Solve: (9+7+3)(4+5+3)(7-3-4) - Expression Evaluation Challenge

Order of Operations with Zero Products

Solve the following problem

(9+7+3)(4+5+3)(734)= (9+7+3)(4+5+3)(7-3-4)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:03 Always solve the parentheses first
00:06 Given that within the parentheses there's only addition/subtraction, solve from left to right
00:16 Between the parentheses there's multiplication
00:22 Any number multiplied by 0 will always equal 0
00:26 This is the solution to the question
00:30 Any number multiplied by 0 will always equal 0!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem

(9+7+3)(4+5+3)(734)= (9+7+3)(4+5+3)(7-3-4)=

2

Step-by-step solution

Let's simplify this expression whilst following the order of operations. Exponents precede multiplication and division, which in turn precede addition and subtraction, and parentheses precede all of the above,

Therefore, we'll start by simplifying the expressions inside of the parentheses first:
(9+7+3)(4+5+3)(734)=19120 (9+7+3)(4+5+3)(7-3-4)= \\ 19\cdot12\cdot0

Now we'll calculate the multiplication result step by step from left to right, remembering also that multiplying any number by 0 gives a result of 0:

19120=2280=0 19\cdot12\cdot0 =\\ 228\cdot0 =\\ 0

Since the commutative property of multiplication applies, and in the expression we simplified above there is multiplication between all terms, the order of operations in this calculation doesn't matter (it's not necessary to perform the leftmost multiplication first etc. as we did), however, it is recommended to practice performing operations from left to right as this is the natural order of arithmetic operations (in the absence of parentheses, or other preceding arithmetic operations according to the order of operations mentioned at the beginning of this solution)

Therefore, the correct answer is answer B.

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always evaluate expressions inside parentheses first
  • Technique: Calculate (9+7+3)=19 (9+7+3) = 19 , (4+5+3)=12 (4+5+3) = 12 , (734)=0 (7-3-4) = 0
  • Check: Any number multiplied by zero equals zero: 19×12×0=0 19 \times 12 \times 0 = 0

Common Mistakes

Avoid these frequent errors
  • Ignoring the zero in the final parentheses
    Don't calculate 19×12=228 19 \times 12 = 228 and stop there = wrong answer 228! Students often focus on the larger numbers and miss that (7-3-4) = 0. Always evaluate all parentheses completely, because multiplying by zero makes the entire result zero.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( 12+3\cdot0= \)

FAQ

Everything you need to know about this question

Why does the whole answer become 0 when only one part equals 0?

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This is the Zero Product Property! When you multiply any number by zero, the result is always zero. So 19×12×0=0 19 \times 12 \times 0 = 0 , no matter how big the other numbers are.

Do I really need to calculate 19 × 12 if one factor is 0?

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No! Once you see that one factor equals zero, you know the answer is zero immediately. However, it's good practice to show all your work step by step.

What if I made an error calculating (7-3-4)?

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Let's check: 734=44=0 7-3-4 = 4-4 = 0 . Work left to right for subtraction! A common mistake is calculating 7(3+4)=0 7-(3+4) = 0 , but that's wrong—there are no inner parentheses around 3+4.

Should I multiply from left to right or does order matter?

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With multiplication only, order doesn't matter due to the commutative property. But it's good practice to work left to right to build consistent habits for more complex problems.

How can I avoid missing the zero?

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Always circle or highlight your results from each set of parentheses before multiplying. Write: (9+7+3)=19, (4+5+3)=12, (7-3-4)=0. The zero will stand out!

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