Calculate the Product: Solving 99 × 19 Step by Step

Multiplication Strategies with Two-Digit Numbers

99×19= 99\times19=

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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 19 into 10 plus 9
00:11 Make sure to multiply the outer factor with each term in parentheses
00:21 Solve the multiplication
00:27 Break down 99 into 90 plus 9 using the distributive law
00:34 Make sure to multiply the outer factor with each term in parentheses
00:44 Solve each multiplication separately and then add
00:58 Use long addition
01:13 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

99×19= 99\times19=

2

Step-by-step solution

To make it easier for us to solve, we will use the divisibility rule by 19:

99×(10+9)= 99\times(10+9)=

Let's multiply 99 by each term in parentheses:

(99×10)+(99×9)= (99\times10)+(99\times9)=

Let's solve the expression in the first parentheses:

990+(99×9)= 990+(99\times9)=

We'll separate the expression in parentheses in a way that uses the divisibility rule by 99:

990+(90+9)×9= 990+(90+9)\times9=

Let's multiply 9 by each term in parentheses and we get:

990+(90×9)+(9×9)= 990+(90\times9)+(9\times9)=

Let's solve each of the expressions in parentheses:

990+810+81= 990+810+81=

Let's solve the expression from left to right.

We'll solve the left expression by adding vertically:

990+810 990\\+810\\

We'll make sure to follow the correct order when solving the expression, ones with ones, tens with tens, and so on, and we get:

1,800 1,800

Now we get the expression:

1,800+81=1,881 1,800+81=1,881

3

Final Answer

1881 1881

Key Points to Remember

Essential concepts to master this topic
  • Distributive Property: Break down numbers into easier parts to multiply
  • Technique: Split 19 into (10 + 9), then 99 × 10 = 990 and 99 × 9 = 891
  • Check: Add partial products: 990 + 891 = 1,881 matches our answer ✓

Common Mistakes

Avoid these frequent errors
  • Incorrectly calculating 99 × 9
    Don't rush through 99 × 9 = 811 instead of 891! This happens when you miscalculate (90 × 9) + (9 × 9) = 810 + 81. Always double-check each step: 90 × 9 = 810, then 9 × 9 = 81, so 810 + 81 = 891.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why break 19 into 10 + 9 instead of using standard multiplication?

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Breaking numbers apart using the distributive property makes calculations easier! 99×10=990 99 \times 10 = 990 is simple, and 99×9 99 \times 9 can be calculated step by step.

How do I remember to add all the partial products correctly?

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Write down each step clearly: 99×10=990 99 \times 10 = 990 and 99×9=891 99 \times 9 = 891 . Then add: 990 + 891 = 1,881. Don't skip the intermediate steps!

Can I use this method for other two-digit multiplications?

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Absolutely! For any multiplication like a×bc a \times bc , you can split it into a×(b0+c)=(a×b0)+(a×c) a \times (b0 + c) = (a \times b0) + (a \times c) . This works great for mental math!

What if I get a different answer when I check my work?

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Go back and recalculate each partial product separately. The most common errors happen in 99×9 99 \times 9 or when adding the final results together.

Is there a faster way to calculate 99 × 19?

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Yes! Think of 99 as (100 - 1), so 99×19=(1001)×19=190019=1881 99 \times 19 = (100 - 1) \times 19 = 1900 - 19 = 1881 . Both methods give the same answer!

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