Solve Division Problem: Calculate 458 ÷ 7

Q: What does the fraction 3/7 actually mean?

The fraction $ \frac{3}{7} $ means you have 3 parts out of 7 equal parts. It's the leftover amount that couldn't make another whole group of 7.

Q: How do I know which numbers to use when breaking apart 458?

Look for multiples of 7 that add up to 458! Start with the largest: 420 (7×60), then 35 (7×5), leaving remainder 3. This makes: $ (420+35+3) ÷ 7 $.

Q: Is there an easier way to do this division?

You can use long division directly, but breaking numbers into parts helps you understand what's happening and avoid calculation errors. Both methods give the same answer!

Q: Can I convert the mixed number to an improper fraction?

Yes! $ 65\frac{3}{7} = \frac{(65×7)+3}{7} = \frac{458}{7} $. Both forms are correct, but mixed numbers are often easier to understand.

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 458 into 420 plus 38

00:15 Break down 38 into 35 plus 3

00:24 Divide each factor separately

00:37 Solve each division and then sum

00:47 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

$458:7=$

2

Step-by-step solution

In order to simplify the resolution process, we first separate 458 into a smaller addition exercise and choose numbers that are divisible by 7:

$(420+38):7=$

We then further separate 38 into a smaller addition exercise and choose numbers that are divisible by 7:

$(420+35+3):7=$

We divide each of the terms inside of the parentheses by 7:

$\frac{420}{7}+\frac{35}{7}+\frac{3}{7}=$

Finally we solve the fractions as follows:

$60+5+\frac{3}{7}=65\frac{3}{7}$

3

Final Answer

$65\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: When remainder exists, express as fraction with divisor as denominator
Decomposition Method: Break 458 into parts divisible by 7: (420+35+3)÷7
Check: Verify 65×7+3 = 455+3 = 458 ✓

Common Mistakes

Avoid these frequent errors

Stopping at whole number quotient and ignoring remainder
Don't write just 65 when 458÷7 leaves remainder 3 = incomplete answer! This ignores part of the original number being divided. Always express remainder as fraction: 65 3/7.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just write 65 as my answer?

+

Because 65×7 = 455, not 458! You're missing the remaining 3 that couldn't be divided evenly. The complete answer must include this remainder as $\frac{3}{7}$ .

What does the fraction 3/7 actually mean?

+

The fraction $\frac{3}{7}$ means you have 3 parts out of 7 equal parts. It's the leftover amount that couldn't make another whole group of 7.

How do I know which numbers to use when breaking apart 458?

+

Look for multiples of 7 that add up to 458! Start with the largest: 420 (7×60), then 35 (7×5), leaving remainder 3. This makes: $(420+35+3) ÷ 7$ .

Is there an easier way to do this division?

+

You can use long division directly, but breaking numbers into parts helps you understand what's happening and avoid calculation errors. Both methods give the same answer!

Can I convert the mixed number to an improper fraction?

+

Yes! $65\frac{3}{7} = \frac{(65×7)+3}{7} = \frac{458}{7}$ . Both forms are correct, but mixed numbers are often easier to understand.

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Solve Division Problem: Calculate 458 ÷ 7

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