Question

Use properties of rational numbers to simplify the expression. 29/4 + 34/7 + 39/4

Answer 1

To simplify the expression \(\frac{29}{4} + \frac{34}{7} + \frac{39}{4}\), we can first combine the fractions with the same denominator and then add them all together.

1. Combine the fractions with a common denominator. The fractions \(\frac{29}{4}\) and \(\frac{39}{4}\) have the same denominator, so we can add them directly:
\[
\frac{29}{4} + \frac{39}{4} = \frac{29 + 39}{4} = \frac{68}{4}
\]

2. Now simplify \(\frac{68}{4}\):
\[
\frac{68}{4} = 17
\]

3. Now we need to add \(\frac{34}{7}\) to the result:
\[
17 + \frac{34}{7}
\]

To add these together, we convert 17 to a fraction with a denominator of 7:
\[
17 = \frac{17 \times 7}{7} = \frac{119}{7}
\]

4. Now add \(\frac{119}{7} + \frac{34}{7}\):
\[
\frac{119 + 34}{7} = \frac{153}{7}
\]

Thus, the simplified expression is:
\[
\frac{153}{7}
\]

If desired, \(\frac{153}{7}\) can also be expressed as a mixed number:
\[
\frac{153}{7} = 21 \frac{6}{7}
\]

So, the final simplified expression can be written as either \(\frac{153}{7}\) or \(21 \frac{6}{7}\).