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Given a=10, b=200, and c=3000, verify the commutative and associative properties for addition and multiplication.

Mathematics

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Answers

8 parts
a
210
b
2000
c
3210
d
6000000
e
630000
f
0
g
3000
h
200

Step-by-step solution

16 steps

Given a=10a=10, b=200b=200, and c=3000c=3000.

Part a· 2 steps

Complete and calculate a+b=b+aa+b = b+a

  1. Complete the expression.

    a+b=b+aa+b = b+a
  2. Substitute the values and calculate.

    10+200=200+1010+200 = 200+10 210=210210 = 210

    The completed expression is a+b=b+aa+b = b+a. The calculated value is 210\boxed{210}.

Part b2000

Complete and calculate a×b=b×aa \times b = b \times a

  1. Complete the expression.

    a×b=b×aa \times b = b \times a
  2. Substitute the values and calculate.

    10×200=200×1010 \times 200 = 200 \times 10 2000=20002000 = 2000

    The completed expression is a×b=b×aa \times b = b \times a. The calculated value is 2000\boxed{2000}.

Part c3210

Complete and calculate (a+b)+c=a+(b+c)(a+b)+c = a+(b+c)

  1. Complete the expression.

    (a+b)+c=a+(b+c)(a+b)+c = a+(b+c)
  2. Substitute the values and calculate.

    (10+200)+3000=10+(200+3000)(10+200)+3000 = 10+(200+3000) 210+3000=10+3200210+3000 = 10+3200 3210=32103210 = 3210

    The completed expression is (a+b)+c=a+(b+c)(a+b)+c = a+(b+c). The calculated value is 3210\boxed{3210}.

Part d6000000

Complete and calculate (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c)

  1. Complete the expression.

    (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c)
  2. Substitute the values and calculate.

    (10×200)×3000=10×(200×3000)(10 \times 200) \times 3000 = 10 \times (200 \times 3000) 2000×3000=10×6000002000 \times 3000 = 10 \times 600000 6000000=60000006000000 = 6000000

    The completed expression is (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c). The calculated value is 6000000\boxed{6000000}.

Part e630000

Complete and calculate (a+b)×c=a×c+b×c(a+b) \times c = a \times c + b \times c

  1. Complete the expression.

    (a+b)×c=a×c+b×c(a+b) \times c = a \times c + b \times c
  2. Substitute the values and calculate.

    (10+200)×3000=(10×3000)+(200×3000)(10+200) \times 3000 = (10 \times 3000) + (200 \times 3000) 210×3000=30000+600000210 \times 3000 = 30000 + 600000 630000=630000630000 = 630000

    The completed expression is (a+b)×c=a×c+b×c(a+b) \times c = a \times c + b \times c. The calculated value is 630000\boxed{630000}.

Part f0

Complete and calculate a−aa-a

  1. Complete the expression.

    a−a=0a-a = 0
  2. Substitute the value and calculate.

    10−10=010-10 = 0

    The completed expression is a−a=0a-a = 0. The calculated value is 0\boxed{0}.

Part g3000

Complete and calculate c×1c \times 1

  1. Complete the expression.

    c×1=cc \times 1 = c
  2. Substitute the value and calculate.

    3000×1=30003000 \times 1 = 3000

    The completed expression is c×1=cc \times 1 = c. The calculated value is 3000\boxed{3000}.

Part h200

Complete and calculate b+0b+0

  1. Complete the expression.

    b+0=bb+0 = b
  2. Substitute the value and calculate.

    200+0=200200+0 = 200

    The completed expression is b+0=bb+0 = b. The calculated value is 200\boxed{200}.

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