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Simplifying (rac{2}{9} + rac{7}{12}) + rac{5}{12}
Simplify the expression (rac{2}{9} + rac{7}{12}) + rac{5}{12} by using the associative property of addition to group the terms with identical denominators.
The second and third terms both have a denominator of . Change the grouping to pair them together:
rac{2}{9} + (rac{7}{12} + rac{5}{12})
Perform the addition within the parentheses:
rac{2}{9} + (rac{12}{12})
Simplify the resulting fraction to :
Add to get a mixed number:
1 rac{2}{9}
Finally, convert the mixed number to an improper fraction:
0
1
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OpenStax
Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Algebra
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The equation shows the associative property of addition.
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Name the property shown and write its name:
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An inventory clerk at a logistics center is calculating the total weight of three packages using the expression (rac{2}{9} + rac{7}{12}) + rac{5}{12} tons. To simplify the mental calculation, the clerk regroups the terms as rac{2}{9} + (rac{7}{12} + rac{5}{12}). Which mathematical property justifies this regrouping?
A payroll specialist is tallying fractional hours spent on three different project phases, initially calculated as . True or False: By changing the grouping to combine the fractions with identical denominators first, the specialist simplifies the problem to the intermediate step .
A logistics coordinator at a shipping center needs to find the total weight of three packages. The weights are given by the expression (rac{2}{9} + rac{7}{12}) + rac{5}{12} kilograms. Arrange the following steps in the correct order to simplify this expression by regrouping the terms with identical denominators.
A project supervisor is calculating the total weight of three components measured in tons using the expression (rac{2}{9} + rac{7}{12}) + rac{5}{12}. To simplify the mental math, the supervisor regroups the terms to add and first. This specific sum, , simplifies to the whole number ____.
A logistics coordinator is calculating the total weight of three cargo crates in tons using the expression (rac{2}{9} + rac{7}{12}) + rac{5}{12}. Match each part of the simplification process with its corresponding mathematical role or resulting value.
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