Foundations

Given the numbers $-3, -\sqrt{2}, 0.\stackrel{-}{3} , \frac{9}{5}, 4,\sqrt{49}$ list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers. 

Locate on the number line: ⓐ $0.9$ ⓑ $-0.75$

Simplify the following expression using the distributive property.

$7\left(3n+9\right)-\left(4n-13\right)$

Is 4,962 divisible by (a) 2 ? (b) 3 ? (c) 5 ? (d) 6 ? (e) 10 ?

Is 3,765 divisible by (a) 2? (b) 3? (c) 5? (d) 6? (e) 10? 

Find the prime factorization of 80. 

Find the prime factorization of 60.

Find the LCM of 9 and 12 using the Prime Factors Method. 

Find the LCM of 18 and 24 using the Prime Factors method.

Simplify $30÷5+10\left(3-2\right)$.

Simplify $70÷10+4\left(6-2\right)$.

Simplify,  $9+5^3-\left[4\left(9+3\right)\right]$.

Simplify $7^2-2\left[4\left(5+1\right)\right]$.

Evaluate when x=3 (a)x²  (b)4^x  (c)3x²+4x+1

Evaluate when x=3 (a)x²  (b)4^x  (c)3x²+4x+1

Evaluate for  x=6: (a)x³  (b)4^x  (c)6x²-4x-7 

Evaluate when x = 3, a. x  b. 4^x  c.3x² + 4x + 1.

Simplify: 3x² + 7x + 9 + 7x² + 9x + 8.

Simplify:4y²+5y+2+8y²+4y+5

Simplify: 3x²+7x+9+7x²+9x+8

Simplify: 4y²+5y+2+ 8y²+4y+5

Translate the English phrase into an algebraic expression:
(a) The sum of 17y2 and 19
(b) The product of 7 and y

(c) Eleven more than x
(d) Fourteen less than 11a

Translate the English phrase into an algebraic expression:

a. the difference of 14x² and 13

b. the quotient of 12x and 2

c. 13 more than z

d. 18 less than 8x

Translate the English phrase into an algebraic expression:

(a) the difference of 14x²and 13

(b) the quotient of 12x and 2

(c) 13 more than z

(d)18 less than 8x

Translate the English phrase into an algebraic expression:
(a) Four times the sum of p and q.
(b) The sum of four times p and q.

Translate the English phrase into an algebraic expression:
(a) The difference of two times x and 8.
(b) Two time the difference of x and 8.

The length of a rectangle is 7 less than the width. Let w represent the width of the rectangle. Write an expression
for the length of the rectangle.

The width of a rectangle is 6 less than the length. Let l represent the length of the rectangle. Write an expression
for the width of the rectangle.

Geoffrey has dimes and quarters in his pocket. The number of dimes is eight less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

84

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

96

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

896

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

942

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

22,335

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

39,075

In the following exercises, find the prime factorization.

86

In the following exercises, find the prime factorization.

78

In the following exercises, find the prime factorization.

455

In the following exercises, find the prime factorization.

400

In the following exercises, find the prime factorization.

432

In the following exercises, find the prime factorization.

627

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

8, 12

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

12, 16

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

28, 40

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

84, 90

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

55, 88

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

60, 72

In the following exercises, simplify each expression. 

$2^3-12÷\left(9-5\right)$

In the following exercises, simplify each expression. 

$3^2-18÷\left(11-5\right)$