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Mathematics

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Step-by-step solution

14 steps

Here are the solutions to your math problems:

1. Write down the missing numbers in the following patterns:

a) The pattern increases by 5 each time.

−25,−20,−15,−10,−5,0,5,10,15,20-25, -20, \boxed{-15}, \boxed{-10}, \boxed{-5}, 0, 5, 10, \boxed{15}, \boxed{20}

b) The pattern increases by 1 each time.

−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,7,8,9,10,11-6, -5, -4, \boxed{-3}, \boxed{-2}, -1, 0, 1, 2, 3, \boxed{4}, \boxed{5}, 6, 7, 8, 9, 10, 11

2. Use one of the following signs, <,>,<, >, or ==, to make these sentences true:

a) 27>127 \boxed{>} 1

b) 13+6>013 + 6 \boxed{>} 0 (since 13+6=1913+6=19)

c) 4>04 \boxed{>} 0

d) −5>−8-5 \boxed{>} -8

3. Write down the missing numbers to complete the following sentences:

a) −9×3=−27-9 \times \boxed{3} = -27

b) 32÷4=832 \div \boxed{4} = 8

c) 36÷2=1836 \div 2 = \boxed{18}

d) 5×7=355 \times \boxed{7} = 35

e) 64÷8=864 \div \boxed{8} = 8

4. Arrange the following numbers:

a) Arrange the following numbers in ascending order: 48,−50,−12,048, -50, -12, 0

−50,−12,0,48\boxed{-50, -12, 0, 48}

b) Arrange the following numbers in descending order: −36,24,−15,1-36, 24, -15, 1

24,1,−15,−36\boxed{24, 1, -15, -36}

5. Evaluate (find the value of):

a) 12−6−(−10)12 - 6 - (-10)

  1. Simplify the double negative.

    12−6+1012 - 6 + 10
  2. Perform the operations from left to right.

    6+10=166 + 10 = \boxed{16}

    b) −4+9+(−11)-4 + 9 + (-11)

  3. Simplify the addition of a negative number.

    −4+9−11-4 + 9 - 11
  4. Perform the operations from left to right.

    5−11=−65 - 11 = \boxed{-6}

    c) 7−14−(−21)7 - 14 - (-21)

  5. Simplify the double negative.

    7−14+217 - 14 + 21
  6. Perform the operations from left to right.

    −7+21=14-7 + 21 = \boxed{14}

    6. Calculate:

    a) 5×(−3)×25 \times (-3) \times 2

  7. Multiply the first two numbers.

    −15×2-15 \times 2
  8. Multiply the result by the last number.

    −30\boxed{-30}

    b) 6×(−2)×46 \times (-2) \times 4

  9. Multiply the first two numbers.

    −12×4-12 \times 4
  10. Multiply the result by the last number.

    −48\boxed{-48}

    c) 3×(−8)×23 \times (-8) \times 2

  11. Multiply the first two numbers.

    −24×2-24 \times 2
  12. Multiply the result by the last number.

    −48\boxed{-48}

    d) −4×(−7)×1-4 \times (-7) \times 1

  13. Multiply the first two numbers.

    28×128 \times 1
  14. Multiply the result by the

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