Solve 122×12÷4: Two-Step Arithmetic Operation

Q: Should I multiply 122×12 first or divide 12÷4 first?

Great question! Since multiplication and division have equal priority, work from left to right. So multiply 122×12 = 1,464, then divide by 4. Or use the fraction method: $ 122\times\frac{12}{4} = 122\times3 $.

Q: Why does the explanation break down 122 into (100+20+2)?

This uses the distributive property to make mental math easier! Instead of calculating 122×3 directly, you can do $ (100+20+2)\times3 = 300+60+6 $, which is often simpler to compute.

Q: Is 122×12÷4 the same as 122×(12÷4)?

Yes, in this case! Since 12÷4 = 3, both give 122×3 = 366. However, be careful - this only works when the division gives a clean result. Always follow proper order of operations.

Q: What if I get confused about order of operations?

Remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). When you see multiplication and division together, just go left to right!

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 break down 122 into 100 plus 20 plus 2

00:14 Convert division to fraction

00:25 Calculate 12 divided by 4

00:29 Multiply the outer factor with each factor in parentheses

00:44 Solve each multiplication separately and then sum

01:06 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

$122\times12:4=$

2

Step-by-step solution

First, we break down 122 into smaller numbers and write the division exercise in the form of a fraction:

$(100+20+2)\times\frac{12}{4}=$

We solve the fraction exercise:

$(100+20+2)\times3=$

We then multiply the terms inside the parentheses by 3 and obtain the following result:

$(100\times3)+(20\times3)+(2\times3)=$

Lastly we solve each of the exercises inside of the parentheses:

$300+60+6=366$

3

Final Answer

366

Key Points to Remember

Essential concepts to master this topic

Order Rule: Follow PEMDAS - multiplication and division from left to right
Technique: Convert division to fraction: $122\times12\div4 = 122\times\frac{12}{4}$
Check: Verify: $122\times3 = 300+60+6 = 366$ ✓

Common Mistakes

Avoid these frequent errors

Solving multiplication and division in wrong order
Don't solve 122÷4 first then multiply by 12 = 122÷4×12 = 30.5×12 = 366! Wait, that's coincidentally correct, but the proper method is left-to-right. Don't solve 122×12÷4 as 122×(12÷4) = 122×3 without understanding why. Always follow left-to-right order or convert division to fraction multiplication.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Should I multiply 122×12 first or divide 12÷4 first?

+

Great question! Since multiplication and division have equal priority, work from left to right. So multiply 122×12 = 1,464, then divide by 4. Or use the fraction method: $122\times\frac{12}{4} = 122\times3$ .

Why does the explanation break down 122 into (100+20+2)?

+

This uses the distributive property to make mental math easier! Instead of calculating 122×3 directly, you can do $(100+20+2)\times3 = 300+60+6$ , which is often simpler to compute.

Is 122×12÷4 the same as 122×(12÷4)?

+

Yes, in this case! Since 12÷4 = 3, both give 122×3 = 366. However, be careful - this only works when the division gives a clean result. Always follow proper order of operations.

What if I get confused about order of operations?

+

Remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). When you see multiplication and division together, just go left to right!

How can I check if 366 is correct?

+

Work backwards! If 366÷4 = 91.5, and 91.5÷12 ≈ 7.6, that doesn't equal 122. Better method: $\frac{366}{122} = 3$ , and $\frac{12}{4} = 3$ ✓

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Solve 122×12÷4: Two-Step Arithmetic Operation

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