Calculate the Product: 18 × 69 Step-by-Step

Multiplication using Distributive Property

18×69= 18\times69=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this math problem together.
00:07 We'll use the distributive law to make it easier.
00:11 First, think of eighteen as twenty minus two.
00:15 Now, let's write sixty-nine as seventy minus one.
00:20 Great! Open the parentheses correctly.
00:23 Multiply each term in the first set of parentheses by each term in the second set.
00:46 Tackle each multiplication one at a time, and then subtract the results.
01:08 Remember, when you multiply two negative numbers, the result is positive.
01:26 Do the subtraction part first to find the answer.
01:43 And that's how we find the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

18×69= 18\times69=

2

Step-by-step solution

To make it easier for us to solve, let's break down 12 and 19 into more convenient numbers, preferably round ones.

We get:

(202)×(701)= (20-2)\times(70-1)=

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:

(20×70)(20×1)(2×70)(2×1)= (20\times70)-(20\times1)-(2\times70)-(2\times-1)=

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

1,40020140+2= 1,400-20-140+2=

We'll use the associative property and first solve:

20140=160 20-140=160

Now we get:

1,400160+2= 1,400-160+2=

Let's solve from left to right:

1,400160=1,240 1,400-160=1,240

1,240+2=1,242 1,240+2=1,242

3

Final Answer

1242

Key Points to Remember

Essential concepts to master this topic
  • Distributive Rule: (ab)(cd)=acadbc+bd (a-b)(c-d) = ac - ad - bc + bd
  • Technique: Rewrite as (202)×(701) (20-2) \times (70-1) for easier calculation
  • Check: Verify: 140020140+2=1242 1400 - 20 - 140 + 2 = 1242

Common Mistakes

Avoid these frequent errors
  • Incorrect sign handling in distributive property
    Don't write (202)×(701) (20-2) \times (70-1) as 1400201402=1238 1400 - 20 - 140 - 2 = 1238 ! The last term should be positive because (2)×(1)=+2 (-2) \times (-1) = +2 . Always remember: negative times negative equals positive.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why break down 18 and 69 into (20-2) and (70-1)?

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Breaking numbers into round numbers minus small amounts makes mental math much easier! It's easier to work with 20 and 70 than 18 and 69 directly.

What if I forget the distributive property steps?

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Remember FOIL - First, Outer, Inner, Last! Multiply the first terms, then outer, then inner, then last terms from each parentheses.

Why do I get a positive 2 at the end?

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Because (2)×(1)=+2 (-2) \times (-1) = +2 ! When you multiply two negative numbers, the result is always positive. This is a key rule in multiplication.

Can I just multiply 18 × 69 directly without breaking it down?

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Yes, you can use traditional multiplication or a calculator! The distributive method is just one strategy that helps with mental math and understanding number relationships.

How do I know which way to break down the numbers?

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Look for ways to create round numbers (like 10, 20, 50, 70) that are close to your original numbers. The goal is to make the arithmetic easier!

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