Solve the Division Problem: 224 ÷ 16

Q: Why break 224 into 160 + 64 specifically?

These numbers are multiples of 16! Since 160 = 16 × 10 and 64 = 16 × 4, they divide evenly. This makes the calculation much easier: $ 160 ÷ 16 + 64 ÷ 16 = 10 + 4 = 14 $

Q: What if I can't find good numbers to split with?

Look for multiples of your divisor! For dividing by 16, think of numbers like 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, etc. Pick the largest ones that add up to your dividend.

Q: Is this method always faster than long division?

For mental math, yes! Breaking numbers into friendly parts is much faster than writing out long division steps. Plus, you're less likely to make arithmetic errors.

Q: Can I break the number into more than two parts?

Absolutely! You could write $ 224 = 160 + 48 + 16 $ or other combinations. The key is making sure all parts are divisible by 16.

Q: How do I check my answer is correct?

Multiply your answer by the divisor: $ 14 × 16 = 224 $. If you get back to your original number, you're right! This is called inverse operations.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's begin by solving a math problem.

00:09 We'll use the distributive property. Ready?

00:13 First, split 224 into 160 plus 64.

00:19 Next, divide each number by the factor outside the parentheses, then add them.

00:24 Now, do each division separately, and then sum them up.

00:28 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following division exercise:

$224:16=$

2

Step-by-step solution

Begin by applying the division distributive law in order to split the number 224 into the sum of 160 and 64. This ultimately simplifies the division operation allowing us to solve the exercise without a calculator

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

$(160+64):16=$

Apply the formula of the distributive law $(a+b):c=a:c+b:c$

Continue to solve according to the order of operations

$10+4=14$

Therefore the answer is option B - 14.

Shown below are the various steps of the solution

$224:16=(160+64):6=160:16+64:16=10+4=14$

3

Final Answer

$14$

Key Points to Remember

Essential concepts to master this topic

Distributive Law: Split dividend into sum of easier divisible numbers
Technique: Break 224 into 160 + 64, both divisible by 16
Check: Verify 14 × 16 = 224 to confirm answer ✓

Common Mistakes

Avoid these frequent errors

Dividing incorrectly without breaking down numbers
Don't just guess or use long division immediately = errors and confusion! Large numbers are harder to divide mentally. Always break the dividend into friendly numbers that divide evenly first.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why break 224 into 160 + 64 specifically?

+

These numbers are multiples of 16! Since 160 = 16 × 10 and 64 = 16 × 4, they divide evenly. This makes the calculation much easier: $160 ÷ 16 + 64 ÷ 16 = 10 + 4 = 14$

What if I can't find good numbers to split with?

+

Look for multiples of your divisor! For dividing by 16, think of numbers like 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, etc. Pick the largest ones that add up to your dividend.

Is this method always faster than long division?

+

For mental math, yes! Breaking numbers into friendly parts is much faster than writing out long division steps. Plus, you're less likely to make arithmetic errors.

Can I break the number into more than two parts?

+

Absolutely! You could write $224 = 160 + 48 + 16$ or other combinations. The key is making sure all parts are divisible by 16.

How do I check my answer is correct?

+

Multiply your answer by the divisor: $14 × 16 = 224$ . If you get back to your original number, you're right! This is called inverse operations.

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Solve the Division Problem: 224 ÷ 16

Division Using Distributive Law

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