Solve: Multiplying 8.5 × 10 and Dividing by 2

Order of Operations with Decimal Multiplication

8.5×102=? \frac{8.5\times10}{2}=\text{?}

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Step-by-step video solution

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00:00 Let's solve numerator and denominator separately

Step-by-step written solution

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1

Understand the problem

8.5×102=? \frac{8.5\times10}{2}=\text{?}

2

Step-by-step solution

First we'll solve the multiplication exercise in the numerator:

8.5×10=85 8.5\times10=85

and we'll get:

852=42.5 \frac{85}{2}=42.5

3

Final Answer

42.5 42.5

Key Points to Remember

Essential concepts to master this topic
  • Order: Follow PEMDAS - multiplication before division in expressions
  • Technique: Calculate 8.5 × 10 = 85 first, then divide 85 ÷ 2
  • Check: Verify 42.5 × 2 = 85 and 85 ÷ 10 = 8.5 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing before multiplying
    Don't divide 8.5 ÷ 2 = 4.25 first, then multiply by 10 = 42.5! This ignores order of operations and can lead to wrong answers in complex problems. Always follow PEMDAS: multiply 8.5 × 10 = 85 first, then divide by 2.

Practice Quiz

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\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I multiply first instead of going left to right?

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When you have a fraction like this, the multiplication in the numerator must be done before dividing by the denominator. Think of it as 8.5×102 \frac{8.5 \times 10}{2} - you need the complete numerator first!

What if I accidentally divided first?

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If you divided 8.5 ÷ 2 = 4.25 first, then multiplied by 10, you'd get 42.5 - the same answer! But this only works because multiplication and division have equal priority. Always follow proper order to avoid mistakes in harder problems.

How do I multiply 8.5 × 10 quickly?

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When multiplying any decimal by 10, just move the decimal point one place to the right! So 8.5 becomes 85.0 or simply 85.

Why is my answer a decimal?

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You get 42.5 because 85 ÷ 2 doesn't divide evenly. This is normal! Many real-world problems have decimal answers, so don't worry if your result isn't a whole number.

How can I check if 42.5 is correct?

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Use reverse operations: multiply 42.5 × 2 = 85, then divide 85 ÷ 10 = 8.5. Since you get back to the original number, your answer is correct!

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