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Simplify the following expressions using properties of operations: a) 462 × 999 + 462 b) 385 × 6 + 285 × 4 c) 15625 × 15625 - 15625 × 5625 d) 13476 × 93 + 7 × 13476

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Answers

4 parts
a

462000\text{462000}

b

3450\text{3450}

c

156250000\text{156250000}

d

1347600\text{1347600}

Step-by-step solution

15 steps

Here are the solutions for question 4, using properties:

Part a· 4 steps

  1. Identify the common factor.

    462×999+462=462×999+462×1462 \times 999 + 462 = 462 \times 999 + 462 \times 1

  2. Apply the distributive property a×b+a×c=a×(b+c)a \times b + a \times c = a \times (b+c).

    462×(999+1)462 \times (999 + 1)

  3. Perform the addition.

    462×1000462 \times 1000

  4. Perform the multiplication.

    462000462000

    The value is 462000\boxed{\text{462000}}.

Part b

3450\text{3450}

  1. Perform the first multiplication.

    385×6=2310385 \times 6 = 2310

  2. Perform the second multiplication.

    285×4=1140285 \times 4 = 1140

  3. Perform the addition.

    2310+1140=34502310 + 1140 = 3450

    The value is 3450\boxed{\text{3450}}.

Part c

156250000\text{156250000}

  1. Identify the common factor.

    15625×15625−15625×562515625 \times 15625 - 15625 \times 5625

    The common factor is 15625.

  2. Apply the distributive property a×b−a×c=a×(b−c)a \times b - a \times c = a \times (b-c).

    15625×(15625−5625)15625 \times (15625 - 5625)

  3. Perform the subtraction.

    15625×1000015625 \times 10000

  4. Perform the multiplication.

    156250000156250000

    The value is 156250000\boxed{\text{156250000}}.

Part d

1347600\text{1347600}

  1. Identify the common factor.

    13476×93+7×13476=13476×93+13476×713476 \times 93 + 7 \times 13476 = 13476 \times 93 + 13476 \times 7

  2. Apply the distributive property a×b+a×c=a×(b+c)a \times b + a \times c = a \times (b+c).

    13476×(93+7)13476 \times (93 + 7)

  3. Perform the addition.

    13476×10013476 \times 100

  4. Perform the multiplication.

    13476001347600

    The value is 1347600\boxed{\text{1347600}}.

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