Solve (7-4-3)(15-6-2)+3×5×2: Order of Operations Challenge

Order of Operations with Multiple Parentheses

Solve the following problem:

(743)(1562)+352= (7-4-3)(15-6-2)+3\cdot5\cdot2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:12 Let's solve the problem step by step.
00:16 Remember, always begin by solving what's inside the parentheses first.
00:28 Inside the parentheses, solve multiplication from left to right.
00:34 Think of everything inside the parentheses as one whole factor.
00:43 And always remember, any number times zero equals zero!
00:48 Great! Let's move on and solve the expression.
00:52 Here is how it looks when it's solved!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

(743)(1562)+352= (7-4-3)(15-6-2)+3\cdot5\cdot2=

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 that parentheses precede all of the above:

Therefore, we'll start by simplifying the expressions inside of the parentheses first:
(743)(1562)+352=07+352= (7-4-3)(15-6-2)+3\cdot5\cdot2= \\ 0\cdot7+3\cdot5\cdot2=

We'll continue to perform the multiplications in the two terms we obtained in the expression in the last stage, this is because multiplication comes before addition. In each term we'll perform the multiplications step by step from left to right, also remember that multiplying any number by 0 gives a result of 0:

07+352=0+152=30 0\cdot7+3\cdot5\cdot2= \\ 0+15\cdot2= \\ 30

Note that since the commutative property of multiplication applies, and in the second term from the left 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 left 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 known order of operations mentioned at the beginning of this solution)

Therefore the correct answer is answer D.

3

Final Answer

30

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication, finally addition from left to right
  • Technique: Calculate (743)=0 (7-4-3) = 0 and (1562)=7 (15-6-2) = 7 before multiplying
  • Check: Verify 0×7+30=30 0 \times 7 + 30 = 30 by substituting back ✓

Common Mistakes

Avoid these frequent errors
  • Solving from left to right without parentheses first
    Don't calculate 7-4-3×15 by working left to right = wrong order! This ignores parentheses priority and gives completely wrong results. Always solve everything inside parentheses before doing any other operations.

Practice Quiz

Test your knowledge with interactive questions

\( 0+0.2+0.6= \) ?

FAQ

Everything you need to know about this question

Why do I solve parentheses before multiplication?

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PEMDAS rules tell us the order! Parentheses always come first, then multiplication. Think of parentheses as saying 'do me first!' to avoid confusion.

What happens when I multiply by zero?

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Any number multiplied by zero equals zero! In this problem, (743)=0 (7-4-3) = 0 , so 0×7=0 0 \times 7 = 0 . This is a key math rule to remember.

Should I work from left to right in the parentheses?

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Yes! Within parentheses, follow normal order: left to right for addition and subtraction. So 743 7-4-3 becomes 33=0 3-3 = 0 .

Can I skip steps when one part equals zero?

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It's tempting, but show your work! Even when 0×7=0 0 \times 7 = 0 is obvious, writing each step helps you catch mistakes and shows your understanding.

How do I remember the order of operations?

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Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember 'Please Excuse My Dear Aunt Sally!'

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