Solve Division Problem: 65 ÷ 13 Step by Step

Division with Decomposition Strategy

Solve the exercise:

=65:13

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's learn how to solve this problem!
00:07 We'll use the distributive property to help us.
00:11 First, we break down sixty-five into two times twenty-six, plus thirteen.
00:26 Next, we'll divide each of these parts separately.
00:39 Solve each division, then add the results together.
00:51 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the exercise:

=65:13

2

Step-by-step solution

In order to simplify the resolution process, we begin by breaking down the number 65 into a smaller addition exercise.

We choose numbers that are divisible by 13:

(26+26+13):13= (26+26+13):13=

We then divide each of the terms within parentheses by 13:

26:13=2 26:13=2

26:13=2 26:13=2

13:13=1 13:13=1

To finish we add up all of the results that we obtained:

2+2+1=4+1=5 2+2+1=4+1=5

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Break dividend into parts divisible by the divisor
  • Technique: Write 65 as 26 + 26 + 13, all divisible by 13
  • Check: Verify by multiplication: 5 × 13 = 65 ✓

Common Mistakes

Avoid these frequent errors
  • Randomly guessing factors without checking divisibility
    Don't just pick any numbers that add to 65 like 30 + 35 = wrong breakdown! These aren't divisible by 13, so you can't simplify each part. Always choose addends that are multiples of your divisor.

Practice Quiz

Test your knowledge with interactive questions

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FAQ

Everything you need to know about this question

Why break 65 into smaller parts instead of dividing directly?

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The decomposition method makes division easier by using numbers you already know! When you see 26 ÷ 13 = 2 and 13 ÷ 13 = 1, the math becomes much simpler than trying to divide 65 ÷ 13 in your head.

How do I know which numbers to use when breaking down 65?

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Look for multiples of 13 that add up to 65! Think: 13 × 1 = 13, 13 × 2 = 26. Since 26 + 26 + 13 = 65, these work perfectly because each part divides evenly by 13.

What if I can't find good numbers to break down the dividend?

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Start with easy multiples of your divisor! For 65 ÷ 13, try: 13 × 5 = 65. This means you can write it as 13+13+13+13+13 13 + 13 + 13 + 13 + 13 , then divide each 13 by 13 to get 1 + 1 + 1 + 1 + 1 = 5.

Is this method faster than regular long division?

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It depends on the numbers! This method is great for mental math when you can quickly spot multiples. For bigger numbers or when multiples aren't obvious, long division might be more efficient.

Can I use different combinations of numbers that add to 65?

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Yes, but they must all be divisible by 13! You could use 39 + 26 (since 39 = 13 × 3), but avoid combinations like 32 + 33 because these don't divide evenly by 13.

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