MENTAL MATHS CLASS 6

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1. −102 − (−92)
   = −102 + 92 = −10

2. 4 − 5 + 6 − 7 − (−4)
   = 4 − 5 + 6 − 7 + 4 = 2

3. 72 and −190
   = 72 + (−190) = −118

4. 1800 + 60 + (−20)
   = 1800 + 60 − 20 = 1840

5. 55 + (−7 × 5) − 12
   = 55 − 35 − 12 = 8

6. Subtract the sum of −1777 and 777 from 4000
   Sum = −1777 + 777 = −1000
   4000 − (−1000) = 5000

7. −502 + 605 + (−120)
   = −502 + 605 − 120 = −17

8. How many integers are greater −12 but less than −7
   Integers: −11, −10, −9, −8 → 4 integers

9. Additive inverse of 375 − (115 + 160)
   375 − (115 + 160) = 375 − 275 = 100
   Additive inverse of 100 = −100

10. (−225) × 550 + 1225 × 550
    = (−225 + 1225) × 550 = 1000 × 550 = 550000

11. Two integers with difference 6 and sum −18
    Let the integers be x and y:
    x + y = −18, x − y = 6 → Solving, x = −6, y = −12
    Answer: −6 and −12

12. 1 − 2 + 3 − 4 + 5 − 6 + ... + 16
    Grouping pairs: (1−2)+(3−4)+(5−6)+...+(15−16) = (−1)+(−1)+... = 8 pairs × (−1) = −8

13. Product of first 3 multiples of 5
    5, 10, 15 → 5 × 10 × 15 = 750 → 750

14. (−125) × (−537) × (−8)
    = Positive × Negative = −537000

15. Odd integers < 100 multiple of 3 & 5 (i.e., 15)
    Multiples of 15 < 100: 15, 45, 75 → all odd → 3

16. Subtract the sum of (−1032) and 878 from −34
    Sum = −1032 + 878 = −154
    −34 − (−154) = −34 + 154 = 120

17. −1999 − 1999 × 99
    = −1999 − (1999 × 99) = −1999 × (1 + 99) = −1999 × 100 = −199900

18. (−3) + (−12) ÷ (−4) − 3 × (−3)
    = −3 + 3 − (−9) = −3 + 3 + 9 = 9

19. 32 − [32 − (32 − (32 − 32))]
    Inner to outer:
    = 32 − [32 − (32 − 0)]
    = 32 − [32 − 32]
    = 32 − 0 = 32

20. Three × (one less than difference of 19 and 5)
    Diff = 14, one less = 13 → 3 × 13 = 39

21. Some number added to −11 = 37
    Number = 48
    48 ÷ (−12) = −4
    −4 × (−8) = 32

22. 90 ÷ (90 ÷ (90 ÷ 3))
    = 90 ÷ (90 ÷ 30) = 90 ÷ 3 = 30

23. 100 − 8000 ÷ 40 + 95
    = 100 − 200 + 95 = −105 + 95 = −10

24. 90 − (−3) × (−3) × (−3)
    = 90 − (−27) = 90 + 27 = 117

Here are the solutions for the math problems numbered 25 to 42:

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25. $(-1)^{95} \times (-1)^{15} = -1 \times -1 = 1$

26. $(-35) \times 895 + 895 \times (-65) = 895 \times (-35 - 65) = 895 \times (-100) = -89,500$

27.
Sum of first 10 positive integers = $1+2+...+10 = 55$
Sum of first 10 negative integers = $-1 -2 -3 ... -10 = -55$
Total sum = $55 + (-55) = 0$

28. $324 \div (-27) = -12$

29. $\left\{(-30 \div 5) \div 2\right\} = (-6) \div 2 = -3$

30. $-27 \times ? = 729 \Rightarrow ? = 729 \div (-27) = -27$

31. $2401 \div (-49) = -49$

32.
Rate = 600 feet/hour
Time = 6 hours
Change = $600 \times 6 = 3600$ feet (descent, so: –3600 feet)

33.
Increasing order:
$-9, -6, -3, -2, 0, 5, 6, 7$

34.
$510 - [270 - (90 - 80 + 70)]$
= $510 - [270 - (80)] = 510 - 190 = 320$

35.
$x \times (-3) = 0 \Rightarrow x = 0$

36.
Distance = 160 km, Speed = 40 km/hr
Time = $160 \div 40 = 4$ hours

37.
Correct = 5 × 6 = 30
Incorrect = 8 × (−3) = −24
Not attempted = 2 × 0 = 0
Total score = $30 - 24 = 6$

38.
$x \times (-13) = -351 \Rightarrow x = 27$

39.
Up: 1 + 2 = 3 inches
Down: 4 inches
Net = $3 - 4 = -1$ inch (snail is 1 inch below starting point)

40.
Product of first 5 positive integers = $1 \times 2 \times 3 \times 4 \times 5 = 120$

41.
Multiplicative inverse of $-125 = -1/125$
Multiplicative inverse of $-50 = -1/50$

42.
$(-20) \div (-8) \div (-2) \times 3$
= $2.5 \div (-2) = -1.25$
= $-1.25 \times 3 = -3.75$

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