Calculate the Product: 102 × 11 × 10 Step by Step

Multiplication Order with Distributive Property

102×11×10= 102\times11\times10=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll use the distribution law and divide 102 into a whole number and 'remainder'
00:13 Make sure to multiply each factor
00:29 Solve each multiplication separately and then sum
00:35 This is the first multiplication
00:44 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

102×11×10= 102\times11\times10=

2

Step-by-step solution

According to the order of operations rules, since the exercise has only multiplication operations, we will solve the exercise from left to right.

We will solve the left exercise in the following way, by breaking down 102 into a smaller addition exercise:

(100+2)×11= (100+2)\times11=

Now we'll multiply 11 by each of the numbers in parentheses:

(100×11)+(2×11)= (100\times11)+(2\times11)=

We'll solve each of the exercises in parentheses and get:

1,100+22=1,122 1,100+22=1,122

Now we'll get the exercise:

1,122×10= 1,122\times10=

Since this is a multiplication exercise with a round number ending in 0, we can solve the exercise without calculation by adding a 0 to the number 1,122

It's important to place the comma in the appropriate place, and we'll get the number:

11,220 11,220

3

Final Answer

11220 11220

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Multiply from left to right when only multiplication operations
  • Distributive Method: Break 102 into (100+2)×11 = 1,100+22 = 1,122
  • Round Number Check: Multiplying by 10 adds one zero: 1,122×10 = 11,220 ✓

Common Mistakes

Avoid these frequent errors
  • Adding operations that don't exist
    Don't change 102×11×10 into 102+11+10 = 123! This completely changes the problem from multiplication to addition. Always identify the correct operations (all multiplication here) and work from left to right.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why do I work from left to right instead of right to left?

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The order of operations says when you have only multiplication (or only addition), work left to right. This ensures everyone gets the same answer! You could multiply 11×10 first, but left-to-right is the standard rule.

Is breaking down 102 into 100+2 really necessary?

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Not always, but it makes the calculation much easier! Instead of doing 102×11 in your head, you can do 100×11=1,100 100×11=1,100 and 2×11=22 2×11=22 , then add them.

How do I multiply by 10 without a calculator?

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Multiplying by 10 is easy - just add one zero to the end of the number! So 1,122×10=11,220 1,122×10 = 11,220 . Remember to keep commas in the right places for large numbers.

What if I get a different answer doing it a different way?

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If you follow the order of operations correctly, you should always get the same answer! Try: 102×(11×10)=102×110=11,220 102×(11×10) = 102×110 = 11,220 . Double-check your arithmetic if you get something different.

Can I use the distributive property with other numbers too?

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Absolutely! You can break down any number into easier parts. For example: 98×7=(1002)×7=70014=686 98×7 = (100-2)×7 = 700-14 = 686 . This technique works great for mental math!

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