Question

Write the phrase as an expression. Then simplify the expression.

the product of 8 and a number y multiplied by 9

expression for the phrase:

simplified expression:

Answer 1

The phrase 'the product of 8 and a number y multiplied by 9' is expressed as 9 × 8y and simplified to 72y by multiplying the constants. The expression is checked for reasonableness and confirmed as being logical.

Step-by-step explanation:

First, we need to write the phrase 'the product of 8 and a number y multiplied by 9' as an algebraic expression. The word 'product' signifies multiplication. So, we start by multiplying 8 by a number y, which can be written as 8y. Then, we multiply this product by 9, which gives us the expression 9 × 8y.

To simplify this expression, we multiply the constants together. So, 9 × 8 equals 72. Therefore, the simplified expression is 72y.

Here is the step-by-step breakdown:

1. Write down the expression for the given phrase: 9 × 8y.
2. Simplify the expression by multiplying the numbers: 72y.

Finally, we check if our simplified expression is reasonable. Multiplying the number 8 by the variable y gives a multiple of 8, and then multiplying by 9 should indeed give a multiple of 72 when y is 1, so the expression 72y makes sense.