Solve the Two-Digit Multiplication: 29 × 28

Distributive Property with Two-Digit Factorization

Which expression is the exercise 29X28 equal to?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the expression representing the correct factoring of the exercise
00:03 Let's use the distributive law
00:07 Let's break down 29 to 30 minus 1
00:12 Let's multiply each factor and then subtract
00:32 Let's solve the multiplication and find the expression
00:35 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

Which expression is the exercise 29X28 equal to?

2

Step-by-step solution

We begin by breaking down 29 into a subtraction exercise:

(301)×28= (30-1)\times28=

We then multiply each term inside the parentheses by 28 and we obtain the following:

30×281×28= 30\times28-1\times28=

Let's observe the multiplication exercise on the right and remember that each term multiplied by 1 is equal to the term itself.

That is:

30×2828 30\times28-28

3

Final Answer

30X28 less 28

Key Points to Remember

Essential concepts to master this topic
  • Factor Method: Rewrite 29 as (30-1) to use distributive property
  • Technique: (301)×28=30×281×28 (30-1) \times 28 = 30 \times 28 - 1 \times 28
  • Check: Verify that 30×2828=84028=812 30 \times 28 - 28 = 840 - 28 = 812

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting when distributing
    Don't write (30-1) × 28 = 30 × 28 + 28 = 868! This ignores the negative sign in the factorization. Always remember that (30-1) × 28 means you subtract 1 × 28 from 30 × 28.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why break 29 into 30-1 instead of other combinations?

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Breaking 29 into 30-1 makes multiplication easier because 30 is a round number! You could use 20+9, but multiplying by 30 is much simpler than multiplying by awkward numbers.

How does the distributive property work here?

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The distributive property says a(bc)=abac a(b-c) = ab - ac . So (301)×28=30×281×28 (30-1) \times 28 = 30 \times 28 - 1 \times 28 . We distribute the 28 to both terms inside the parentheses.

What if I just multiply 29 × 28 directly?

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That works too! But this question is testing whether you understand equivalent expressions. The factorization method shows you can break complex multiplication into easier steps.

Why is 1 × 28 just equal to 28?

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The multiplicative identity property states that any number times 1 equals itself. So 1×28=28 1 \times 28 = 28 , making our final expression 30×2828 30 \times 28 - 28 .

How do I know which answer choice is correct?

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Look for the expression that matches your factorization: 30×2828 30 \times 28 - 28 . The correct answer shows 30×28 less 28, which means subtraction.

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