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Mathematics

Within Mathematics

Person in a science lab. One beaker contains an orange liquid, and one beaker contains a green liquid. Caption: It's orange. That means its pH is 5.

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.

Man in suit with eyes bulging and lips pursed raises tensed hands in the air.

People feeding dried hay to goats. Caption: How can we figure out how much energy is stored in this hay?

Man with light brown hair is in front of an orange 3-dimensional background. Caption. "Let's use a number line to help our friend with addition."

Orange background with a white division symbol in the top left, a man with light brown hair in the top right, and the text, "divided by," across the bottom. Caption. "'goes into,' 'divided by,' and 'divisible.'"

Smiling man with black hair next to a graphic of a coordinate plane with the words, "Right angle," written over it in purple. Caption. "Okay, back to our discussion about our friend, the line."

Woman with light brown, curly hair sits in a tan armchair in a studio. A drawing of a brown ant is at the bottom of the screen. Caption. "And we can measure the distance."

9 by 9 multiplication table is on screen next to a brunette woman wearing a bright orange shirt. Caption. "Then extending that process to other whole numbers."

Man with black hair sits in a yellow chair in a studio with a blue and green 3-dimensional background. The camera angle makes him look like his is coming out of the bottom right corner. Caption. "Let's look at examples."

Curly-haired brunette woman sits in a tan armchair in a studio. The text, "6.752," is across the bottom of the screen. Caption. "In 6.752 seconds."

Orange background with a man with light brown hair in the top left, a graphic of half of a pizza next to the text, "equals 1/2," in the top right, and the text, "1 of 2 pieces," across the bottom. Caption. "Now you are left with 1 of 2 slices."

Woman with light brown, curly hair sits in a tan armchair in a studio with a wood floor and blue 3-dimensional background. She holds her hands up as she talks to the camera. Caption. "Anyway."

Ocean wave cresting and crashing on itself against a blue sky background. Caption. "We need more points to capture the fine-scale structure."

Multicolored streaks of light fading towards a single point in the center of the screen. Caption: Matter is made of up of tiny particles called atoms.

Closeup side view of a midsection with arms holding a large tube up to a machine. Caption. Jenna can calculate the percent of nitrogen in the sample.

Man in suit with eyes closed and lips pursed in mid-speech. American flag in background. Title bar reads, "Mario Matthews. Regional Director, United States Census Bureau." Caption. Because the United States is such a dynamic country.

Smiling man kneels with arm resting on one leg and lips parted in mid-speech. Field of grass swarming with brown chickens in background. Caption. The big thing is certified organic grain.

Youth wear blue shirts and carry instruments in a marching band procession. Caption. As we investigate circles.

Middle-aged man with mustache wears tinted aviator glasses and looks at man whose back faces camera at left edge of frame. Caption. They had other things in common.

Closeup of 1 man speaking to another with a serious, narrow-eyed expression. Caption. Where you'll see how we check a bag of cans.

Ancient Incan illustration sits beside a few cacao seeds on a white background. Caption. Cacao seeds are used to make chocolate.

Rocket-like object. Time to go outside… Caption: (man) T-minus 10, 9, 8….

Gloved hand reaching into a container emitting a foggy, mist-like cloud. Caption: Look at all this moisture being frozen.

Person holding a sheet of a shiny metal. Caption: An element is often thought of as a pure substance

A lit match. Caption: Energy comes in many different forms.

4Fe+3O2+4H2O converts to 2Fe2O3*2H2O. Caption: This causes the iron to become a hydrated iron oxide,

People riding on a wagon pulled by two horses. Caption: Two horses add more force or pull the wagon.

Young man smiles at camera with text below him that reads, "Whoo!" A young woman stands behind him smiling and looking down with text below her that reads, "Hey."

Woman speaks to camera with a braille backdrop. Caption. Math is a fact of life. It's true.

Woman speaks to camera with a braille backdrop. Caption. On the coordinate plane.

Man speaks to camera gesturing out with 1 hand against an orange backdrop. Caption. Collections of data, which are called data sets.

Woman speaks to camera, smiling and raising her eyebrows. Text on image reads, "Fractions and decimals." Spanish. Fractions and decimals show part of a whole.

