complete the following by using the cancellation technique

3/4 x 2/4 x 6/9

Reduce first:

3/4 * 1/2 * 2/3
Write them side by side and cross simplify
You can cross out the 3's and write 1's and you can cross out the 2's and write 1's
Now you are left with
1*1*1/4*1*1=1/4

To simplify the expression 3/4 x 2/4 x 6/9 using the cancellation technique, follow these steps:

Step 1: Look for common factors in the numerators and denominators.
In the given expression, the numerator of the first fraction (3/4) cannot be canceled with any of the other denominators.
However, the denominator of the second fraction (2/4) can be canceled with the numerator of the third fraction (6/9).

Step 2: Simplify the expression by canceling out the common factor.
Simplify 2/4 and 6/9 by dividing both the numerator and denominator by their greatest common factor.
The greatest common factor of 2 and 4 is 2, so divide both by 2 to get 1/2.
The greatest common factor of 6 and 9 is 3, so divide both by 3 to get 2/3.

Step 3: Multiply the remaining fractions.
Now that the expression has been simplified, multiply the remaining fractions: 3/4 x 1/2 x 2/3.

Step 4: Multiply the numerators together.
Multiply the numerators (3 x 1 x 2) to get 6.

Step 5: Multiply the denominators together.
Multiply the denominators (4 x 2 x 3) to get 24.

Step 6: Write the simplified fraction.
The simplified fraction is 6/24.

Step 7: Further simplify the fraction, if possible.
To simplify the fraction 6/24, find the greatest common factor of 6 and 24, which is 6.
Divide both the numerator and denominator by 6 to get the simplified fraction: 1/4.

Therefore, by using the cancellation technique, the expression 3/4 x 2/4 x 6/9 simplifies to 1/4.

To complete the multiplication using the cancellation technique, follow these steps:

1. Simplify each fraction individually (if possible):

3/4 cannot be simplified further.
2/4 can be simplified to 1/2 by canceling out the common factor of 2.
6/9 can be simplified to 2/3 by canceling out the common factor of 3.

2. Multiply the simplified fractions together:

3/4 x 1/2 x 2/3

3. Multiply the numerators (top numbers) together:

3 x 1 x 2 = 6

4. Multiply the denominators (bottom numbers) together:

4 x 2 x 3 = 24

5. Write the product as a fraction:

6/24

6. Simplify the fraction, if possible. In this case, the fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 6:

6 ÷ 6 / 24 ÷ 6 = 1/4

So, the final result of the multiplication using the cancellation technique is 1/4.