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

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

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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