Calculate the Product: Solving 74 × 8 Step by Step

Q: Why break 74 into 70 + 4 instead of just multiplying directly?

Breaking numbers down makes multiplication much easier! It's simpler to multiply by 70 (7 × 8 = 56, add a zero) than to handle 74 all at once. This method reduces errors too.

Q: Can I break down 74 differently, like 60 + 14?

Yes! You could use $ (60 + 14) \times 8 = 480 + 112 = 592 $. However, using multiples of 10 like 70 + 4 makes mental math much easier.

Q: What if I get different numbers when I break it down?

Double-check your addition! Make sure 70 + 4 actually equals 74, and that your final addition 560 + 32 is correct. Write each step clearly.

Q: Is this the same as the standard algorithm for multiplication?

Yes! This distributive method shows why the standard algorithm works. When you multiply 74 × 8 vertically, you're actually doing $ (70 \times 8) + (4 \times 8) $ step by step.

Q: How do I know which method to use for multiplication?

Use whatever method feels most comfortable! The distributive property is great for mental math, while the standard algorithm works well on paper. Both give the same answer.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use the distributive law

00:07 Let's break down 74 into 70 plus 4

00:10 We'll multiply each factor separately, then add

00:21 We'll solve each multiplication and then sum

00:32 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

$74\times8=$

2

Step-by-step solution

In order to simplify the resolution process, we begin by breaking down the number 74 into a smaller addition exercise.

It is easier to choose round whole numbers, hence the following calculation:

$(70+4)\times8=$

We then multiply each of the terms within the parentheses by 8:

$(8\times70)+(8\times4)=$

Lastly we solve the exercises within the parentheses:

$560+32=592$

3

Final Answer

592

Key Points to Remember

Essential concepts to master this topic

Rule: Use distributive property to break down larger numbers into manageable parts
Technique: Split 74 into 70 + 4, then multiply: (70 × 8) + (4 × 8)
Check: Verify 560 + 32 = 592 by adding step by step ✓

Common Mistakes

Avoid these frequent errors

Multiplying digits separately without proper place value
Don't multiply 7 × 8 = 56 and 4 × 8 = 32, then write 5632! This ignores place value completely. Always recognize that 74 = 70 + 4, so multiply 70 × 8 = 560, then add 4 × 8 = 32.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why break 74 into 70 + 4 instead of just multiplying directly?

+

Breaking numbers down makes multiplication much easier! It's simpler to multiply by 70 (7 × 8 = 56, add a zero) than to handle 74 all at once. This method reduces errors too.

Can I break down 74 differently, like 60 + 14?

+

Yes! You could use $(60 + 14) \times 8 = 480 + 112 = 592$ . However, using multiples of 10 like 70 + 4 makes mental math much easier.

What if I get different numbers when I break it down?

+

Double-check your addition! Make sure 70 + 4 actually equals 74, and that your final addition 560 + 32 is correct. Write each step clearly.

Is this the same as the standard algorithm for multiplication?

+

Yes! This distributive method shows why the standard algorithm works. When you multiply 74 × 8 vertically, you're actually doing $(70 \times 8) + (4 \times 8)$ step by step.

How do I know which method to use for multiplication?

+

Use whatever method feels most comfortable! The distributive property is great for mental math, while the standard algorithm works well on paper. Both give the same answer.

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Calculate the Product: Solving 74 × 8 Step by Step

Multiplication with Distributive Property

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