Class 7 Maths Ganita Prakash Part 1 Chapter 2 MCQs – Arithmetic Expressions

There are five days from Monday to Friday.
Total expenditure = 5 × 25 = ₹125
The expression means five equal amounts of ₹25. It does not include Saturday or Sunday, so multiplying by seven would count two extra days.

The right side has value 64 ÷ 2 = 32. The left side must have the same value.
8 × □ = 32
□ = 32 ÷ 8 = 4
Checking gives 8 × 4 = 64 ÷ 2 = 32.

The first addend decreases by 1, but the second addend increases by 3.
Net change in the sum = −1 + 3 = 2
Therefore, 1,022 + 128 is greater by 2. This comparison can be made without calculating either full sum.

In 272 − 144, both the starting number and the number subtracted are one less. These changes cancel.
273 − 145 = 128
272 − 144 = 128
Subtracting the same amount from both numbers in a difference leaves that difference unchanged.

The values are:
120 ÷ 3 = 40
67 − 20 = 47
67 − 19 = 48
5 × 11 = 55
Since 40 < 47 < 48 < 55, the expression 120 ÷ 3 has the smallest value.

The expression has the terms 30 and 5 × 4. The product is evaluated before the terms are added.
30 + 5 × 4 = 30 + 20 = 50
Adding 30 and 5 first would instead evaluate the different expression (30 + 5) × 4.

Subtracting 2 × 4 is the same as adding its negative.
23 − 2 × 4 + 16 = 23 + (−2 × 4) + 16
The terms are 23, −2 × 4 and 16. The multiplication stays within one term, and its negative sign is retained.

I first evaluate the multiplication and division within the terms.
48 − 10 × 2 + 16 ÷ 2
= 48 − 20 + 8
= 36
The negative term is −20, so it is subtracted before the remaining 8 is added.

The two terms, −4 and 6, exchange positions while keeping their signs. Their sum remains 2. This is the commutative property of addition. The associative property concerns changing grouping, whereas this equality changes only the order of the terms.

The negative terms can be grouped together without changing the sum.
(−7) + 10 + (−11) = (−7 − 11) + 10
= −18 + 10
= −8
The total negative amount is 18, which is 8 more than the positive amount 10.

The two costs are added before subtracting them from the money paid.
Total cost = 15 + 56 = ₹71
Change = 100 − (15 + 56) = 100 − 71 = ₹29
Both purchases reduce the amount returned to Irfan.

Cost of seven dosas = 7 × 23 = ₹161
Total with the tip = 161 + 5 = ₹166
The tip is added once because it is for the whole group. Multiplying 23 + 5 by seven would count seven tips.

33 = 8 × 4 + 1
Eight complete groups use 32 students, leaving one student. Nine complete groups would require 36 students, which is three more than available. The remainder is smaller than the group size of 4, so no further complete group can be formed.

Number of new packets = 100 ÷ 2 = 50
Total packets = 4 + 50 = 54
The original four packets are already packed, so they are added after dividing the new rice into packets. The expression is 4 + (100 ÷ 2).

Adult tickets cost 4 × 40 = ₹160. Child tickets cost 3 × 20 = ₹60.
Total cost = 4 × 40 + 3 × 20
= 160 + 60 = ₹220
The two ticket types have different prices, so their costs are calculated separately.

Subtracting the whole sum means subtracting both 40 and 3.
200 − (40 + 3) = 200 − 40 − 3
= 160 − 3 = 157
Keeping +3 after removing the brackets would add back an amount that should have been subtracted.

The value inside the brackets is 250 − 100 = 150.
500 − (250 − 100) = 500 − 150 = 350
Equivalently, removing the brackets gives 500 − 250 + 100. The minus before the brackets changes both signs inside.

Inside the brackets, −12 − 10 = −22. Subtracting −22 adds 22.
14 − (−12 − 10) = 14 + 12 + 10 = 36
Both negative terms change to positive terms when the brackets preceded by a minus are removed.

The starting number increases from 207 to 210, an increase of 3. To keep the difference unchanged, the number subtracted must also increase by 3.
68 + 3 = 71
Check: 207 − 68 = 139 and 210 − 71 = 139.

The sum 9 + 12 is 21, and 34 − 21 = 13.
34 − (9 + 12) = 13
The brackets make the entire sum 9 + 12 the quantity being subtracted. Grouping only 34 − 9 would leave the original value 37.

Each friend spends 43 + 24 = ₹67.
Total bill = 3 × (43 + 24)
= 3 × 43 + 3 × 24
= 129 + 72 = ₹201
The factor 3 applies to both items because all three friends buy both.

There are four groups of 5 and three more groups of 5. Together, these make seven groups of 5.
4 × 5 + 3 × 5 = (4 + 3) × 5 = 35
The common factor 5 can be taken outside the sum.

