Add 945 and 45: Vertical Addition Practice

Vertical Addition with Multi-digit Numbers

945+  45776 \begin{aligned} &945 \\ +& \\ &~~45 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:02 Each time we consider joining 2 digits, and then we'll place
00:05 Let's start by combining ones with ones
00:08 We'll place the ones, add 1 to the tens
00:12 We'll combine tens with tens, remember to add 1 to the calculation
00:17 We'll place tens in tens, add 1 to hundreds
00:21 We'll place 0 in the missing digits
00:24 We'll combine hundreds with hundreds, remember to add 1
00:27 We'll place the hundreds in hundreds, add 1 to thousands
00:32 We'll place 0 in the missing digits
00:35 We'll combine thousands with thousands, and place in thousands
00:38 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

945+  45776 \begin{aligned} &945 \\ +& \\ &~~45 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we need to add 945 and 45 using vertical addition. We'll do this step by step:

Step 1: Write both numbers vertically, aligning them by place value:

945+45000 \begin{array}{c} 945 \\ +45 \\ \underline{\phantom{000}} \end{array}

Step 2: Start adding from the rightmost column (the units):

  • Add the units place: 5+5=105 + 5 = 10. Write 0 in the units place and carry over 1 to the next tens place.

1945+45000 \begin{array}{c} &1 \\ 945 \\ +45 \\ \underline{\phantom{00}0} \end{array}

Step 3: Move to the tens place and add, including the carryover:

  • Add tens place: 4+4+1=94 + 4 + 1 = 9. Write 9 in the tens place.

945+45090 \begin{array}{c} 945 \\ +45 \\ \underline{\phantom{0}90} \end{array}

Step 4: Finally, add the hundreds place:

  • Add hundreds place: Since there is no carryover, 9+0=99 + 0 = 9.

945+45990 \begin{array}{c} 945 \\ +45 \\ \underline{990} \end{array}

Therefore, the sum of 945 and 45 is 990 990 .

3

Final Answer

990

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up digits by place value before adding
  • Technique: Add column by column from right: 5+5=10, carry 1
  • Check: Verify 945+45=990 by adding left to right: 900+40+50=990 ✓

Common Mistakes

Avoid these frequent errors
  • Not carrying over properly when sum exceeds 9
    Don't write 10 in the units column when 5+5=10! This gives wrong totals like 94510 instead of 990. Always write the ones digit and carry the tens digit to the next column.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &90 \\ +& \\ &~~9\\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does it mean to 'carry over' a number?

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When two digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column on the left. For example, 5+5=10, so write 0 and carry 1.

Why do I need to line up the numbers by place value?

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Lining up by place value ensures you're adding units to units, tens to tens, etc. If numbers aren't aligned properly, you'll add the wrong digits together and get an incorrect answer.

What if one number has fewer digits than the other?

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That's normal! In this problem, 45 has no hundreds digit, so we treat it as 045. The missing digits are essentially zeros, so 9+0=9 in the hundreds column.

How can I check if my addition is correct?

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Try these methods:

  • Add the numbers in reverse order (45+945)
  • Use estimation: 945 is close to 950, 45 is close to 50, so 950+50=1000 (close to 990)
  • Add left to right: 900+40+50=990 ✓

I keep making carryover mistakes. Any tips?

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Write the carried digit small and above the next column so you don't forget it! Also, practice saying out loud: '5 plus 5 equals 10, write 0 carry 1' to reinforce the process.

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