Closeup of a train track overgrown with grass as it extends into the distance. Caption. A good example of parallel lines are the rails of a train track.

Young child reaching into a container being offered by an adult. Caption: they'll select a small number to study.

Senior woman faces camera and looks slightly down as if participating in a recorded interview. Title card identifies her as Marlyn Wescoff Meltzer, Interviewed in 1997. Caption. You know how to run an adding machine.

Closeup of man with furrowed brow and lips puckered in mid-speech. Map in background. Caption. Here we collected, in one year we collected.

Closeup aerial view of a board with flippers and raised attachments creating lanes and obstacles. A person off camera gestures toward board with 1 hand and holds a ball in the other.

Illustration of a bird on a branch looking at a small worm on a branch close by. Caption: One day, a hungry robin saw an inchworm,

Spherical object and a wavy line passing through something in the center. Caption: light particles that shoot off in opposite directions

Illustration of a train on the tracks. Caption: (Shawn) This electric train needs three doors.

Cartoon of a toy room with Max the Train parked on the tracks and looking at Bill the monster truck nearby. Bill says Hi, Max. Max says, Hi, Blazin' Bill.

Cartoon of Robo, J, 5, a pink robot hovering next to Robo, O, 5, a short, squat blue robot. They are next to a fountain surrounded by a colorful flower border. Caption. Sound of Robots beeping.

Cartoon landscape of a rainbow-colored hot air balloon surrounded by dark gray clouds and rain. A helicopter hovers nearby with 2 balloon parachutes next to the basket. Caption. Allie as narrator. Both teams are now flying through the rainy clouds.

Cartoon of a kitchen with an angled wood plank leading down from the second shelf of the refrigerator to the kitchen sink. A few potatoes and tomatoes roll down the plank. Caption. 5 tomatoes.

Digital illustration of a cat on the roof of a blue house. A tall flower stands to the left and an apple tree to the right. Caption. The cat is made from circles for the head and body.

Illustrated cartoon. Back of a young girl's head. She has short, shaggy hair and wears a black and white checkered shirt.

Dry brushed animation of a smiling man in a chef's uniform with a red neckerchief and mustache. Caption. Narrator. Tito, you charge that.

Dry brushed animation of a girl turning around in her seat and gesturing to the side in a theater filled with people. Legs of a person and a stool appear on the stage in the background. Caption. Is this almost over? This guy is terrible.

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 woman wearing cat eye glasses and carrying a purse as she gestures toward a storefront with a sign that reads, "40 percent off everything!" Caption. Why do they make this so confusing?

Dry brushed animation of a smiling woman wearing cat eye glasses in a shoe store. Caption. This pair is free!

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.

Person in a science lab working with complex machinery. Caption: There is almost no limit to the ways we transmute matter.

Cartoon of Max the Train, Jake the Fire Engine, and Blazin' Bill the Monster Truck floating down a river surrounded by dense trees on a log raft. Caption. Look! I see 1 of Bubble's wooden shapes.

Man leans against a wall and types on a keyboard inside the International Space Station. Caption. The metric system is also preferred in certain fields.

Boy wearing goggles floats underwater and holds his breath with his mouth closed. Caption. All of these forms of measurement are known as.

Spheres in a cube, lined up in an alternating positive and negative pattern. Caption: by mutual Columbic attraction in a regular pattern.

Pile of coins sits on a carpeted floor in front of a pair of crossed legs. Caption. To understand how this works.

Split screen of 2 fish tanks. 1 is labeled, "More," with an arrow pointing down and the number 15 below. The other is labeled, "Less," with an arrow pointing down and the number 13 below. Caption. So this tank has more fish and this tank has less fish.

Person on skis in a crouched position. Motion: change in position. Caption: This skier was in motion.

Girl stands at carnival booth facing a small basketball hoop that hangs from a wall covered with stuffed animals. A young woman wearing an apron stands to the side. Caption. Numbers allow us to count and keep track of information.

The periodic table of elements. A color-coded grid with letters representing each element. Caption: Each row of the table represents a pattern of chemical properties

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.

Weather illustration panels for a Monday to Wednesday forecast, with Monday as "Sunny", Tuesday as "Chance of Rain," and Wednesday as "Rain". An arrow labeled Unlikely points to Sunny. Caption. From unlikely on Monday to very likely on Wednesday.

