Question

Because of the commutative property of multiplication, it is true that 3/4 x4 = 4 x 3/4 However these expressions can be calculated in different ways even though the solutions will be the same. First show how 3/4 can be solved using repeated addition

Answer 1

To demonstrate how to use repeated addition to represent the multiplication of \( \frac{3}{4} \) and \( 4 \), we can express the multiplication as adding \( \frac{3}{4} \) a certain number of times.

Since \( 4 \) is the number of times we are adding \( \frac{3}{4} \), we can write it as:

\[
\frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}
\]

This means we are adding \( \frac{3}{4} \) four times.

Now, let's calculate that step-by-step:

1. First, add the first two \( \frac{3}{4} \):
\[
\frac{3}{4} + \frac{3}{4} = \frac{3 + 3}{4} = \frac{6}{4}
\]

2. Next, add the next \( \frac{3}{4} \) to the result:
\[
\frac{6}{4} + \frac{3}{4} = \frac{6 + 3}{4} = \frac{9}{4}
\]

3. Finally, add the last \( \frac{3}{4} \):
\[
\frac{9}{4} + \frac{3}{4} = \frac{9 + 3}{4} = \frac{12}{4}
\]

Now we can simplify \( \frac{12}{4} \):
\[
\frac{12}{4} = 3
\]

Thus, using repeated addition, we find that \( \frac{3}{4} \times 4 = 3 \). This matches the result we would obtain using standard multiplication methods.