Solve Using Reference Equation: Finding 39+39 Using 40+40=80

Reference Addition with Strategic Subtraction

40+40=80 40+40=80

Use the above equation to help solve the following problem:

39+39=? 39+39=\text{?}

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

40+40=80 40+40=80

Use the above equation to help solve the following problem:

39+39=? 39+39=\text{?}

2

Step-by-step solution

To solve this problem, we'll use the information that 40+40=80 40 + 40 = 80 . We'll employ the following steps:

  • Step 1: Realize that 39 39 is 1 less than 40 40 . Therefore, 39+39 39 + 39 can be rewritten using the relationship 40+40 40 + 40 as (40−1)+(40−1)(40 - 1) + (40 - 1).
  • Step 2: Simplify the expression to calculate the total: (40+40)−(1+1)=80−2 (40 + 40) - (1 + 1) = 80 - 2 .
  • Step 3: Subtract 2 from 80 to obtain the result.

Now, let's perform the calculation:

40+40=80 40 + 40 = 80 implies that 39+39=80−2=78 39 + 39 = 80 - 2 = 78 .

Therefore, the solution to the problem is 78 78 .

3

Final Answer

78 78

Key Points to Remember

Essential concepts to master this topic
  • Rule: Use known addition facts to solve related problems
  • Technique: Since 39 = 40 - 1, then 39 + 39 = 80 - 2
  • Check: Verify 39 + 39 = 78 by adding: 30 + 30 + 9 + 9 = 78 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting only 1 instead of 2 from the reference equation
    Don't subtract just 1 from 80 to get 79! Since we have two 39s (each 1 less than 40), we lose 2 total from the sum. Always subtract the total difference: 80 - 2 = 78.

Practice Quiz

Test your knowledge with interactive questions

Add fifty units to the number 31.

What is the resulting number?

FAQ

Everything you need to know about this question

Why can't I just subtract 1 from 80 to get 79?

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Because you're adding two numbers that are each 1 less than 40! Since 39=40−1 39 = 40 - 1 , when you add 39 + 39, you're losing 1 from each addend, so you lose 2 total from the reference sum.

What if the reference equation was different, like 38 + 38?

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Same strategy! Find how much each number differs from your reference. If you knew 40+40=80 40 + 40 = 80 and wanted 38+38 38 + 38 , you'd calculate 80−4=76 80 - 4 = 76 since each 38 is 2 less than 40.

Can I use this method with bigger numbers?

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Absolutely! This works great with any numbers. For example, if you know 50+50=100 50 + 50 = 100 , you can quickly find 49+49=98 49 + 49 = 98 or 51+51=102 51 + 51 = 102 .

How do I remember which direction to adjust?

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Think logically: if your numbers are smaller than the reference numbers, your sum will be smaller than the reference sum. If your numbers are larger, your sum will be larger!

Is there a faster way to check my answer?

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Yes! You can break it down: 39+39=(30+30)+(9+9)=60+18=78 39 + 39 = (30 + 30) + (9 + 9) = 60 + 18 = 78 . This confirms your reference method worked correctly.

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