Practice with Flashcards or Watch the Video

Understanding the Basics

When multiplying numbers like 40 and 70, the process can be simplified by breaking these numbers into smaller components. For example:

• 40 can be decomposed into 4 × 10.

• 70 can be decomposed into 7 × 10.

Thus, multiplying 40 by 70 is the same as multiplying (4 × 10) by (7 × 10).

Simplifying the Expression

To make multiplication easier, we can reorder the factors due to the commutative property of multiplication (order doesn’t matter in multiplication):

• 40 × 70 becomes 4 × 10 × 7 × 10.

Reordering, we get:

• (4 × 7) × (10 × 10).

Performing the Multiplication

First, multiply the single-digit numbers:

• 4 × 7 = 28.

Next, handle the multiples of 10:

• 10 × 10 = 100.

Combining these results, we get:

• 28 × 100 = 2800.

Thus, 40 × 70 equals 2800.

Another Example

Let’s multiply 90 by 30 using the same method:

• Decompose 90 into 9 × 10.

• Decompose 30 into 3 × 10.

Reorder the factors:

• 90 × 30 becomes 9 × 10 × 3 × 10.

Reordering, we get:

• (9 × 3) × (10 × 10).

Perform the multiplication:

• 9 × 3 = 27.

• 10 × 10 = 100.

Combining these results, we get:

• 27 × 100 = 2700.

Therefore, 90 × 30 equals 2700.

Conclusion

Multiplying multiples of 10 becomes straightforward when you break down the numbers and use the pattern of adding zeros. Practice with our flashcards and watch the Khan Academy video to become proficient at this technique.