Question

evaluate each expression. then circle whether the answer is prime or composite.
19+(13×6)=____
(58 + 74)÷11=____
compare each expression using >, <, or =.
find the unknown measure of the rectangle.
then find the perimeter.
7 cm
prime composite
prime composite

Explanation:

Step1: Calculate \(19+(13\times6)\)

First, calculate the multiplication inside the parentheses: \(13\times6 = 78\).
Then, add \(19\) to the result: \(19 + 78=97\).
Check if \(97\) is prime. A prime number has only two distinct positive divisors: \(1\) and itself.
Test divisibility for numbers less than \(\sqrt{97}\approx9.85\).
Check divisibility by \(2\): \(97\) is odd.
Check divisibility by \(3\): \(9 + 7=16\), \(16\) is not divisible by \(3\).
Check divisibility by \(5\): Does not end in \(0\) or \(5\).
Check divisibility by \(7\): \(97\div7\approx13.86\). So \(97\) is prime.

Step2: Calculate \((58 + 74)\div11\)

First, calculate the sum inside the parentheses: \(58+74 = 132\).
Then, divide by \(11\): \(132\div11 = 12\).
Check if \(12\) is prime. \(12=2\times6=3\times4\), so it has more than two positive divisors. Thus, \(12\) is composite.

Answer:

\(19+(13\times6)=97\) (prime), \((58 + 74)\div11=12\) (composite)