Question

Work out the following problems using the Distributive, Associative, or Commutative property. Identify which property or properties you used with each problem.

1.1 1/3 × 2 1/3 × 3
a) Distributive
b) Associative
c) Commutative
d) None of the above

Answer 1

To solve 1 1/3 × 2 1/3 × 3, we can use the associative property to regroup and simplify the expression, resulting in the answer 9 1/3.

Step-by-step explanation:

When tackling the problem 1 1/3 × 2 1/3 × 3, we can apply either the associative or commutative property of multiplication. Both of these properties can help us simplify and perform the calculation efficiently. First, let's convert the mixed numbers to improper fractions to make the multiplication easier:

1 1/3 becomes 4/3 and 2 1/3 becomes 7/3.

The expression can now be written as (4/3 × 7/3) × 3. Using the associative property, which allows us to change the grouping of the factors without changing the result, we can regroup and multiply 7/3 by 3 first, as it simplifies easily:

(4/3 × (7/3 × 3) = (4/3 × 7) = 28/3,

which is the same as 9 1/3 when converted back to a mixed number.

Therefore, by using the associative property, we have worked out the following problem and identified the property used.