Algebra

Within Mathematics

Black and white still frame of man in glasses looking down at phone with lips parted in mid-speech. Caption. From there, you'll know whether he has enough money.

Man in tan suit and glasses sits with arm out, hand resting on staff. His mouth is open as if speaking fervently. Caption. In algebra, we don't dilly dally or mess about.

Digital illustration of a scale weighted with small goats in pink sweaters on both sides. Caption. Take away 4 goats, the scale evens out again.

Cartoon of man with cash in hand. Sign reads, "On sale now! All in one computer." Title bar to side reads, "50 dollars in account. Job, 8 dollars an hour." Caption. It pays 8 bucks an hour.

Man in tan suit and glasses grasps head and furrows brow with lips parted mid-speech. Caption. What are these symbols trying to tell us?

Inset of woman smiling with mouth open mid-speech. Text overlay reads, "Polynomial. An algebraic expression that contains 2 or more monomials. 2X plus 3. 4X squared minus 3X. 5X sup 4 plus X cubed minus 14." Caption. Right, all polynomials.

Canted closeup of woman with mouth open in mid-speech standing in front of a tree trunk. Caption. Remember a quadratic equation has a degree of 2.

Closeup of a White teenage girl's face. Her right hand holds a marker. Caption. Let's use different letters. Oops, sorry, I mean variables.

White teenage girl sitting cross legged on a blanket pointing to a formula written on a small whiteboard. Caption. So this is the formula for how many slices altogether.

Line chart with Y axis labeled, "Distribution, meters," and X axis labeled, "Time in seconds." A line begins from 0,0 and rises steadily to points A at 20, 100, B at 30, 100 and C at 60, 180. Caption. I covered 90 meters in 30 seconds.

Young woman holds up and examines a shirt on a hanger in a store setting. Caption. So 30 percent off a T-shirt that normally sells for 36 dollars.

A black screen.

Closeup of a person working a math problem on a piece of paper. They are mapping a line using coordinates, slope, and the slope intercept equation. Caption. And it's good to know this, that Y is equal to M, X plus B.

Equation written of black on a white background as follows, 1 over 100 equals 1 over 10 squared equals 10 to the negative power of 2. Caption. Is the same as 10 to the power of negative 2.

White math formulas on a green background shows 15 divided by 3 equals 5 and 15 divided by 5 equals 3. Caption. Both 3 and 5 divide evenly into 15.

White math formulas on a green background. X plus 4 times X plus 6 equals X squared plus 6X plus 4X plus 24. Text above reads, F, O, I, L with L highlighted in red and pointing to 4 and 6. Caption. 4 multiplied by 6 is 24.

Inset of a yellow number line on a green surface. Title card reads, "Summary." Caption. Integers can easily be shown on a number line.

X, Y coordinate plane. Line is graphed with coordinates at 0, 1 and 1, 4. Equation next to graph reads, gradient M equals rise over run equals 3 over 1 equals 3.

Dry brushed animation of a man in a black beanie and bandit mask. Stacks of money fill background. Caption. I'll just fill the briefcase with these stacks of fifties.

Dry brushed animation of a smiling boy with 1 hand held up to the side. Carnival rides and carnival goers fill the background. Caption. But it's too tall.

Periwinkle background with white title text across the top that reads, "Missing addends. Finding a missing part." Below is a clip art drawing of a black-haired woman thinking about a math problem with a missing part.

Closeup of a black and red chess board with white pieces in the foreground and black pieces in the background. Caption. As we investigate perimeter and area.

Man surfs a wave. A double-sided arrow points up to a line perpendicular to the man's head and down to a line perpendicular to man's feet. The arrow is labeled, "1.9 meters." Caption. The distance above his head is around half his height.

Closeup of a forearm with palm up and 2 fingers pressing on the wrist. Caption. The concept of ratios as well as the use of rates.

Closeup of a calculator screen. Caption. Roughly equivalent to 6.3.

Inset of a young man gesturing with his hands and opening his mouth to speak. Text reads, "Part 1, section A. Integer." Caption. Then we'll get to exponents.

Digital illustration of a Christmas tree. Title bars read, "Part 2, section B. Tree diagrams and factorization." Caption. Except they have numbers on them.

Teenage boy and stuffed animal lie in bed and look up at the ceiling with their mouths gaping open. Caption. Hanging like a mobile from your ceiling.

Circular inset of a young man with pursed lips. Title bars read, "Part 5 and Section B, Putting Inequalities on the Number Line." Math equation on background reads 9 is greater than or equal to X. Caption. All right, with that beneath our belts.

Algebraic equation on maroon and green color block background. Title bars read, "Section B. Equations. Part 1." Math equation on background reads 3, X plus 5 equals 20. Caption. We've got to figure out the value for X.

Algebraic equation on green background. Title bars read, "Section B. Graphing linear equations. Part 2." Text at bottom reads, "In letter form first." Caption. We'll look at it in letter form first.

Closeup of 3 boulders in a row with grass and trees in the background. Caption. During the next few minutes.

Split screen. The left is a white background with a polynomial math equation written and simplified in blue. To the right, a woman works through the problem using a screen in front of her. Caption. Now I need to distribute that negative 1 to that negative 6.

Aerial side view of a computer screen displaying a white screen with a math word problem written and worked out in long form in blue. The text at the top reads, "Example 3. What is the slope of the line that contains the given points?" Caption. The slope of the line that contains these two points.

