CBSE Class 7 Mathematics Integers Worksheet Set 07

Question. Find the value of 16 + 8 4 – 2 × 3.
Answer : 12

Question. Determine the integer whose product with (–7) is 154.
Answer : –22

Question. Subtract (–56) from 144.
Answer : 200

Question. Find the product of 2 × (–27) × 15.
Answer : –810

Question. Evaluate : (–1) × (–2) × (–3) × (–4) × (–5).
Answer : –120

Question. What will be the product of (–53) and (18).
Answer : –954

Question. Find the value of 625 × (–2) + (–625) × 98.
Answer : –62500

Question. What will be the value of a if a × (–2) = (–30)?
Answer : 15

Question. Determine the integer when it is divided by (–17), the answer is 21.
Answer : –357

Question. Determine the integer whose product by –3 become zero.
Answer : 0

Question. Find the product of (–45) × 55 × (–10).
Answer : 24750

Question. What will be the quotient if 369 is divided by (–1)?
Answer : –369

Question. Find the remainder if (–269) is divided by 269.
Answer : 0

Question. What will be the quotient if (–15625) is divided by (–125) ?
Answer : 125

Question. An elevator descends into a mine shaft at the rate of 7 m/min. If it starts from 5 m above the ground level. How long will it take to reach 205 m down the earth?
Answer : 30 min.

Question. What will be the value of P if P × (–8) = 120?
Answer : –15

Question. A diver dives in the sea 270 m down. If the speed of diver is 3m/sec. How long will he take?
Answer : 90 sec.

Question. Simplify : {–13 – (–27)} + {–25 – (–40)}
Answer : 29

Question. Simplify : (–20) + (–8) (–2) × 3.
Answer : –8

Question. At Srinagar, temperature was –7°C on Tuesday and then it dropped by 2°C on Wednesday. What was the temperature of Srinagar on Wednesday
Answer : –9°C.

Question. Product of two integers is 630. If one integer is –30, find the other.
Answer : –21

Question. Determine the integer whose product with (–13) is –325.
Answer : 25

Question. Simplify : (|–17| + |17|) |–2|.
Answer : 17

Question. A man drives his car at the speed of 40 km/hr. How long will it take to cover 160 km?
Answer : 4 hours

Question. In a class test containing 10 questions, 5 marks are awarded for every correct answer and (–2) marks are awarded for every incorrect answer. Mohan gets 4 correct and 6 incorrect answers. What is his score?
Answer :  8
 

Multiple Choice Questions

Question 1. Sum of two negative number is always
(a)Positive
(b) Negative
(c) 0
(d) 1
Answer: (b) Negative
In simple words: When you add two negative numbers together, the final answer will always be negative.

Exam Tip: Remember that adding integers with the same sign always keeps that same sign in the final result.

Question 2. Which of the following statement is false:
(a) - 7 + ( - 6 ) = - 13
(b) - 5 + 1 = 4
(c) 2 + (- 1 ) = 1
(d) 8 + (- 9 ) = 1
Answer: (b) - 5 + 1 = 4
In simple words: Adding 1 to -5 gives -4, not 4, so this statement is incorrect.

Exam Tip: Be careful with signs. When adding a positive and a negative number, subtract the smaller value from the larger one and use the sign of the larger value.

Question 3. What integers or number should be added to - 5 to get 4
(a) 1
(b) - 1
(c) - 9
(d) 9
Answer: (d) 9
In simple words: To reach 4 from -5, you must count up by 9 steps.

Exam Tip: Set up a simple equation like \( -5 + x = 4 \) to solve these problems without making quick mistakes.

Question 4. Predecessor of -9 is
(a) - 8
(b) 8
(c) - 10
(d) 10
Answer: (c) - 10
In simple words: The predecessor is the number that is one step to the left on a number line, which is -10.

Exam Tip: For negative integers, the predecessor is always more negative, which means you subtract 1 from the number.

Question 5. Identify the property used in the following: 2 * 13 + 8 * 13 = (2 + 8) * 13
(a)Commutative
(b) Closure
(c) Associative
(d) Distributive
Answer: (d) Distributive
In simple words: This property lets you group numbers that are being multiplied by the same value.

Exam Tip: When you see a single number multiplied by a sum, it is always the distributive property.

Question 6. Which number is multiplicative identity for the whole numbers
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1
In simple words: Multiplying any whole number by 1 does not change its value.

Exam Tip: Do not confuse the multiplicative identity (which is 1) with the additive identity (which is 0).

Question 7. What will be multiplicative inverse of - 8
(a) 8
(b) \( \frac{1}{8} \)
(c) - \( \frac{1}{8} \)
(d) 0
Answer: (c) - \( \frac{1}{8} \)
In simple words: The multiplicative inverse is the flipped version of the number, keeping the same negative sign.

Exam Tip: The sign of a number never changes when you find its multiplicative inverse. Just turn the integer into its reciprocal fraction.

Question 8. Which property is reflected in the following: 7 * 5 = 5 * 7
(a)Closure
(b) Commutative
(c) Associative
(d) Distributive
Answer: (b) Commutative
In simple words: This rule means you can multiply two numbers in any order and still get the same result.

Exam Tip: Look for a simple swap in the order of two numbers to identify the commutative property.

Question 9. 0 / 10 gives
(a) 0
(b) 10
(c) 1
(d) - 10
Answer: (a) 0
In simple words: If you share zero things among ten people, everyone gets nothing.