Gloved hand holding an electronic chip with a pair of tweezers. Caption: they call it an artificial leaf.

Woman stands with fingertips touching and lips parted in mid-speech. Bar graph superimposed on left side of screen. Caption. If we were to run the experiment over again many times.

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 an open green eye with a purple colored contact lens, black mascara on the eyelashes, and black eyeliner on the top lid. Caption. With several special properties.

White background with faint gray gridlines and math equation that reads, "23 and seven eighths equals 23.875." A big red arrow points at and labels the decimal point. Caption. Fractional quantities, such as 23 or seven eighths.

Closeup of a person holding a segment of orange with an arrow pointing to a halved orange. Segments on the halved orange are labeled 1 to 10. Caption. Each segment is a tenth of the whole orange.

Several ocean going sailboats docked with sails down is in front of a street lined with multi-story buildings with many windows and pitched roofs. Caption. The city of Copenhagen in Denmark is at sea level.

Top side view of a pizza with cheese, red sauce, and Canadian bacon on a large stainless steel pizza spatula over a gray background.

Centered, front view of the Taj Mahal. A dashed white line is overlaid down the center, with an arrow and the word "Axis" overlaid and pointing to it. A white rectangle overlay is around one of the pillars on the left. Caption. 1 side is a reflection of the other side.

Top side view of a pizza with cheese, red sauce, and Canadian bacon on a large stainless steel pizza spatula over a gray background. Caption. Most likely, family or friends ate the rest of the pizza.

Middle-aged man with mustache wears sunglasses and holds onto railing of a boat as he leans forward. Caption. That's too fast in there.

Person at a computer looking at a projection of a wire frame human face on a screen. Caption: how robots interact with humans,

Small airplane midflight. Caption: Momentum is the same direction as velocity.

A sliding scale weighing something. Caption: Weight is a scalar.

Two people looking at yellow fluid in a bottle. Caption: in a universal scientific language.

Speedometer. Caption: Velocity is a vector quantity.

Speedometer. Caption: Velocity is often confused with speed.

Simple line drawing of a house on a hill with a roof and 2 windows.

Person turning a spigot. Caption: it is multiplied at the axle, overcoming the resistance force.

School of fish swimming in a tank. Caption: Sometimes they sink like these rocks.

Dense points of light on a black background. Caption: The oldest could be 11 to 13 billion years old,

Rotational motion theta equals s over r. Caption: We showed you that equation awhile ago.

An illustration depicts a blue down arrow and a red up arrow representing T A L and T H 2 O in contact with each other. The junction of the two arrows is labeled T e. On screen text, Physics, Part 5, Section A. Caption: is higher than the initial temperature of the water.

Animation of a circular wheel in motion. On screen Text, Projectile motion A. An arrow indicates same time. Caption: It takes the same time to rise as to fall.

A graphical representation of the x y coordinate plane. 2 units from the origin are marked on the positive and negative sides of the x and y axes. An upward arrow extends from the origin to (0, 2). On screen text, what are scalars and vectors. Caption; woman, this vector's direction is 90 degrees.

A woman is in ski outfits. An animation of a red sphere with on screen text, more inertia, greater mass. Caption: The red sphere has greater mass.

Multiplying vectors c. Vector A and Vector B roughly parallel in the same direction. Caption: in the direction of the first vector.

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.

Man faces camera and speaks slightly off to 1 side like he is in an interview. Text on image reads, "Easy to remember, and a little bit enjoyable."

Rear view of teenage girl sits at ia control panel in a room filled with equipment monitoring panels with switches, lights and racks from the mid-1900s. A man wearing a hard hat stands between the control panel and equipment panels as he speaks to the girl.

Medium view of a man facing camera like he is giving a lesson as a subject expert. Caption. Either by the lengths of their sides or by their angles.

Man faces and speaks directly to camera like he's lecturing. An overlay formula reads, "Right triangle hypotenuse minus leg theorem over hypotenuse and leg of right triangle."

Man crouches on asphalt pavement. He rests his head on his hand which is propped on his knee. He gazes into the distance like he is thinking. An overlay measurement is labeled as 14 feet.

