Solve (5×4-10×2)×(3-5): Order of Operations Practice

Order of Operations with Parentheses

(5×410×2)×(35)= (5\times4-10\times2)\times(3-5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:03 Always solve the parentheses first
00:06 Multiplication precedes subtraction
00:14 0 multiplied by any number always equals 0
00:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(5×410×2)×(35)= (5\times4-10\times2)\times(3-5)=

2

Step-by-step solution

This simple rule is the order of operations which states that multiplication precedes addition and subtraction, and division precedes all of them,

In the given example, a multiplication occurs between two sets of parentheses, thus we simplify the expressions within each pair of parentheses separately,

We start with simplifying the expression within the parentheses on the left, this is done in accordance with the order of operations mentioned above, meaning that multiplication comes before subtraction, we perform the multiplications in this expression first and then proceed with the subtraction operations within it, in reverse we simplify the expression within the parentheses on the right and perform the subtraction operation within them:

What remains for us is to perform the last multiplication that was deferred, it is the multiplication that occurred between the expressions within the parentheses in the original expression, we perform it while remembering that multiplying any number by 0 will result in 0:

Therefore, the correct answer is answer d.

3

Final Answer

0 0

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication and division left to right
  • Technique: Simplify (5×410×2)=(2020)=0 (5×4-10×2) = (20-20) = 0 and (35)=2 (3-5) = -2
  • Check: Final multiplication 0×(2)=0 0 × (-2) = 0 confirms our answer ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without considering parentheses first
    Don't solve 5×4-10×2×3-5 = 20-10×2×3-5 = wrong answer! This ignores the parentheses grouping and creates calculation errors. Always solve expressions inside parentheses completely before moving to operations between them.

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 need to solve parentheses first?

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Parentheses show grouping - they tell you which calculations belong together! Without solving them first, you'll mix up the order and get the wrong answer.

What if one of my parentheses equals zero?

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Great observation! When any factor in multiplication equals zero, the entire product becomes zero. So 0×(2)=0 0 × (-2) = 0 no matter what the other number is.

Do I multiply or subtract first inside parentheses?

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Inside parentheses, follow PEMDAS too! Multiplication comes before subtraction, so solve 5×410×2 5×4-10×2 by doing both multiplications first, then the subtraction.

Can I distribute instead of solving parentheses?

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Not in this case! Distribution works when you have something like 3(x+2) 3(x+2) . Here you have two separate groups multiplied together, so solve each group first.

How do I remember the order of operations?

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

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