Morning Mathematical Monsters & Maniacs!
(Today’s post is sponsored by the letter “M”)
Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.
Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.
And what better way to start your week, then by discussing math Monday morning?
While celebrating Pi day last week, we looked at an epic math episode from the Season 26 finale and I left you with a math joke. This week we’ll officially break down the math joke and go through some of the math problems from that episode.
Mathlete’s Feat (Season 26, Episode 22)
When discussing π last week, I left you with a joke from Season 26, Episode 22 Mathlete’s Feat.
So what does it all mean?
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = -1. Knowing that i2 = -1, i can be solved for as √-1. i = √-1.
23 is simply the same as 2 x 2 x 2, which gives us 8.
The eighteenth letter of the Greek alphabet is sigma. Expressed as an upper case, it is Σ, and as a lowercase σ. In mathematics, the symbol Σ is used as a summation operator to calculate the sum.
And as was discussed at great length last week, the symbol π is known as Pi.
So to summarize, the board in question states:
i 8 sum Pi and it was delicious
Or if you will:
I ate some pie, and it was delicious
Ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ow, my ribs ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha!
Ok, enough laughing. Now onto some serious stuff.
During the episode, the Springfield Elementary School Math team is competing against Waverly Hills Elementary’s Math team, in an event organized by Benjamin, Doug and Gary. Lets take a look at some of the questions and solve them.
Question 1: What is the least common multiple of 6, 8, and 16?
In mathematics, the least common multiple (also known as lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. The least common multiple of three integers a, b, and c, usually denoted by LCM(a, b, c), is the smallest positive integer that is divisible by a, b, and c.
So to solve for the LCM(6,8,16), let’s look at the multiples of 6, 8, and 16:
6 – 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
8 – 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
16 – 16, 32, 48, 64, 80, 96, 112, 128, 144, 160
As you can see, 48 is the least common multiple, as it is the smallest number that is divisible by 6, 8, and 16.
While LCM(6,8,16) is 48, let’s just take a few seconds to appreciate LCM(6,8) is 24, LCM(6,16) is also 48, and LCM(8,16) is 16.
Question 2: What is the value of (3+52) / 4 – (x+1) when x = 7?
In mathematics, the order of operations is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. The order of operations is as follows:
- Bracket/parenthesis
- Exponents and roots
- Multiplication and division
- Addition and subtraction
Mnemonics used to memorize the order include:
- BEDMAS – Bracket, exponent, division, multiplication, addition, subtraction
- PEDMAS – Parenthèsis, exposants, division, multiplication, addition, soustraction
- PEMDAS – Parenthesis, exponent, multiplication, division, addition, subtraction
- BIDMAS – Bracket, indices, division, multiplication, addition, subtraction
- BODMAS – Bracket, order, division, multiplication, addition, subtraction
(3+52) / 4 – (x+1) = (3+52) / 4 – (7+1) = (55) / 4 – (8) = 13.75 – 8 = 5.75
Question 3: If x + 4y = 5 and 5x + 6y = 7, then 3x + 5y = ?
Thanks to reader JMP for the correction: If x + 4y = 5 and 5x + 6y = 7, we can add both equations together to get x + 4y + 5x + 6y = 5 + 7, or 6x + 10y = 12. If we divide this by 2, we get 3x + 5y = 6.
48, 5.75, 6! Woohoo! We did it. Here’s our Award:
Now are you ready to go join your local mathlete team and compete in the mathlympics? Did you remember this episodes? Were you able to solve the problems on your own? Sound off in the comments below. You know we love hearing from you.