Calculate the Product: Solving 27 × 4 × 25 Step by Step

Q: Why should I multiply 4 × 25 first instead of going left to right?

Smart grouping saves time! Since $ 4 \times 25 = 100 $, you get an easy number to work with. Then $ 27 \times 100 $ just means adding two zeros to 27.

Q: What if I already calculated 27 × 4 = 108 first?

No problem! You can still finish correctly. Just calculate $ 108 \times 25 $. Try breaking it down: $ 108 \times 25 = 108 \times (20 + 5) = 2,160 + 540 = 2,700 $.

Q: How do I recognize when numbers multiply to make 100?

Look for factor pairs of 100: 4 × 25, 5 × 20, 10 × 10. These create friendly numbers ending in zeros that are much easier to multiply with!

Q: Can I use this grouping strategy with any multiplication problem?

Yes! The associative property lets you group factors however you want. Always look for combinations that create round numbers like 10, 100, or 1000 first.

Q: What's the fastest way to multiply by 100?

Simply add two zeros to the end of the number! So $ 27 \times 100 = 2,700 $. This works because 100 = 10 × 10, and each 10 adds one zero.

Multiplication Strategies with Strategic Grouping

$27\times4\times25=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:02 We will use the commutative property and solve this multiplication first, then continue

00:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$27\times4\times25=\text{ ?}$

Step-by-step solution

Since we only have a multiplication operation in the exercise, we can solve the easier part first (the right-hand side):

$4\times25=100$

Now we get:

$27\times100=$

This exercise is simple and doesn't require much calculation. Since we are multiplying by 100, the only operation we need to add is two zeros to 27:

$2,700$

Final Answer

$2,700$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplication can be done in any order due to associative property
Technique: Group easier calculations first like $4 \times 25 = 100$
Check: Verify by calculating left to right: $27 \times 4 = 108$ , then $108 \times 25 = 2,700$ ✓

Common Mistakes

Avoid these frequent errors

Calculating from left to right without looking for easier combinations
Don't automatically calculate $27 \times 4 = 108$ first, then struggle with $108 \times 25$ = more complex arithmetic! This makes the problem unnecessarily difficult. Always look for friendly number pairs like $4 \times 25 = 100$ first.

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why should I multiply 4 × 25 first instead of going left to right?

Smart grouping saves time! Since $4 \times 25 = 100$ , you get an easy number to work with. Then $27 \times 100$ just means adding two zeros to 27.

What if I already calculated 27 × 4 = 108 first?

No problem! You can still finish correctly. Just calculate $108 \times 25$ . Try breaking it down: $108 \times 25 = 108 \times (20 + 5) = 2,160 + 540 = 2,700$ .

How do I recognize when numbers multiply to make 100?

Look for factor pairs of 100: 4 × 25, 5 × 20, 10 × 10. These create friendly numbers ending in zeros that are much easier to multiply with!

Can I use this grouping strategy with any multiplication problem?

Yes! The associative property lets you group factors however you want. Always look for combinations that create round numbers like 10, 100, or 1000 first.

What's the fastest way to multiply by 100?

Simply add two zeros to the end of the number! So $27 \times 100 = 2,700$ . This works because 100 = 10 × 10, and each 10 adds one zero.

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