Seated man faces camera while holding a book in a living room setting. He speaks directly to camera as if he is being interviewed as a subject expert. Caption. As we continue our geometric portrait series.

Star Maths cartoon. Rear view of a girl and a boy standing. The boy holds a gun in his hand. Piles of metal and other debris lay before them in an outdoor salvage area. Caption. These label guns aren't very accurate.

Star Maths cartoon. 2 people sit in a red vehicle with a glass-enclosed cabin. Vehicle has thick treads on its tires for rough terrain. Brown hills are in the background. Caption. Sector 145 should be just coming up.

Star Maths cartoon. A binocular outline view of a mountain peak. Caption. Oh, yes! And there's Mervin's Peak.

Star Maths cartoon. Boy turns to watch an older man exiting the darkened room. Caption. Boy as narrator. Where are we going? Caption. Man as narrator. Into space, of course!

Star Maths cartoon. Man sits and leans against a pipe-like post. This pipe is connected to another pipe that has an attached monitor displaying a bar graph with 4 vertical bars. Caption. The name's Botler, by the way.

Star Maths cartoon. Group of 6 multi-colored robots flying together across a barren, desert area. Caption. Amber as narrator. Look at them. They're good, aren't they?

Star Maths cartoon. Rear view of the heads of a girl and boy looking out of a spacecraft window. They watch hovering spacecrafts drop objects into a large dirt pit below. Caption. This storm has been going on for 3 whole days now.

Star Maths cartoon. Woman sits in a spacecraft pilot's chair while a boy and girl stand next to her. All 3 look sideways and in the same direction. Caption. Rocks in space. They can do damage.

Star Maths cartoon. Girl stands while she speaks to a robot in a room about to be painted. A digital screen on the wall displays rectangular shades of color. A ladder and covered furniture are in the background. Caption. Can you mix new colors?

Star Maths cartoon. Closeup of an older man standing in a room. He appears to be speaking to another person. Caption. All this for only 1,250 igmus?

Star Maths cartoon. Side view of a boy and girl sitting at a dining table eating. Caption. Do you want all of them?

Star Maths cartoon. Large robot hovers next to an industrial floor scale in a warehouse. Text on the scale face reads, "100."

Star Maths cartoon. Person sits at a worktable in a manufacturing plant filled with equipment. 3 robots are to his side. Caption. But I'm making music, man!

Star Maths cartoon. Closeup of a digital number board with 3 rows ending in numbers of tens. The end of row 1 displays the numbers 8, 9, 10. The end of row 2 displays 18, 19, 20, and the end of row 3 displays 28, 29, and 30. Caption. 18, 19, 20.

Star Maths cartoon. A girl and boy use binocular-like devices as they scan the horizon off to the side of camera. Behind them, a vehicle sits on a dirt plain surrounded by brown hills. Caption. Go on, Ten! Go on!

Star Maths cartoon. A boy and girl are seated and turned towards each other in conversation. The girl points her index finger at the boy. Caption. You were channel-hopping.

Star Maths cartoon. Boy looks at a handheld device in 1 hand while his other hand is palm up. He stands outdoors with hills and mountains in the background. Text on the screen reads, "Meters." Caption. We need to measure out 1,000 meters.

Star Maths cartoon. A small and taller robot stand next to each other, conversing. Caption. Eleven, clear up the picnic.

Star Maths cartoon. Man walks through an archway as he speaks on a telephone. A boy and girl sit in the background in a living room and watch T, V. Caption. Do you want me to come meet you?

Star Maths cartoon. Girl sits on a couch in a manufacturing plant. Caption. Hi, I'm Lisa. You must be Amber!

Star Maths cartoon. 1 large robot and 1 small robot are standing and facing each other in a futuristic living room. Caption. No names, just numbers, Miss Amber.

Star Maths cartoon. Red, all terrain vehicle drives through a hilly dirt area with 2 trees that have sparse foliage. Caption. Amber as narrator. Well, there's not much junk this morning.

Star Maths cartoon. Girl holding a pen sits while a boy stands at the head of a table. A notebook rests on the table top which has a digital map display showing planets and stars. Caption. She was probably quite far away.

Star Maths cartoon. An empty all terrain vehicle with 3 wheels on each side is parked outdoors on a dirt surface in a desert-like area. Caption. Ha! Let's see where it landed.

