Exam 1: Some Basic Concepts of Arithmetic and Algebra

State the property that justifies the statement. For example, $3 + ( - 4 ) = ( - 4 ) + 3$ because of the commutative property for addition. $- 3 + ( 9 - 2 ) = ( - 3 + 9 ) - 2$

Find the quotient of the numbers below (divide). $( - 84 ) \div 6$

Use the divisibility rules to help determine the prime factorization of the given number. For example, $18 = 2 \cdot 3 \cdot 3$ . 770 = __________

Zero divided by zero is 1.

Find the least common multiple of the numbers below. 114, 66 and 30

The factors of a number are also divisors of the number.

Evaluate the algebraic expression for the given values of the variables for m = 11 and q = $-$ 4. $m + 10 q + 7 m q$

Find the greatest common factor of the numbers below. 51, 87 and 69

Simplify the numerical expression below. $-$ 72( $-$ 7 $-$ 43)

Simplify the numerical expression below. $15 + 5 [ 8 ( 12 - 10 ) ]$

Find the quotient. $\frac { - 144 } { - 12 }$

Subtraction can be done in vertical format. Find the difference. -40 17

Evaluate the algebraic expression for the given values of the variables. $5 ( 2 a - 5 b )$ for $a = - 3$ and $b = - 4$ .

Find the greatest common factor of the following numbers. 52 and 92

The horizontal format is used extensively in algebra, but occasionally the vertical format shows up. You should therefore have some exposure to the vertical format. Find the sum. - 16 - 11

Find the least common multiple of the numbers below. 207, 45 and 153

Find the quotient. $\frac { - 78 } { 6 }$

Subtraction can be done in vertical format. Find the difference. -11 11

Simplify the algebraic expression below, and then evaluate the resulting expression for the given values of the variables. 6 u + 23 k + 5 u $-$ 12 k for u = 2, k = 8

Simplify the algebraic expression below by combining similar terms. $-$ 30 ( x + 27) $-$ 18 ( x + 2) + 4 ( x + 16)