Exam Tip: Zero divided by any non-zero number is always zero. However, dividing a number by zero is not possible.

Question 10. ( -50 ) / ___ = -1 , number in the blank will be
(a) 49
(b) 50
(c) - 50
(d) 51
Answer: (b) 50
In simple words: Dividing -50 by positive 50 leaves you with -1.

Exam Tip: Pay close attention to signs. Dividing a negative number by a positive number results in a negative quotient.

Solve

Question 1. Find the value using suitable property
(a) -125 * 729 * 8
(b) (-66) * (-999) + 66
(c) -38 * 101
(d) 449 * (-55) + (- 449) * 45
(e) 1489 * (-119) - 1489 * (-19)
Answer:
(a) We can rearrange the numbers using the associative property:
\( -125 \times 729 \times 8 = (-125 \times 8) \times 729 \)
\( = -1000 \times 729 \)
\( = -729000 \)

(b) Rewrite \( 66 \) as \( 66 \times 1 \) and use the distributive property:
\( (-66) \times (-999) + 66 = 66 \times 999 + 66 \times 1 \)
\( = 66 \times (999 + 1) \)
\( = 66 \times 1000 \)
\( = 66000 \)

(c) Split \( 101 \) into \( (100 + 1) \) and use the distributive property:
\( -38 \times 101 = -38 \times (100 + 1) \)
\( = (-38 \times 100) + (-38 \times 1) \)
\( = -3800 - 38 \)
\( = -3838 \)

(d) Take out the common factor of \( 449 \) using the distributive property:
\( 449 \times (-55) + (-449) \times 45 = 449 \times (-55) - 449 \times 45 \)
\( = 449 \times [(-55) - 45] \)
\( = 449 \times (-100) \)
\( = -44900 \)

(e) Take out the common factor of \( 1489 \) using the distributive property:
\( 1489 \times (-119) - 1489 \times (-19) = 1489 \times [(-119) - (-19)] \)
\( = 1489 \times [-119 + 19] \)
\( = 1489 \times (-100) \)
\( = -148900 \)
In simple words: Using rules like the distributive property helps us group numbers to make the multiplication much easier to work out.

Exam Tip: Try to combine numbers that multiply to 10, 100, or 1000 first, as this simplifies the calculation and prevents mistakes.

Question 2. Jack divided -350 and -7.What was the quotient?
Answer:
To find the quotient, divide \( -350 \) by \( -7 \):
Quotient \( = \frac{-350}{-7} \)
When we divide a negative number by another negative number, the final result is positive:
Quotient \( = 50 \)
In simple words: Dividing -350 by -7 gives a positive answer of 50.

Exam Tip: Remember the sign rule for division: dividing two integers with matching signs always yields a positive quotient.

Question 3. A diver descended 20 feet in to the water from a boat at the surface of a lake. He then rose 12 feet and descended another 18 feet.At this point what is his depth in the water?
Answer:
We can represent going down (descent) as negative values and going up (ascent) as positive values:
First descent \( = -20 \) feet
Rising up \( = +12 \) feet
Second descent \( = -18 \) feet
Now, add these values to get the final position:
Final position \( = -20 + 12 - 18 \)
\( = -8 - 18 \)
\( = -26 \) feet
So, the diver is now at a depth of 26 feet below the surface.
In simple words: The diver swam down 20 feet, came back up 12 feet, and then went down 18 feet, ending up 26 feet deep in the water.

Exam Tip: Use positive signs for rising up and negative signs for moving down to write a clear expression and avoid sign errors.

Question 4. The temperature was 10 degree below zero and dropped 24 degrees.What is the new temperature?
Answer:
The starting temperature is 10 degrees below zero, which we write as \( -10^\circ \).
Since the temperature fell by 24 degrees, we subtract 24:
New temperature \( = -10 - 24 = -34^\circ \)
Therefore, the new temperature is 34 degrees below zero.
In simple words: Starting at 10 below zero and dropping another 24 degrees brings the final temperature to 34 below zero.

Exam Tip: Phrases like "below zero" and "dropped" mean you are working with negative directions on a temperature scale.

Question 5. In a class test containing 15 questions.4 marks are given for every correct answer and -2 marks are given for every incorrect answer.
a) Teena attempts all questions, but only10 of her answers are incorrect.What is her total score?
b) One of her friends scores -4 marks in this test, though she has got 8 correct answers. How many questions has she attempted incorrectly?
Answer:
a) Teena attempts all 15 questions, out of which 10 are incorrect.
Number of correct answers \( = 15 - 10 = 5 \)
Marks for correct answers \( = 5 \times 4 = 20 \)
Marks for incorrect answers \( = 10 \times (-2) = -20 \)
Teena's total score \( = 20 + (-20) = 0 \) marks.

b) Her friend scores a total of -4 marks and has 8 correct answers.
Marks from correct answers \( = 8 \times 4 = 32 \)
Let the number of incorrect answers be \( x \).
Marks from incorrect answers \( = x \times (-2) = -2x \)
Total score \( = 32 + (-2x) = -4 \)
\( \implies 32 - 2x = -4 \)
\( \implies -2x = -4 - 32 \)
\( \implies -2x = -36 \)
\( \implies x = 18 \)
So, she attempted 18 questions incorrectly.
In simple words: Teena got a score of 0 because her correct answers balanced out her mistakes. Her friend must have got 18 incorrect answers to finish with -4 marks.

Exam Tip: Always multiply the count of correct and incorrect answers by their respective marks, then sum them up to form a solvable equation.