Class 7 Maths · Original EZT practice
Integers (Class 7): original worked practice
A negative sign can tell you where you are, what change happens next, or what operation to perform. Keep those jobs separate. A number-line sketch often catches a sign slip before a calculation grows.
10 original worked examples, 10 fresh self-check questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 17 October 2026:
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Add numbers with opposite signs
Choose the method: Compare absolute values, subtract the smaller magnitude and keep the sign of the larger magnitude.
EZT practice question
Calculate (-18) + 11.
Show the worked solution
- 18 - 11 = 7.
- The negative addend has the larger absolute value.
Answer: -7
Check: From -18, move 11 steps right to -7.
Watch for this: Larger magnitude is not the same as larger signed number.
Now try it yourself
Calculate (-9) + 23.
Check your answer
14
Move 23 right from -9, or calculate 23 - 9.
Subtract a negative
Choose the method: Subtracting any integer means adding its additive inverse.
EZT practice question
Calculate 12 - (-9).
Show the worked solution
- The additive inverse of -9 is 9.
- 12 - (-9) = 12 + 9.
Answer: 21
Check: 21 + (-9) = 12, reversing the subtraction.
Watch for this: Two minus signs become plus only when they mean subtracting a negative.
Now try it yourself
Calculate -8 - (-15).
Check your answer
7
-8 + 15 = 7.
Describe a signed change
Choose the method: Choose the starting value, then add the signed change.
EZT practice question
At sunset the temperature is -4°C. It falls by 7°C. What is the new temperature?
Show the worked solution
- A fall of 7°C is change -7°C.
- -4 + (-7) = -11.
Answer: -11°C
Check: -11 is 7 below -4 on a temperature scale.
Watch for this: A fall is not a positive addition.
Now try it yourself
A lift is at floor -6 and rises 9 floors. Where does it stop?
Check your answer
Floor 3
-6 + 9 = 3, with ground numbered 0.
Multiply two signed integers
Choose the method: Multiply the absolute values. Equal signs give a positive product; different signs give a negative product.
EZT practice question
Calculate (-7) × (-8), then (-7) × 9.
Show the worked solution
- 7 × 8 = 56; two negative factors give a positive product.
- 7 × 9 = 63; one negative factor gives a negative product.
Answer: 56 and -63
Check: (-7) × (-8) + (-7) × 8 = (-7) × 0 = 0.
Watch for this: Sign rules for multiplication are not rules for adding two negatives.
Now try it yourself
Calculate (-12) × (-6), then 5 × (-11).
Check your answer
72 and -55
Same signs give 72; different signs give-55.
Count negative factors
Choose the method: For a product of non-zero integers, an odd number of negative factors gives negative; an even number gives positive.
EZT practice question
Calculate (-3) × (-4) × (-5).
Show the worked solution
- (-3) × (-4) = 12.
- 12 × (-5) = -60.
Answer: -60
Check: There are 3 negative factors, so the product must be negative.
Watch for this: A zero factor makes the entire product zero regardless of sign count.
Now try it yourself
Calculate (-2) × (-7) × (-1) × (-3).
Check your answer
42
There are 4 negative factors and 2 × 7 × 1 × 3 = 42.
Divide and multiply back
Choose the method: A quotient is the number which, multiplied by the divisor, gives the dividend. The divisor cannot be zero.
EZT practice question
Calculate (-168) ÷ 14 and (-168) ÷ (-14).
Show the worked solution
- Different signs: -168 ÷ 14 = -12.
- Equal signs: -168 ÷ (-14) = 12.
Answer: -12 and 12
Check: -12 × 14 = -168; 12 × (-14) = -168.
Watch for this: Integer division need not give an integer: 1 ÷ 2 is 1/2.
Now try it yourself
Calculate (-156) ÷ (-13), then 0 ÷ (-9).
Check your answer
12 and 0
12 × (-13) = -156; 0 × (-9) = 0.
Spot a shared factor
Choose the method: Multiplication distributes over addition: ab + ac = a(b + c).
EZT practice question
Calculate 34 × (-27) + (-27) × (-44).
Show the worked solution
- Use commutativity to put -27 first in both products.
- (-27) × (34 - 44) = (-27) × (-10).
Answer: 270
Check: -918 + 1188 = 270.
Watch for this: Keep the sign attached to each term when collecting the factor.
Now try it yourself
Calculate 19 × (-16) + (-16) × (-29).
Check your answer
160
(-16) × (19 - 29) = 160.
Regroup a product
Choose the method: Commutativity changes order; associativity changes grouping. Both apply to integer multiplication.
EZT practice question
Calculate 16 × 37 × (-125).
Show the worked solution
- Group 16 × (-125) = -2000.
- Multiply -2000 × 37.
Answer: -74000
Check: 16 × 37 = 592; 592 × (-125) = -74000.
Watch for this: Do not apply this regrouping rule to subtraction or division.
Now try it yourself
Calculate 25 × 18 × (-4).
Check your answer
-1800
25 × (-4) = -100; -100 × 18 = -1800.
Net gain or loss
Choose the method: Set gains positive and losses negative, keeping the same units.
EZT practice question
A stall gains Rs 320 on Friday and loses Rs 205 on Saturday. Find the net change.
Show the worked solution
- Net change = 320 + (-205).
- 320 - 205 = 115.
Answer: Gain of Rs 115
Check: A loss 205 removes 205 from the gain 320.
Watch for this: A positive net change does not tell you the stall's total balance.
Now try it yourself
A stall gains Rs 180, then loses Rs 245. Find the net change.
Check your answer
Loss of Rs 65
180 - 245 = -65.
Turn a scoring rule into an expression
Choose the method: Multiply each outcome count by its signed score, then add.
EZT practice question
A quiz gives 5 points per correct answer and -2 per wrong answer. Arun gets 13 correct and 7 wrong. What is his score?
Show the worked solution
- Correct-answer points: 13 × 5 = 65.
- Wrong-answer points: 7 × (-2) = -14.
- Total = 65 - 14.
Answer: 51 points
Check: 13 + 7 = 20 answered questions; each contributes once.
Watch for this: Do not subtract the penalty twice.
Now try it yourself
Same scoring rule: 11 correct and 9 wrong. Find the score.
Check your answer
37 points
11 × 5 + 9 × (-2) = 55 - 18 = 37.
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Questions about this practice page
- Is Integers Chapter 1 in every Class 7 book?
- No. The older chapter-number search is the context for this page; the linked NCERT exemplar covers integers. Ganita Prakash has a different chapter/part arrangement. Match the topic name and your school plan, not only the chapter number.
- Is zero positive or negative?
- Neither. It is an integer, but not a positive or negative integer.
- Why does subtracting a negative add?
- Subtraction adds the opposite. For 12 - (-9), the opposite of -9 is 9, giving 21. Check by adding the original subtrahend back: 21 + (-9) = 12.
- Can integer division involve zero?
- A zero dividend is fine if the divisor is non-zero: 0 ÷ 7 = 0. Division by zero is undefined in ordinary arithmetic. For 0 ÷ 0 there is no unique quotient; for a non-zero number divided by 0 there is no quotient.
- Are these textbook exercise questions?
- No. The questions and explanations are original topic practice, not an exercise-number answer key or a promise about every school's syllabus.