Solve Addition Problem: Computing 133 + 30

Two-Digit Addition with Place Value Decomposition

133+30= 133+30=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's use the distribution law
00:07 Let's break down 133 into 100 plus 33
00:16 Let's break down 33 into 30 plus 3
00:25 Let's use the commutative law and arrange the exercise in a convenient way to solve
00:41 Let's solve one addition operation at a time
00:54 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

133+30= 133+30=

2

Step-by-step solution

In order to solve the question, we first use the distributive property for 133:

(100+33)+30= (100+33)+30=

We then use the distributive property for 33:

100+30+3+30= 100+30+3+30=

We rearrange the exercise into a more practical form:

100+30+30+3= 100+30+30+3=

We solve the middle exercise:

30+30=60 30+30=60

Which results in the final exercise as seen below:

100+60+3=163 100+60+3=163

3

Final Answer

163

Key Points to Remember

Essential concepts to master this topic
  • Decomposition: Break numbers into hundreds, tens, and ones for easier addition
  • Technique: Regroup: 133 + 30 becomes 100 + 30 + 30 + 3
  • Check: Count by tens from 133: 143, 153, 163 ✓

Common Mistakes

Avoid these frequent errors
  • Adding digits in wrong place values
    Don't add 3 + 3 = 6 in the hundreds place = 600! This confuses place values and creates massive errors. Always align digits by place value: tens with tens, ones with ones.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why break 133 into 100 + 33 instead of just adding normally?

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Breaking numbers apart helps you see the place values clearly! When you separate 133 into 100 + 33, you can easily add the tens (30 + 30 = 60) without confusion.

Can I just line up the numbers and add from right to left?

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Yes! That's another great method called column addition. Line up 133 over 30, add ones first (3 + 0 = 3), then tens (3 + 3 = 6), then hundreds (1 + 0 = 1).

What if I get confused about which digits to add together?

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Remember: place value is key! In 133 + 30, the 3 in the tens place of 133 adds to the 3 in the tens place of 30. The 0 in ones place of 30 adds to the 3 in ones place of 133.

Is there a way to check my answer without doing the problem again?

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Try estimation! Round 133 to 130, so 130 + 30 = 160. Your exact answer of 163 should be close to this estimate, which it is!

Why did the explanation rearrange the numbers?

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Rearranging uses the commutative property - you can add numbers in any order! Putting 100 + 30 + 30 + 3 groups the tens together (30 + 30 = 60) making mental math easier.

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