Solve Division Problem: 102 ÷ 2 Step-by-Step

Q: Why split 102 into 100+2 instead of other combinations?

We choose 100+2 because both numbers divide evenly by 2! You could use 90+12 or 80+22, but 100÷2=50 and 2÷2=1 are the easiest mental calculations.

Q: What if I can't split the number easily?

Look for multiples of your divisor! When dividing by 2, try to include numbers like 10, 20, 100. When dividing by 3, use 30, 60, 90. This makes the math much simpler.

Q: Is this method faster than long division?

For mental math, absolutely! The distributive property lets you solve $ 102÷2 $ in your head without writing anything down. It's especially helpful for larger numbers.

Q: How do I check if my splitting is correct?

Make sure your parts add up to the original number! In this case: 100+2=102 ✓. Then verify each part divides evenly by your divisor.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's use the distributive law

00:07 Break down 100 to 100 plus 2

00:14 Divide each factor separately

00:24 Solve each division and then sum

00:32 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

Solve the following exercise:

=102:2

2

Step-by-step solution

Apply the distributive property of division and proceed to split the number 102 into a sum of 100 and 2. This ultimately renders the division operation easier and allows us to solve the exercise without a calculator.

Note - it's best to choose to split the number based on knowledge of multiples. In this case of the digit 2 because we need to divide by 2. Additionally, in this case, splitting by tens and ones is suitable and makes the division operation easier.

Reminder - The distributive property of division essentially allows us to split the larger term in the division problem into a sum or difference of smaller numbers, which makes the division operation easier and gives us the ability to solve the exercise without a calculator

We will use the formula of the distributive property

$(a+b):c=a:c+b:c$

$102:2=(100+2):2$

$(100+2):2=100:2+2:2$

$100:2+2:2=50+1$

$50+1=51$

Therefore the answer is section a - 51.

3

Final Answer

51

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Split dividend into easier parts: $(a+b):c = a:c + b:c$
Technique: Break 102 into 100+2, then divide each: 100÷2 + 2÷2
Check: Multiply answer by divisor: 51 × 2 = 102 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of maintaining division operation
Don't write 102÷2 as 100÷2 + 2 = 50+2 = 52! This ignores that the 2 must also be divided by 2. Always divide each part separately: 100÷2 + 2÷2 = 50 + 1 = 51.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why split 102 into 100+2 instead of other combinations?

+

We choose 100+2 because both numbers divide evenly by 2! You could use 90+12 or 80+22, but 100÷2=50 and 2÷2=1 are the easiest mental calculations.

What if I can't split the number easily?

+

Look for multiples of your divisor! When dividing by 2, try to include numbers like 10, 20, 100. When dividing by 3, use 30, 60, 90. This makes the math much simpler.

Is this method faster than long division?

+

For mental math, absolutely! The distributive property lets you solve $102÷2$ in your head without writing anything down. It's especially helpful for larger numbers.

Does this work with any division problem?

+

Yes, but it's most helpful when you can split the dividend into parts that divide evenly. For problems like 127÷3, traditional long division might be easier.

How do I check if my splitting is correct?

+

Make sure your parts add up to the original number! In this case: 100+2=102 ✓. Then verify each part divides evenly by your divisor.

What if I get different remainders in each part?

+

That's fine! Just add the remainders together at the end. For example: $(30+5)÷4 = 30÷4 + 5÷4 = 7R2 + 1R1 = 8R3$

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Solve Division Problem: 102 ÷ 2 Step-by-Step

Division with Distributive Property

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