Integers: multiplication and division
Class 7 Maths · Integers · 34 questions with answers
A child can get through Class 6 integers on a number line, counting steps left and right. Multiplication breaks that, because there is nothing to count - the sign has to come from a rule that is understood rather than remembered. This sheet works through the rule, then mixes operations so the rule has to be chosen rather than applied automatically.
- Gives the correct sign for a product or quotient without hesitating
- Handles three or more factors by counting the negative signs
- Applies order of operations when signs and brackets are mixed
- Turns a described situation into a signed calculation
Exercise 1 of 3 · 14 questions
Work these out.
Write the answer · Warm-up
Here’s one done for you
(-3) × (-4) = 12. Count the negative signs: there are two. An even number of negatives gives a positive answer; an odd number gives a negative one. That single rule covers multiplication and division both, and it is worth saying out loud a few times rather than memorising four separate cases.
- 1)(-3) × (-4)
- 2)(-7) × 5
- 3)8 × (-6)
- 4)(-9) × (-2)
- 5)(-45) ÷ 9
- 6)(-36) ÷ (-6)
- 7)56 ÷ (-8)
- 8)(-1) × (-1) × (-1)
- 9)(-5) × (-8)
- 10)6 × (-7)
- 11)(-11) × (-3)
- 12)(-72) ÷ 8
- 13)(-64) ÷ (-8)
- 14)81 ÷ (-9)
Answers
- 1) 12 - two negatives, so the answer is positive.
- 2) -35 - one negative, so the answer is negative.
- 3) -48 - one negative, so the answer is negative.
- 4) 18 - two negatives, so the answer is positive.
- 5) -5 - one negative, so the answer is negative.
- 6) 6 - two negatives, so the answer is positive.
- 7) -7 - one negative, so the answer is negative.
- 8) -1 - three negatives, which is an odd number of them, so the answer is negative.
- 9) 40 - two negatives, so the answer is positive.
- 10) -42 - one negative, so the answer is negative.
- 11) 33 - two negatives, so the answer is positive.
- 12) -9 - one negative, so the answer is negative.
- 13) 8 - two negatives, so the answer is positive.
- 14) -9 - one negative, so the answer is negative.
Exercise 2 of 3 · 11 questions
Work these out, one step at a time. Show each step.
Write the answer · Guided
Here’s one done for you
(-8) + (-3) × 2 = -14. The trap is doing it left to right and getting (-11) × 2 = -22. Multiplication comes before addition, so (-3) × 2 = -6 first, and then (-8) + (-6) = -14. When signs and order of operations arrive in the same question, work out the order first and the signs second - trying to do both at once is where the errors come from.
- 1)(-2) × (-3) × (-4)
- 2)(-5) × 4 ÷ (-2)
- 3)(-8) + (-3) × 2
- 4)(-15) ÷ 3 + (-4)
- 5)12 ÷ (-4) × 3
- 6)(-6) × (-6) ÷ (-9)
- 7)(-3) × (-2) × (-5)
- 8)(-9) + 4 × (-2)
- 9)(-24) ÷ 6 - (-7)
- 10)20 ÷ (-5) × (-3)
- 11)(-7) × 3 + 30
Answers
- 1) -24. First (-2) × (-3) = 6, then 6 × (-4) = -24. Three negatives, so negative.
- 2) 10. First (-5) × 4 = -20, then (-20) ÷ (-2) = 10.
- 3) -14. Multiply first: (-3) × 2 = -6. Then (-8) + (-6) = -14.
- 4) -9. Divide first: (-15) ÷ 3 = -5. Then (-5) + (-4) = -9.
- 5) -9. Left to right: 12 ÷ (-4) = -3, then (-3) × 3 = -9.
- 6) -4. First (-6) × (-6) = 36, then 36 ÷ (-9) = -4.
- 7) -30. First (-3) × (-2) = 6, then 6 × (-5) = -30. Three negatives, so negative.
- 8) -17. Multiply first: 4 × (-2) = -8. Then (-9) + (-8) = -17.
- 9) 3. Divide first: (-24) ÷ 6 = -4. Then (-4) - (-7) = -4 + 7 = 3.
- 10) 12. Left to right: 20 ÷ (-5) = -4, then (-4) × (-3) = 12.
- 11) 9. Multiply first: (-7) × 3 = -21. Then -21 + 30 = 9.
Exercise 3 of 3 · 9 questions
Write the calculation, then the answer in a sentence.
Write the answer · Practice
Here’s one done for you
The submarine: descending is negative, so 5 m down for 8 minutes is (-5) × 8 = -40, which is 40 m below the surface. Notice the two separate decisions - first which direction counts as negative, then the arithmetic. Children who go straight to the numbers usually get the size right and the sign wrong, and the sign is half the mark.
- 1)A submarine descends 5 m every minute for 8 minutes. Where is it relative to the surface?
- 2)The temperature is 5°C and falls 3°C every hour for 6 hours. What is the temperature then?
- 3)A shopkeeper loses ₹25 on each of 14 items. What is the total loss?
- 4)In a quiz, a correct answer scores +4 and a wrong one -2. A student gets 9 right and 6 wrong. What is the score?
- 5)A diver is 30 m below the surface and rises 4 m each minute for 5 minutes. Where is the diver now?
- 6)A well is dug 3 m deeper each day for 7 days. How deep is it relative to the ground?
- 7)A cricketer loses 6 runs for each of 5 no-balls and gains 40 runs otherwise. What is the net figure?
- 8)The temperature at midnight was -8°C and rose 2°C every hour for 9 hours. What was it then?
- 9)A trader gains ₹35 on each of 12 items and loses ₹20 on each of 9 others. What is the net result?
Answers
- 1) (-5) × 8 = -40. The submarine is 40 m below the surface.
- 2) 5 + (-3) × 6 = 5 + (-18) = -13. The temperature is -13°C.
- 3) (-25) × 14 = -350. The total loss is ₹350.
- 4) 9 × 4 + 6 × (-2) = 36 + (-12) = 24. The student scores 24.
- 5) -30 + 4 × 5 = -30 + 20 = -10. The diver is 10 m below the surface.
- 6) (-3) × 7 = -21. The well is 21 m below the ground.
- 7) 40 + 5 × (-6) = 40 + (-30) = 10. The net figure is 10 runs.
- 8) -8 + 2 × 9 = -8 + 18 = 10. The temperature was 10°C.
- 9) 12 × 35 + 9 × (-20) = 420 + (-180) = 240. The net gain is ₹240.
While your child works
- If your child hesitates on a sign, ask them to count the negative signs out loud. Even means positive, odd means negative - one rule instead of four.
- Mixed questions are the real test. Ask 'what do we do first?' before any arithmetic happens.
- In word problems, ask 'which direction is negative here?' first. That decision made explicitly fixes most sign errors.