Is the product of 15 and [tex]$\frac{2}{3}$[/tex] more or less than 15? Explain your answer in complete sentences.
Answer (2)
The product of 15 and 3 2 is 10, which is less than 15. Thus, the product is less than 15. The final conclusion is that 10 is less than 15.
;
Calculate the product of 15 and 3 2 : 15 × 3 2 = 10 .
Compare the product (10) with 15.
Since 10 < 15 , the product is less than 15.
The product of 15 and 3 2 is less than 15 .
Explanation
Problem Analysis We are asked to determine if the product of 15 and 3 2 is more or less than 15. To do this, we need to calculate the product and then compare it to 15.
Calculating the Product First, let's calculate the product of 15 and 3 2 .
15 × 3 2 = 3 15 × 2 = 3 30 = 10
The result of the multiplication is 10.
Comparison Now, we compare the result, 10, with the original number, 15. Since 10 is less than 15, the product of 15 and 3 2 is less than 15.
Final Answer Therefore, the product of 15 and 3 2 is less than 15.
Examples
Understanding whether multiplying by a fraction increases or decreases a number is useful in many real-life situations. For example, if a store offers a discount of 4 1 on an item, you know that the new price will be less than the original price. Similarly, if you are scaling a recipe and need to use 3 2 of the original amount of an ingredient, you know you'll be using less of that ingredient than the recipe originally called for. These concepts are also important in understanding proportions and ratios, which are fundamental in fields like cooking, construction, and finance.
