Final answer:
A real-world application of the distributive property is calculating the total number of plants a gardener would plant if she had multiple rows with a fixed number of two types of flowers in each. The distributive property simplifies multiplication across the sum of the two different flower counts.
Step-by-step explanation:
Imagine a gardener who needs to plant 12 rows of flowers, with each row having both tulips and roses. If she plants 5 tulips and 7 roses in every row, the distributive property can be used to find the total number of tulips and roses planted. The total can be calculated using the expression 12 × (5 + 7). Using the distributive property, this can be written as (12 × 5) + (12 × 7). Thus, the gardener plants a total of 60 tulips and 84 roses, which simplifies to 144 flowers.
Multiplication or division by the same number on both sides of an equation does not change equality. This is demonstrated when dealing with displacements in physics, where the distributive property simplifies the calculation of multiple displacement changes in position when vectors are involved.