Question

1. p/q + (r/s + t/u) = ( p/q + r/s) + t/u . State the property used.

Answer 1

The associative property of addition states that when adding three or more numbers, the grouping of the numbers does not affect the result. In other words, you can regroup the numbers being added without changing the sum.

In the given equation,
`\displaystyle\sf (p)/(q) + \left((r)/(s) + (t)/(u)\right) = \left((p)/(q) + (r)/(s)\right) + (t)/(u)`, we have three fractions being added together:
`\displaystyle\sf (p)/(q)`,
`\displaystyle\sf (r)/(s)`, and
`\displaystyle\sf (t)/(u)`.

According to the associative property of addition, we can choose to group the fractions differently without changing the sum. In this case, we can group
`\displaystyle\sf (p)/(q)` and
`\displaystyle\sf (r)/(s)` together first, and then add
`\displaystyle\sf (t)/(u)` to the sum. Alternatively, we can group
`\displaystyle\sf (r)/(s)` and
`\displaystyle\sf (t)/(u)` together first, and then add
`\displaystyle\sf (p)/(q)` to the sum.

No matter how we choose to group the fractions, the sum remains the same. Therefore, the equation
`\displaystyle\sf (p)/(q) + \left((r)/(s) + (t)/(u)\right) = \left((p)/(q) + (r)/(s)\right) + (t)/(u)` demonstrates the associative property of addition.