Question

1. julie has 27 grapes to divide evenly among 3 friends. she thinks there will be no leftovers. use what you know about factor pairs to explain whether or not julie is correct.

Explanation:

Step1: Recall factor pair definition

A factor pair of a number is two factors that multiply to give that number. For \( n \), if \( a \times b = n \), then \( (a,b) \) is a factor pair.

Step2: Find factor pairs of 27

We find pairs of integers that multiply to 27.

• \( 1\times27 = 27 \)
• \( 3\times9 = 27 \)

So factor pairs of 27 are \( (1,27) \), \( (3,9) \).

Step3: Check division by 3

Since 3 is a factor of 27 (from factor pair \( 3\times9 = 27 \)), when we divide 27 by 3, we get \( 27\div3 = 9 \), which is an integer with no remainder.

Answer:

Julie is correct. The factor pairs of 27 include \( (3, 9) \) (since \( 3\times9 = 27 \)). This means 3 is a factor of 27, so dividing 27 grapes evenly among 3 friends (each friend gets \( 27\div3 = 9 \) grapes) results in no leftovers.