Writing Equations Using Symbols 03:32 minutes

Video Transcript

Transcript Writing Equations Using Symbols

Leyla and her trusty helperbot, Fridge, have gotten themselves lost on a strange planet once again. This time, they find themselves trudging through a stinking wasteland known as the Whispering Swamps and Fridge has just fallen neck-deep into a cesspool and can’t get out! But maybe they can get some help from this local hermit it seems like he's communicating with the Whispering Swamp somehow. Leyla strains to listen. A number is four times larger than the square of half the number? The hermit seems to be visualizing an equation. If only Leyla could understand the power of Writing Equations Using Variables! Let’s see if we can visualize the equation that Leyla heard. A number is four times larger than the square of half the number. Let’s start with the variables. Are there any values here that are unknown? The swamp is whispering about “a number.” We're not sure what the value of that number is, so let's call it 'x'. In math, the word “is” means equals. So what's 'x' equal to? 4 times' means we're multiplying by four and 'the square of' tells us we're raising an expression to the second power. The remaining expression 'half the number' goes inside the parentheses as 'x' over two. So THAT is what the swamp meant! It looks like solving the puzzle has almost freed Fridge! As the swamp gurgles out another strange sentence, Leyla is ready to visualize the math again! The sum of four consecutive integers is 46. The first step is to identify and define the variable. We have four unknown consecutive integers and we know that their sum is equal to 46. The keyword “sum” means we're going to add. Now, let's start filling in those empty spaces by calling the second integer 'x'. The word “consecutive" means in order, one after another.

Ok, if the second integer is 'x', that means the first integer is one less than 'x'. We can write that as 'x' minus 1. The third number is one more than 'x', or "x plus 1." And that makes the fourth number two more than 'x', or "x plus 2." Now we have an equation which represents the sum of four consecutive integers that equal 46!

To review, we can turn sentences into mathematical equations if we first, identify and define the variables. Ask yourself the question: what are the unknown numbers? Then assign those unknown numbers a variable, like 'x'. Next, look for math-related keywords like known numbers and words that represent operations. Finally, you can write the equation using parentheses to break up complex parts of the sentence.

Leyla is now a true master! Her visualization skills have levitated poor Fridge out of the whispering swamp with a little help from her new friend, of course.