Algebra Lesson R.10: What is an Equation?

Practice Exercises:

Decide whether or not each of the following is a true statement (yes or no)

1. \(7+4 = 11\)

2. \(1-3 = 4\)

3. \(3 \times 5 = 15\)

4. \(4 \div 8 = \frac{1}{2}\)

Replace the letter \(x\) with the number that makes a true statement (since \(x\) looks a lot like the multiplication symbol, in algebra we usually replace "\(\times\)" with "\(\cdot\)").

5. \(9 + x = 13\)

6. \(4 \cdot x = 20\)

7. \(12 = 3 + x \cdot 3\)

Algebra Lesson R.6: Powers and Exponents

Practice Exercises:

Write the following in exponent form:

     1. \(7 \cdot 7 \cdot 7\)
     2. \(11 \cdot 11 \cdot 11 \cdot 11 \cdot 11 \cdot 11\)
     3. \(2 \cdot 2 \cdot 2 \cdot 2\)

Multiply the following:

     4. \( 8^2\)
     5. \( 2^3 \cdot 3^2\)
     6. \( 1^7\)
     7. \( 0^4\)

Algebra Lesson R.7: Order of Operations

Practice Exercises

1. \((5-3) \times 4\)

2. \(2 + 5^2\)

3. \((2 + 5)^2\)

4. \(8 \times 3 +4\times 5 -3\)

5. \(2- 1 +4^2 -4 \div 2 \)


The following video gives a great explanation of order of operations for anyone who interested in understanding these ideas a little deeper that just memorizing "PEMDAS":

Algebra Lesson R.3: Multiplying and Dividing Real Numbers

Practice Exercises:

Perform the following multiplications

1. \(3 \times (-5)\)

2. \(\frac{1}{3}\times \frac{4}{7}\)

3. \(3\frac{2}{3}\times 1\frac{4}{5}\)

4. \(\left(-\frac{7}{4}\right)\times 8\)

Perform the following divisions

5. \((-8) \div 2\)

6. \( \frac{4}{5} \div \frac{8}{9}\)

7. \(8 \div -.4\)

8. \(-.2 \div .7 \)

Algebra Lesson R.8: Evaluating Algebraic Expressions

Practice Exercises:

Evaluate the following expressions in one variable at the given value

1. \(2x+5\) at \(x=3\)

2. \(3y^2-2y+3\) at \(y=1\)

3. \(\frac{2}{3}t + \frac{1}{3}\) at \( t = \frac{7}{3}\)

Evaluate the following expressions in two variables at the given values

4. \((2-x)(4-y)\) when \(x=4\) and \(y=2\)

5. \((\frac{1}{2}x)(2y)\) when \(x =\frac{4}{3}\) and \(y = 8\)

6. \(.7x + .3y\) when \(x=1\) and \(y=1\)

Algebra Lesson R.11: Plotting Points in the Plane

Practice Exercises:

Draw the coordinate axes as in the video. Plot the point, and state in which quadrant the point lies.

     1. \((1,3)\)
     2. \((-4,2)\)
     3. \((-1,-5)\)
     4. \(3,-3\)

Draw the coordinate axes. Plot the point, and state on which axis/axes the point lies.

     4. \((0,-4)\)
     5. \((5,0)\)
     7. \((0,0)\)

Solutions video:

Algebra Lesson R.2: The Real Number Line Part II (Fractions and Decimals)

Practice Exercises:

Plot the point on the real number line:

     1. \(x=\frac{5}{2}\)
     2. \(x=-\frac{2}{3}\)
     3. \(x=-2.2\)
     4. \(x=1.6\)

Solutions video:

Algebra Lesson R.1: The Real Number Line Part I (Integers)

Practice Exercises:

Plot the point on the real number line:

     1. \(x=5\)
     2. \(x=-4\)
   
Use the real number line to do the following operations:

     3. \(5-6\)
     4. \(-1+3\)
     5. \(-2-2\)

Solutions video:

Algebra Lesson R.4: The Distributive Property of Real Numbers

Practice Exercises:

In the following exercises, use the distributive property to simplify the expression.

     1. \(4(7+8)\)
     2. \(-1(1-2)\)
     3. \(12(2+\frac{1}{2})\)

In the following exercises, use the distributive property to get rid of the parentheses.

     4. \(3(x+7)\)
     5. \(-\frac{1}{2}(x+4)\)
     7. \(7(2x-3)\)

Solutions video:

Algebra Lesson R.5: Introduction to Variables