Calculate the Difference: Solving 30.4 - 12.6 Step by Step

Decimal Subtraction with Regrouping

30.412.6= 30.4-12.6=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll use long subtraction for calculation
00:08 We'll place the decimal point in the appropriate position
00:12 The digit is smaller than the digit we need to subtract from
00:17 So we'll borrow from the next possible digit
00:20 The larger digit will decrease by 1, and our digit will increase by 10
00:24 Again we'll use the same method and borrow from this digit
00:38 Now we'll subtract from the larger number and place
00:50 We'll continue to subtract and place accordingly
01:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

30.412.6= 30.4-12.6=

2

Step-by-step solution

To solve the subtraction problem 30.412.6 30.4 - 12.6 , follow these steps:

Step 1: Write the numbers vertically, ensuring that the decimal points are aligned:

30.412.6\begin{array}{c} 30.4 \\ - 12.6 \\ \hline \end{array}

Step 2: Begin subtracting from the rightmost column, which is the tenths place in this case:

  • The tenths column: 464 - 6. Since 4 is less than 6, we need to borrow from the whole numbers to the left. The 0 in the units column of 30 becomes 10 (because we borrow 1, which makes it 10 in decimal terms), and the 3 becomes 2.
  • Now, 14 - 6 = 8. Write 8 in the tenths place. The result so far is 0.8.

Step 3: Move to the units place (whole numbers column):

  • Subtract 22=02 - 2 = 0.
  • Write 0 in the units place. The result so far is 0.8.

Step 4: Move to the tens place:

  • Subtract 31=13 - 1 = 1 (remember we borrowed 1 earlier, hence it is now 2 in place of originally 3, subtracting 1 gives 1).
  • Write 1 in the tens place. The final result is 17.817.8.

Therefore, the solution to the problem 30.412.6 30.4 - 12.6 is 17.8 17.8 .

3

Final Answer

17.8

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up decimal points to ensure correct place value
  • Borrowing: Convert 30.4 to 29.14 when 4 < 6 in tenths place
  • Check: Add result to subtrahend: 17.8 + 12.6 = 30.4 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points properly
    Don't line up the rightmost digits without considering decimal placement = wrong place values! This leads to answers like 18.8 instead of 17.8. Always align decimal points vertically first, then subtract column by column from right to left.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to borrow when subtracting 4 - 6 in the tenths place?

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Since 4 is smaller than 6, you can't subtract directly. You need to borrow 1 from the units place, which turns the 4 into 14 (in tenths), so 14 - 6 = 8.

What happens to the 0 in the units place when I borrow?

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When you borrow from 0, you actually borrow from the tens place first. The 3 becomes 2, the 0 becomes 10, then you borrow 1 from that 10 for the tenths place, leaving 9 in the units.

How can I check if 17.8 is the right answer?

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Add your answer to the number you subtracted: 17.8+12.6=30.4 17.8 + 12.6 = 30.4 . If you get the original number, your subtraction is correct!

Is there an easier way to do this without borrowing?

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You could think of it as (30+0.4)(12+0.6) (30 + 0.4) - (12 + 0.6) , which equals (3012)+(0.40.6)=18+(0.2)=17.8 (30-12) + (0.4-0.6) = 18 + (-0.2) = 17.8 , but the standard method is more reliable for larger problems.

What if I forget to write the decimal point in my answer?

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Always check your decimal placement! Without the decimal point, 17.8 would become 178, which is clearly wrong since it's much larger than either original number.

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