as “5 times 25” or “the product of 5 and 25”.
3. “Sum” and “more than” describe addition, and “less than” describes subtraction.

Teacher's Note:
1. Sum goes with +, difference with −, product with ×.
2. Reading expressions aloud builds the right habit.

Answer: (c) +

Explanation:
1. Terms are the parts of an expression that are separated by a + sign.
2. Any subtraction is first changed into adding the inverse, e.g. 9 − 4 = 9 + (−4).
3. After this change, every term is separated from the next by a + sign.

Teacher's Note:
1. × and ÷ stay inside a term; they never split it.
2. Turn every − into + (inverse) before listing terms.

Answer: (b) 83 and −14

Explanation:
1. Taking away 14 is the same as adding −14.
2. So 83 − 14 = 83 + (−14).
3. The terms are 83 and −14; the minus sign goes along with 14.

Teacher's Note:
1. The sign in front of a number belongs to that term.
2. 83 has no sign in front, so it is positive.

Answer: (a) the expression inside the brackets

Explanation:
1. A bracket shows the part of the expression that must be worked out first.
2. So we first find the expression inside the brackets.
3. Example: 30 + (5 × 4) = 30 + 20 = 50.

Teacher's Note:
1. Brackets always come first.
2. Then carry on with the rest of the expression.

Answer: (d) 50

Explanation:
1. Work out the bracket first: 5 × 4 = 20.
2. Then add: 30 + 20 = 50.
3. Adding 30 and 5 first would give 35 × 4 = 140, which is wrong.

Teacher's Note:
1. The bracket tells you the order.
2. 140 is the trap answer for those who go left to right.

Answer: (b) >

Explanation:
1. Compare the right side with the left side number by number.
2. The first number goes up by 1 (318 → 319) but the second goes down by 2 (476 → 474).
3. So the right side is 1 less than the left side: 794 and 793.
4. Hence 318 + 476 > 319 + 474.

Teacher's Note:
1. Track how much each number changes.
2. A gain of 1 and a loss of 2 means a net loss of 1.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. 13 + 2 works out to 15, so A is true.
2. R gives the correct meaning of the word “value”, so R is true.
3. A is true exactly because 15 is the number that 13 + 2 evaluates to, so R explains A.

Teacher's Note:
1. R is the definition and A is an example of it.
2. A definition explains its own example.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Terms are separated only by + signs. There is no + inside 6 × 5, so it is one term. A is true.
2. R is also true: for example 10 + 2 and 3 × 4 both equal 12.
3. But R talks about values, not about terms, so it does not explain A.

Teacher's Note:
1. Both statements can be true and still be unrelated.
2. Ask: does R give the reason for A?

Answer: (c) Both Statement I and Statement II are true

Explanation:
1. Statement I: 10 + 2, 15 − 3 and 3 × 4 all have the value 12. True.
2. Statement II: a bracket marks the part to be worked out first. True.
3. So both statements are true.

Teacher's Note:
1. Test each statement with a quick example.
2. Many expressions can share one value.

Answer: (a) (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)

Explanation:
1. 7 + 5 = 12 → (q); 20 − 6 = 14 → (r).
2. 3 × 5 = 15 → (s); 36 ÷ 4 = 9 → (p).
3. So the matching is (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p).

Teacher's Note:
1. Find each value, then match.
2. One correct pair often rules out wrong options quickly.

Answer: (b) 3 × 4 + 2

Explanation:
1. There are 3 rows with 4 dots in each row: 3 × 4 = 12 dots.
2. There are 2 more dots kept aside.
3. Total = 3 × 4 + 2 = 12 + 2 = 14 dots.

Teacher's Note:
1. Equal rows mean multiplication.
2. The extra dots are simply added on.

Answer: (c) 23 + (−2 × 4) + 16

Explanation:
1. Change the subtraction into adding the inverse: − 2 × 4 becomes + (−2 × 4).
2. So 23 − 2 × 4 + 16 = 23 + (−2 × 4) + 16.
3. The terms are 23, −2 × 4 and 16, and the value is 23 − 8 + 16 = 31.

Teacher's Note:
1. The product 2 × 4 stays together as one term.
2. The minus sign moves with the term.

Answer: (a) 35 − 18 + 6

Explanation:
1. The bracket has a minus sign in front of it, so every term inside changes its sign.
2. +18 becomes −18 and −6 becomes +6: 35 − (18 − 6) = 35 − 18 + 6.
3. Check: 35 − 12 = 23 and 35 − 18 + 6 = 23.

Teacher's Note:
1. Minus before a bracket flips every sign inside.
2. Always check with the actual values.

Answer: (d) 7 × 20 + 7 × 3

Explanation:
1. By the distributive property, the multiple of a sum is the sum of the multiples.
2. So 7 × (20 + 3) = 7 × 20 + 7 × 3.
3. Value: 140 + 21 = 161, which equals 7 × 23.

Teacher's Note:
1. Multiply 7 with each term in the bracket.
2. Option (a) forgets to multiply the 3.

Answer: (b) 23

Explanation:
1. The terms are 50, −12 × 3 and 18 ÷ 2.
2. Evaluate each term: −12 × 3 = −36 and 18 ÷ 2 = 9.
3. Add the terms: 50 − 36 + 9 = 23.

Teacher's Note:
1. Evaluate each term first, then add.
2. Do not work strictly left to right.

Answer: (c) ₹500

Explanation:
1. Cost for adults = 3 × 120 = 360.
2. Cost for children = 2 × 70 = 140.
3. Total = 3 × 120 + 2 × 70 = 360 + 140 = ₹500.

Teacher's Note:
1. Each kind of ticket gives one term.
2. ₹190 is the cost of just one adult and one child.

Answer: (c) A is true, but R is false.

