Exam 1: Some Basic Concepts of Arithmetic and Algebra

Simplify the numerical expression below. $17 + 7 \cdot 9$

Find the greatest common factor of the numbers below. 174, 222 and 66

Simplify the numerical expression below. $-$ 42(63) $-$ 42(30)

Find the quotient of the numbers below (divide). $\frac { - 174 } { - 6 }$

Use the divisibility rules to help determine the prime factorization of the following number. For example, $18 = 2 \cdot 3 \cdot 3$ . 38 = __________

Fill in the blanks with a pair of numbers that has the indicated product and the indicated sum. For example, $\frac { 8 } { 5 } \cdot \frac { 5 } { 2 } = 40$ and $\underline { 8 } + \underline { 5 } = 13$ . $- { } _ { - } = 18$ and $- ^ { + } - = 11$

Find the following sum. $-$ 10 + ( $-$ 15)

Factor the composite number 90 into a product of prime numbers, for example $30 = 2 \cdot 3 \cdot 5$ .

Use the number line interpretation to find the sum. 16 + ( $-$ 17)

Simplify the numerical expression below. $10 \cdot 17 \cdot 16 \div 8 + 12$

Use the distributive property to rewrite the simplified expression below. 5(9 + 4) Do not evaluate the expression, just remove the parentheses.

Subtract as indicated below. $-$ 37 $-$ 41

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. -13 -19

Find the sum below. $-$ 1 + ( $-$ 15)

The absolute value of 0 does not exist.

Find the least common multiple of the numbers below. 76, 20 and 28

Simplify the numerical expression below. $- 6 ( - 3 ) + 12 - 7 ( - 4 ) - 15 + 8 ( - 7 )$

Find the least common multiple of the numbers below. 21 and 57

Use the number line interpretation to find the sum. 10 + ( $-$ 13)

Simplify the algebraic expression below by combining similar terms. $-$ 21( x + 8) $-$ 25( x + 26) + 14( x + 20)