Split screen. The left is a white background with a math word problem written in blue. Text at the top reads, "Example 3. Determine if the situation presents a direct variation. Below this, the problem is in typed text and the answer is in handwritten text. To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with a math word problem written in blue. The prompt reads, "Determine if the situation represents an inverse variation." To the right, a woman works through the problem using a screen in front of her. Caption. We want to determine if this is an inverse variation situation.

Aerial side view of a left hand touching a computer screen displaying a partially visible math problem written in blue. Caption. After you've factored your numerator, it's smooth sailing.

Split screen. The left is a white background with blue text that reads, "Example 2. Evaluate 3 minus 10, X, when X equals 2 over 5." Handwriting below reads, 3 minus 10 times 2 over 5. To the right, a woman works through the problem using a screen in front of her.

Aerial side view of a hand touching a computer screen displaying a math problem written and worked out in long form in blue. The problem at the top reads, "How did I get that?" Caption. And I know there's going to be a plus sign in between."

Split screen. The left is a white background with blue text that reads, "Example 4, factor completely. 4x squared minus X minus 3." To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with blue text that reads, "Example 5, factor completely," above a handwritten polynomial equation in the midst being solved. a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with an algebra equation being worked out in long form in blue. Given F, X equals 6, X minus 4, Find F, 1. To the right, a woman works through the problem using a screen in front of her.

Aerial side view of a computer screen displaying a math problem written and worked out in long form in blue. The problem at the top reads, "How did I get that?" Caption. When negative 2 is my input, 12 is my output.

Split screen. The left is a white background with an algebra equation is being worked out in long form in blue. To the right, a woman works through the problem using a screen in front of her.

Aerial side view of a computer screen displaying a math problem written and worked out in long form in blue. The problem at the top reads, "Example 1. Find the zeros of the quadratic function." Caption. I'll set both parts equal to 0, individually.

Split screen. The left is a white background with blue text that reads, "How did I get that?" followed by the algebra equation, 9, X, sup 5, Y minus 4, X sup 3, plus X squared. To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with blue text that reads, "Example 3. The bill at the restaurant was split evenly 4 ways." Handwriting below reads, B is to Bill. To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with a solved math equation with division and exponents. To the right, a woman works through the problem using a screen in front of her. Caption. I could represent this as X to the 3 minus 5.

White background with blue text that reads, "Example 1, simplify. 5 sup 3 to the power of 10. Multiply exponents." Caption. So 3 times 10, that's 30.

Blue handwriting working out a math problem in long form on a white background. The equation reads, open parentheses 5, B cubed times C closed parentheses, squared.

$White background with blue writing showing how to solve the math equation 7 over 2 to the power of 3 using fractions. Caption. That means that 7 halves to the third power.$

Split screen. The left is a white background with blue text that reads, "Simplify the following expressions," followed by 2 math equations. X sup 11 times X sup 5. And, 5 sup 8 times 5 sup 20. Answer buttons are next to each equation. To the right, a woman works through the problem using a screen in front of her. Caption. Work through these problems.

Aerial side view of 2 hands touching a computer screen displaying an algebra problem written in blue. Text above the equation reads, "Find the Product" and the letters, F, O, I, L. Caption. Then the last term came from distributing the 3 to the 7.

Split screen. The left is a white background with blue text that reads, "Properties of Real Numbers. Let R, S, and T be real numbers." Beneath is a table with title fields labeled Property and Explanation. To the right, a woman works through the problem using a screen in front of her. Caption. Still keeps the equation equal and balanced.

Closeup of a large screen on top of a podium with a hand holding a pen writing numbers. Title on the screen reads, "Multiplication Property of Inequality. A equals 1, B equals 2, C equals 3." An if and then table appears below and reads, "If A is less than B and C is positive, then A, C is less than B, C."

White background with blue text that reads, "Properties of Real Numbers. Let R, S, and T be real numbers." Beneath is a table with title fields labeled, "Property, Addition, Multiplication." Caption. Now for multiplication.

$White background with blue text that reads, "Example 4, Simplify," above a math division problem with fractions and exponents written and worked out in long form. Caption. Just subtract my exponents.$

Split screen. The left is a white background with a partially visible math word problem written and worked out in blue handwriting below. To the right, a woman works through the problem using a screen in front of her. Caption. You really just need to pick one, one ordered pair.

Woman with dark hair in a bun wearing a green shirt stands at a podium in front of an illuminated blue and purple background. She holds a pen in her right hand while looking down at a screen in front of her.

Aerial side view of a hand using a stylus to work out a math problem on a computer screen. Text on screen reads, "Example 2. Write the numeric expression in its simplest radical form."

Split screen. The left is a white background with blue text that reads, "Solve for x. 3 times 2 over 3, X equals 4." To the right, a woman works through the problem using a screen in front of her. Caption. Put my multiplication symbol and a 3.

Aerial side view of 2 hands touching a computer screen displaying a white screen with a long form algebra problem written in blue. Caption. That's how we represent that solution.

Woman with dark hair wearing a gray shirt stand at a podium in front of an illuminated blue and purple background. She holds a pen in her right hand while looking down at a screen in front of her.

Aerial side view of 2 hands touching a computer screen displaying a math word problem involving tickets sold for a high school sporting event. Some parts of the problem are highlighted yellow.

Split screen. The left is a white background with a chart with 2 rows and 3 columns labeled, "Verbal, Explanation, Example." The boxes are filled in with a combination of typed and handwritten text. To the right, a woman works through the problem using a screen in front of her.

White background with an X,Y axis with gray grid lines and a blue line sloping downward from left to write. Blue text in the top right reads, "Write the equation of the line." Caption. The Y intercept and count off that slope.