A logistics coordinator is calculating the total weight of three small shipments to be loaded onto a delivery truck. The weights are $\frac{7}{15}$ ton, $\frac{5}{8}$ ton, and $\frac{3}{8}$ ton. They write the total as $(\frac{7}{15} + \frac{5}{8}) + \frac{3}{8}$. Which of the following expressions shows the most efficient way to regroup these weights to simplify the calculation by adding the fractions with common denominators first?

A manufacturing supervisor is calculating the total kilograms of raw material used across three assembly lines. The amounts are recorded as $\left(\frac{7}{15} + \frac{5}{8}\right) + \frac{3}{8}$. To quickly find the total without finding a common denominator for all three, the supervisor applies the associative property of addition. Arrange the steps of this simplified calculation in the correct order.

A logistics supervisor is calculating the total weight of three packages: $\frac{7}{15}$ ton, $\frac{5}{8}$ ton, and $\frac{3}{8}$ ton. To find the sum $(\frac{7}{15} + \frac{5}{8}) + \frac{3}{8}$ efficiently, they apply specific rules and identify key intermediate values. Match each element of this simplification process with its correct description.

A logistics supervisor is summing the weights of three cargo shipments: $\frac{7}{15}$ ton, $\frac{5}{8}$ ton, and $\frac{3}{8}$ ton. To make the mental calculation easier, the supervisor rewrites the expression $\left(\frac{7}{15} + \frac{5}{8}\right) + \frac{3}{8}$ as $\frac{7}{15} + \left(\frac{5}{8} + \frac{3}{8}\right)$. This regrouping is an application of the ____ property of addition.

Simplifying Fraction Groups for Efficient Addition

A pharmacy technician is compounding a custom topical cream by combining three active ingredients. The weights of the ingredients are $\frac{7}{15}$ ounce, $\frac{5}{8}$ ounce, and $\frac{3}{8}$ ounce, with the total weight represented by the expression $\left(\frac{7}{15} + \frac{5}{8}\right) + \frac{3}{8}$ ounces.

True or False: According to the associative property of addition, the technician can regroup this calculation as $\frac{7}{15} + \left(\frac{5}{8} + \frac{3}{8}\right)$, which simplifies the expression inside the parentheses to 1 and yields a total weight of ${}1 \frac{7}{15}$ ounces.

Regrouping Cargo Weights with the Associative Property