Solve (9+120)÷3: Order of Operations Division Problem

Q: Why can't I just divide 9 by 3 and 120 by 3 separately?

Because the addition happens first in the numerator! The fraction bar acts like parentheses, so $ \frac{9+120}{3} $ means (9+120) ÷ 3, not 9÷3 + 120÷3.

Q: What's the point of breaking 9 and 120 into multiples of 3?

It's a clever shortcut! When you see $ \frac{3×3 + 40×3}{3} $, you can cancel out the 3's immediately: $ \frac{3×3}{3} + \frac{40×3}{3} = 3 + 40 $

Q: Can I solve this without factoring?

Absolutely! You can add 9 + 120 = 129 first, then divide: $ \frac{129}{3} = 43 $. Both methods give the same answer.

Q: How do I know when to use the factoring method?

Look for common factors! If the numerator terms and denominator share a factor (like 3 in this problem), factoring can make the division much easier.

Q: What if the numbers don't factor nicely?

No problem! Just follow order of operations: add everything in the numerator first, then divide. The factoring method is just a helpful trick when it works.

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

00:06 Let's factor 9 into factors 3 and 3

00:10 Let's factor 120 into factors 40 and 3

00:23 Let's split the fraction into two fractions

00:30 Let's simplify what we can

00:38 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

$\frac{9+120}{3}=$

2

Step-by-step solution

In order to simplify our calculation, we first separate the addition exercise into two smaller multiplication exercises:

$\frac{(3\times3)+(40\times3)}{3}=$ We then split the resulting equation into an addition exercise between fractions:

$\frac{3\times3}{3}+\frac{40\times3}{3}=$

Lastly we reduce the 3 in both the numerator and denominator, and obtain:

$3+40=43$

3

Final Answer

43

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Simplify numerator first, then divide by denominator
Factoring Technique: Break 9 into 3×3 and 120 into 40×3 to simplify
Verification: Check that $\frac{3×3 + 40×3}{3} = 3 + 40 = 43$ ✓

Common Mistakes

Avoid these frequent errors

Dividing each term separately before addition
Don't calculate $\frac{9}{3} + \frac{120}{3}$ as separate steps = breaking the fraction structure! This changes the problem from $\frac{9+120}{3}$ to something completely different. Always add the numerator terms first, then divide the entire sum by the denominator.

Practice Quiz

Test your knowledge with interactive questions

$12:(2\times2)=$

FAQ

Everything you need to know about this question

Why can't I just divide 9 by 3 and 120 by 3 separately?

+

Because the addition happens first in the numerator! The fraction bar acts like parentheses, so $\frac{9+120}{3}$ means (9+120) ÷ 3, not 9÷3 + 120÷3.

What's the point of breaking 9 and 120 into multiples of 3?

+

It's a clever shortcut! When you see $\frac{3×3 + 40×3}{3}$ , you can cancel out the 3's immediately: $\frac{3×3}{3} + \frac{40×3}{3} = 3 + 40$

Can I solve this without factoring?

+

Absolutely! You can add 9 + 120 = 129 first, then divide: $\frac{129}{3} = 43$ . Both methods give the same answer.

How do I know when to use the factoring method?

+

Look for common factors! If the numerator terms and denominator share a factor (like 3 in this problem), factoring can make the division much easier.

What if the numbers don't factor nicely?

+

No problem! Just follow order of operations: add everything in the numerator first, then divide. The factoring method is just a helpful trick when it works.

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Solve (9+120)÷3: Order of Operations Division Problem

Fraction Division with Algebraic Factoring

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