How to Read Complex Expressions 04:06 minutes

Video Transcript

Transcript How to Read Complex Expressions

Megalopolis is on lockdown! Why? Every ten years, monster llamas, looking to graze, chow through the fields and forests surrounding Megalopolis. But this year, they're headed straight for the city! To fend off the llama monsters, the mayor of Megalopolis launches Neo-Hunter, a mecha for dealing with pretty much anything. But a new pilot, Aerial Earmath, has just completed her training and she’s a little unsure of how to work the guidance system. Luckily for Aerial, her robot friend, K2B2, will help her figure out how to read complex expressions so she can initiate the defense system.

First example - Addition and multiplication

Aerial sees an algebraic expression on the small monitor. To input the coordinates of the launch, she reads the expression: 3 times n plus 6. Oh no! That's wrong! An error message?! Her robot pal, K2B2, is trying to tell her something. In math, certain keywords - such as sum, difference, product and quotient tell you how the expressions are grouped. The correct way to read any algebraic expression is to distinguish what operation should be done and in what order. Thanks to K2B2, we know to group the addition before applying the multiplication and we're able to read the expression correctly, ‘3 times the sum of n and 6.’ Great work! The Neo-Hunter is now programmed to lock onto the correct coordinates but with no time to rest on her laurels Aerial gets another set of coordinates.

Second example - Subtraction and division

This time the expression includes division. At first, Aerial reads out the coordinates as, ’three minus n divided by 5.’ Oh no! Aerial didn't group the operations for this algebraic expression correctly. For fractions, we should read the numerator first, and then read the denominator. To help you stay organized when reading expressions, you can imagine that the numerator has parentheses around it, but it's not entirely necessary. For this example, the coordinates should be read: 'the quotient of the difference of 3 and n and 5.' Aerial thinks one more strike will get rid of the llamas for good.

Third example - Expression in written words

The next coordinate is an expression written out in words! We lucked out! All we have to do is read the expression and see what coordinates come out. ‘The quantity, x plus 8, raised to the 4th power.’ Let's start with what we know: 'x' plus 8. The word 'quantity' lets us know that this portion of the expression should be evaluated before any other operation is performed. In this case raising it to the 4th power. It worked! Neo-Hunter launches the projectiles of pizza? The city is saved! Hip, hip hooray! The llama monsters happily chow down.