Solve -5×-7 + ? = 48-11: Finding the Missing Number

Order of Operations with Negative Numbers

5×7+?=4811 -5\times-7+?=48-11

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Step-by-step video solution

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00:01 Solve both sides of the equation separately
00:16 Subtract 35 from both sides of the equation in order to determine the unknown

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

5×7+?=4811 -5\times-7+?=48-11

2

Step-by-step solution

According to the order of operations rules, we first enter the multiplication problem inside the parentheses:

(5×7)+?=4811 (-5\times-7)+?=48-11

We solve the problem inside the parentheses and the subtraction problem:

5×7=35 -5\times-7=35

4811=37 48-11=37

Now we get the problem:

35+?=37 35+?=37

We move the term and change the sign accordingly:

?=3735 ?=37-35

?=2 ?=2

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Multiply first, then add/subtract from left to right
  • Technique: (-5) × (-7) = 35 because negative times negative equals positive
  • Check: Substitute back: 35 + 2 = 37 and 48 - 11 = 37 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting negative times negative equals positive
    Don't calculate (-5) × (-7) as -35! This ignores the crucial rule that multiplying two negatives gives a positive result. Always remember: negative × negative = positive, so (-5) × (-7) = +35.

Practice Quiz

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\( 8 + 3 \times 2 = \)

FAQ

Everything you need to know about this question

Why does (-5) × (-7) equal positive 35?

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When you multiply two negative numbers, the result is always positive. Think of it as: negative × negative = positive. So (5)×(7)=+35 (-5) \times (-7) = +35 .

What order should I solve this problem?

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Follow PEMDAS/BODMAS: First do multiplication (5)×(7)=35 (-5) \times (-7) = 35 , then subtraction 4811=37 48 - 11 = 37 , finally solve 35+?=37 35 + ? = 37 .

How do I find the missing number?

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Once you have 35+?=37 35 + ? = 37 , isolate the unknown by subtracting 35 from both sides: ?=3735=2 ? = 37 - 35 = 2 .

What if I calculated the multiplication wrong?

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Double-check your multiplication! Remember: positive × positive = positive, negative × negative = positive, and positive × negative = negative.

Can I solve this problem differently?

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The order of operations is fixed - you must do multiplication before addition/subtraction. However, you could simplify both sides first: left side gives 35 + ?, right side gives 37.

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