Calculate the Product: Solving 12×19 Step by Step

Multiplication with Distributive Property

12×19= 12\times19=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve the problem together.
00:07 We'll use the distributive property.
00:10 Break 12 into 10 plus 2.
00:16 Break 19 into 10 plus 9.
00:19 Open parentheses carefully.
00:27 Multiply each term in the first parentheses by each term in the second.
00:47 Add the results from the multiplication.
01:11 Add each sum step by step.
01:29 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12×19= 12\times19=

2

Step-by-step solution

To make solving easier, let's break down 12 and 19 into more convenient numbers, preferably round numbers.

We get:

(10+2)×(10+9)= (10+2)\times(10+9)=

We'll use the distributive property to solve.

First, we'll multiply the first term in the left parentheses by the first term in the right parentheses.

We'll multiply the first term in the left parentheses by the second term in the right parentheses.

We'll multiply the second term in the left parentheses by the first term in the right parentheses.

We'll multiply the second term in the left parentheses by the second term in the right parentheses.

We get:

(10×10)+(10×9)+(2×10)+(2×9)= (10\times10)+(10\times9)+(2\times10)+(2\times9)=

Let's solve what's in the parentheses and we get:

100+90+20+18= 100+90+20+18=

Let's solve from left to right:

190+20+18=210+18=228 190+20+18=210+18=228

3

Final Answer

228

Key Points to Remember

Essential concepts to master this topic
  • Rule: Break down numbers into parts that are easier to multiply
  • Technique: Use (a+b)(c+d)=ac+ad+bc+bd (a+b)(c+d) = ac + ad + bc + bd pattern
  • Check: Add all four products: 100 + 90 + 20 + 18 = 228 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting one of the four multiplication steps
    Don't skip any products when using (10+2)(10+9) (10+2)(10+9) = wrong answer like 210! Missing even one multiplication (like 2×9) gives an incorrect result. Always multiply each term in the first parentheses by each term in the second parentheses.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why break 12 and 19 into smaller parts?

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Breaking numbers into tens and ones makes mental math easier! It's much simpler to multiply 10×10 than to memorize 12×19 directly.

Do I have to use 10+2 and 10+9?

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No! You could use other combinations like (6×2)(201) (6×2)(20-1) , but tens plus ones is usually the easiest method to work with.

What if I get the four products mixed up?

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Write them in order: first×first, first×second, second×first, second×second. For (10+2)(10+9) (10+2)(10+9) : 10×10, 10×9, 2×10, 2×9.

Is this faster than just memorizing 12×19?

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For problems you see often, memorizing helps! But this method works for any two-digit multiplication and helps you understand why multiplication works.

What if I make an adding mistake at the end?

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Double-check by adding in a different order: 100+20=120 100+20=120 , 90+18=108 90+18=108 , then 120+108=228 120+108=228 . Same answer = correct!

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