Star Maths cartoon. A boy, girl and 3 robots stand on a smooth floor in a room with decorative, pipe-like structures and lighting. The boy points up towards a robot standing on a balcony above him. Caption. Botler, number 364, please.

Star Maths cartoon. Girl raises her hand with 3 fingers up and thumb folded in while using a beverage-making machine in a futuristic kitchen. She speaks and looks at a boy near her. Caption. 4 tablespoons of sugar.

Star Maths cartoon. Boy and girl face each other as they sit and talk over a dinner table. Caption. Probably typed the wrong numbers, again.

Star Maths cartoon. Girl stands in a spacecraft and holds 1 hand with thumb up in front of her face as she talks and looks to the side. Caption. Are you sure? 6 goes into 12 twice.

Star Maths cartoon. Hand extends over a paper with a painting of a butterfly's body and 1 set of wings. 6 pots of paint in different colors, brushes, and colored pencils sit on the table top. Caption. I'm making her a card.

Star Maths cartoon. A boy and girl approach a convertible-like car that is parked outdoors. Caption. Relax, Uncle Zak's miles away.

Star Maths cartoon. Boy looks upwards and stands with his arms outstretched on a blue floor outlined with green and black hazard tape. Caption. Help! Sam, get me out of here!

Star Maths cartoon. A boy and girl walk through a storage room with shelving. Flying robots are nearby and are restocking inventory on warehouse shelves. Caption. Boy as narrator. What was that? Caption. Girl as narrator. What?

Star Maths cartoon. Back view of a boy and girl outdoors and looking at a futuristic truck with a glass enclosed cabin and an open cargo bed. A green robot stands in the cargo bed. Caption. Where are you off to, Botler?

Star Maths cartoon. Girl in a spacecraft sits at a table with a microphone and monitor. She looks up at a person to her side. A spotted, cat-like creature sits on the table. A robot stands in the background. Caption. Will Lisa be able to get here?

Man looks slightly off camera with an impassioned look. Behind him, the Qualcomm Thinkabit Lab with a collection of colorful toys. Caption. But this is a way to give back in a personal way.

Person in a lab setting filling a container from a faucet. Caption: A calorimeter is simply anything used to measure heat.

Diagram of a circuit showing a battery with leads on the positive and negative side and a lightbulb in the middle. Reduction. Caption: During this process, one substance must gain electrons,

Shawn the Train, a red locomotive, looks over at a yellow train that runs on a parallel track. Yellow train glances to the side with a concerned expression. Caption. He's across the bridge waiting for us.

Closeup of a T, V screen with black and white still of Fred Flintstone sitting in a stone chair and turning toward viewer with cigarette in his hand.

Geometric illustration of atoms. Caption: So here we've drawn in all the atoms.

Geometric design of a large cat. Caption: (narrator) First, define the surface of the shape geometrically.

Cartoon of Robo, J, 5, a pink robot hovering above a paved outdoor surface looking off at something out of view. Caption. Watch out for the rolling circles.

Cartoon of a yellow toy construction truck parked at an outdoor construction site with various materials scattered about, such as red pillars, gray bricks, and wood pallets. Nearby, a smaller green forklift lifts a blue and green panel in the air. Caption. Forklift as narrator. Okay, lower the rectangle.

Cartoon of a bright purple convertible raised up on monster truck tires driving across a paved outdoor area surrounded by trees. Nearby, a blue raised truck is partially visible.

Person holding a twisted strip of material. Caption: This shape is called a Möbius strip.

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 solved polynomial math equation in blue. To the right, a woman works through the problem using a screen in front of her. Caption. Let's look at this last one.

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.

Computer generated image of a sphere composed of twisted interlocking tubes of various colors. Caption: Fractal research is changing fields such as biology.

Chunk of rock sitting partially submerged in water. Caption: Matter is anything that takes up space.

Two glasses with colored liquid in them. One glass has a person holding a cylindrical electronic device in the liquid. Caption: and check the parts per million of solutes.

Cartoon of a girl and another cartoon character sitting at a table. The girl has an empty plate and the character has a plate full of hot dogs. Caption: Why didn't you get anything to eat?