Explanation:
1. A is true: addition of terms is commutative and associative, so any order gives the same value.
2. The terms of 20 − 4 are 20 and −4. Swapping them gives −4 + 20 = 16, not 4 − 20 (which is −16).
3. So R is false.

Teacher's Note:
1. The minus sign must move with its number.
2. Swapping 20 − 4 to 4 − 20 is a common mistake.

Answer: (d) A is false, but R is true.

Explanation:
1. 5 × 4 + 3 = 20 + 3 = 23, but 5 × (4 + 3) = 5 × 7 = 35. So A is false.
2. In 5 × 4 + 3 the parts separated by + are 5 × 4 and 3, so R is true.

Teacher's Note:
1. A bracket can change the value.
2. Find both values before judging A.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. ((−7) + 10) + (−11) = 3 + (−11) = −8 and (−7) + (10 + (−11)) = (−7) + (−1) = −8.
2. So A is true. R is the associative property, which is true.
3. A happens exactly because addition is associative, so R explains A.

Teacher's Note:
1. Associative = grouping does not matter.
2. It works for negative terms too.

Answer: (b) Only Statement II is true

Explanation:
1. Statement I: (16 − 8) − 3 = 8 − 3 = 5, but 16 − (8 − 3) = 16 − 5 = 11. False.
2. Statement II: 27 − (18 + 4) = 27 − 22 = 5 and 27 + (−18 − 4) = 27 + (−22) = 5. True.
3. So only Statement II is true.

Teacher's Note:
1. Subtraction is not associative.
2. Both expressions in II have the terms 27, −18 and −4.

Answer: (a) Only Statement I is true

Explanation:
1. Statement I: 4 × 23 is one term and 5 is the other. True.
2. Statement II: by the associative property, grouping the terms differently never changes the value. False.
3. So only Statement I is true.

Teacher's Note:
1. A product counts as one term.
2. Grouping terms never changes a sum.

Answer: (b) (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)

Explanation:
1. A bracket after + keeps the signs: 20 + (8 − 5) = 20 + 8 − 5 → (q).
2. A bracket after − flips every sign inside: 20 − (8 + 5) = 20 − 8 − 5 → (r); 20 − (8 − 5) = 20 − 8 + 5 → (p).
3. 20 − (−8 − 5) = 20 + 8 + 5 → (s). So the answer is (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s).

Teacher's Note:
1. Look at the sign just before the bracket.
2. Values 23, 7, 17 and 33 confirm the matching.

Answer: (a) 4 × 6 + 3 × 6 = (4 + 3) × 6

Explanation:
1. Counting the two groups separately: 4 × 6 scouts + 3 × 6 guides = 24 + 18 = 42.
2. Counting all rows together: (4 + 3) rows of 6 = 7 × 6 = 42.
3. So the picture shows 4 × 6 + 3 × 6 = (4 + 3) × 6.

Teacher's Note:
1. Same picture, two ways of counting.
2. This is the distributive property.

Answer: (d) 92 − (45 − 17)

Explanation:
1. 92 − 45 − 17 = 30 (terms 92, −45, −17).
2. (a) both numbers up by 1: 30; (b) same terms in another order: 30; (c) 92 − 62 = 30.
3. (d) 92 − (45 − 17) = 92 − 45 + 17 = 64, which is different. So the answer is (d).

Teacher's Note:
1. Look for the option where a sign changes.
2. A minus before a bracket flips −17 into +17.

Answer: (c) 1368

Explanation:
1. 57 = 47 + 10, so 57 × 24 = (47 + 10) × 24.
2. = 47 × 24 + 10 × 24 = 1128 + 240.
3. = 1368.

Teacher's Note:
1. Ten more groups of 24 means 240 more.
2. Use what is given; no long multiplication needed.

Answer: (d) A is false, but R is true.

Explanation:
1. (8 − 3) × 29 = 5 × 29 = 145 and (3 − 8) × 29 = −5 × 29 = −145.
2. 145 is greater than −145, so A is false.
3. 8 − 3 = 5 and 3 − 8 = −5 are inverses, so R is true.

Teacher's Note:
1. Swapping the numbers in a subtraction gives the inverse.
2. A positive number is greater than a negative one.

Answer: (a) Only Statement I is true

Explanation:
1. The innermost bracket is always worked out first, so Statement I is true.
2. 15 + 5 = 20, then 40 − 20 = 20, then 120 − 20 = 100.
3. The value is 100, not 60, so Statement II is false. Only Statement I is true.

Teacher's Note:
1. Work from the inside out.
2. 60 comes from wrongly doing 120 − 40 − 20.

Answer: (c) (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)

Explanation:
1. 18 + (−5) = −5 + 18 swaps two terms: commutative → (i)-(q).
2. (6 + 2) + 9 = 6 + (2 + 9) changes the grouping: associative → (ii)-(r).
3. 9 × (7 + 4) = 9 × 7 + 9 × 4 shares the multiplier: distributive → (iii)-(p); 30 − (8 + 7) = 30 − 8 − 7 flips the signs → (iv)-(s).
4. Answer: (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s).

Teacher's Note:
1. Swap = commutative; regroup = associative.
2. Multiplier shared over a bracket = distributive.

Answer: (d) 500 − (4 × 45 + 5 × 12 + 3 × 6)

Explanation:
1. The whole bill is 4 × 45 + 5 × 12 + 3 × 6 = 180 + 60 + 18 = 258.
2. The entire bill must be taken away from 500, so it goes inside a bracket after the minus sign.
3. Change = 500 − (4 × 45 + 5 × 12 + 3 × 6) = 500 − 258 = ₹242.

Teacher's Note:
1. Every item's cost must be subtracted.
2. The other options add some costs instead of subtracting them.