Question

Without completing the actual multiplication, determine whether the product of 14.2 and 0.8 will be larger or smaller than 14.2. Use complete sentences to explain your answer.

A. The product will be smaller than 14.2 because multiplying by a number less than 1 reduces the value.
B. The product will be larger than 14.2 because multiplying by a decimal increases the value.
C. The product will be exactly 14.2 because multiplying by 0.8 has no effect on the value.
D. It is impossible to determine the result without completing the multiplication.

Answer 1

The product of 14.2 multiplied by 0.8 will be smaller than 14.2 because multiplying by any number less than 1 always results in a smaller value.

to whether the product of 14.2 and 0.8 will be larger or smaller than 14.2 is: The product will be smaller than 14.2.

When you multiply a number by a value smaller than 1, the result will always be less than the original number. Since 0.8 is less than 1, multiplying 14.2 by 0.8 will reduce the original value of 14.2. Think of it as taking 80% of 14.2, which is less than 100% of it, hence it will definitely yield a smaller product. You do not have to multiply the numbers to see this; it's a basic principle of multiplication.

understanding this rule of multiplication is crucial: multiplying by a number less than one will decrease the original number, thus making the product smaller than the number you started with.