The factor 63 is 10 more than 53, so the product gains ten groups of 18.
63 × 18 = 53 × 18 + 10 × 18
= 954 + 180
= 1,134
The increase is 180, not just 10.

I use 97 = 100 − 3 to make the multiplication easier.
97 × 25 = (100 − 3) × 25
= 100 × 25 − 3 × 25
= 2,500 − 75
= 2,425

In the second sum, 42 increases by 1 while 16 decreases by 1. The total stays unchanged.
42 + 16 = 58
43 + 15 = 58
Both expressions therefore equal 25 × 58, so neither product is greater.

Monthly expenses = 5,000 + 5,000 + 2,000 = ₹12,000
Monthly saving = 20,000 − 12,000 = ₹8,000
Saving in 12 months = 12 × 8,000 = ₹96,000
The yearly saving is the monthly amount left over multiplied by twelve.

Each completed day and night gives a net rise of 3 − 2 = 1 cm. After seven nights, the snail is 7 cm high.
On day 8: 7 + 3 = 10 cm
It reaches the top before another night, so no final slip is counted.

Reading days each week = 7 − 2 = 5
Stories in 8 weeks = 5 × 8 = 40
Each reading day contributes one story. The two pages in a story affect the page count, but they do not double the number of stories.

The terms can be grouped in consecutive pairs.
(1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + (9 − 10)
= −1 − 1 − 1 − 1 − 1
= −5
Each pair contributes the same value, −1.

The product and quotient are evaluated before adding.
4 × 4 + 4 ÷ 4 = 16 + 1 = 17
The expression uses exactly four occurrences of 4. The other expressions have values 3, 16 and 5, so they do not give 17.

The value of an arithmetic expression is found by performing the indicated operation. Here, 13 plus 2 equals 15. Therefore, the value of 13 + 2 is 15 which is the number the expression evaluates to.

In arithmetic expressions without brackets, multiplication is done before addition. Therefore, in 30 + 5 × 4, we first evaluate 5 × 4 which is 20 and then add 30 to get 50.

The expression 6 × 2 equals 12. All other options do not evaluate to 12. Expressions like 3 × 4 or 24 ÷ 2 also yield 12 as value. So 6 × 2 is a valid option here.

The phrase “five times twenty-five” refers to multiplication. So the correct expression is 5 × 25. Multiplication is commonly used to represent repeated addition or total quantity for equal parts.

According to order of operations, evaluate the bracket first. 15 + 56 = 71. Then subtract from 100. So, 100 – 71 = 29. Hence, the value of the expression is 29.

When removing brackets preceded by a minus sign, we change the sign of each term inside. So 200 – (40 + 3) becomes 200 – 40 – 3 which is 157.

Though 1023 is greater than 1022, the second expression adds 3 more. So overall, 1022 + 128 is greater than 1023 + 125. Joy has two more marbles than Raja.

113 – 25 = 88, and 112 – 24 = 88. But both lost one more or less than the other, balancing the value to the same amount. Hence, they are equal.

According to distributive property, multiplying a number with a sum is equal to multiplying the number with each term. So, 2 × (43 + 24) = 2 × 43 + 2 × 24.

Twice of a total is represented by multiplying 2 with the entire sum. So, we use brackets to show grouping: 2 × (43 + 24). This ensures correct evaluation of the expression.

The commutative property states that changing the order of terms in addition does not affect the result. Therefore, 10 + 2 is equal to 2 + 10 by this property.

First evaluate the bracket: 14 – 6 = 8. Then multiply by 10. So, (14 – 6) × 10 = 8 × 10 = 80. This uses the order of operations correctly.

When removing brackets preceded by a minus sign, the signs of the terms inside change. 500 – (250 – 100) becomes 500 – 250 + 100 which gives the same value.

By distributive property, 5 × (4 + 3) = 5 × 4 + 5 × 3. The multiplication is distributed across the addition inside the bracket to yield the same result.

Terms in an expression are separated by a + sign. Subtraction is converted into addition of the inverse for term identification. For example, 13 – 2 + 6 has terms 13, –2 and 6.

Brackets are evaluated first. Inside the brackets, 3 + 2 is done first giving 5, then multiplied by 6 to get 30. So the correct first step is 3 + 2.

5 × 2 = 10, then add 3. So the expression equals 13. It represents three more than 5 times 2. Hence, 10 + 3 is the same as 5 × 2 + 3.

83 – 14 can be written as 83 + (–14). So, the terms are 83 and –14. We convert subtraction into addition of the inverse to identify terms correctly.

Cost of 4 dosas = 4 × 23 = ₹92. Add ₹5 as tip. Total = ₹97. So the expression 4 × 23 + 5 describes the situation correctly and yields the total.

(4 + 3) × 5 means total of 4 and 3 rows, each with 5 children. So total is 7 × 5 = 35. It combines both groups first, then multiplies by the number in each row.