We heard recently about a third-grade teacher teaching her student that “1 divided by zero is zero”. What??!!!
What makes matters even worse is that, according to the report, the principal agreed with the teacher when confronted! So, apparently, both the teacher and principal lacked third-grade math knowledge (see fictitious image above).
This solution is totally nonsensical. Do we honestly have teachers teaching our kids this incorrect math?
Furthermore, when confronted with solid (basic math, in this case) evidence to the contrary it’s not clear if they modified their “belief”. So much for the scientific method, let alone third-grade math not understood by adults in the US educational system (including math teachers and principals, apparently).
While we certainly agree that in the “limit” as x->0, (1/x) would approach infinity. But “at” zero, 1/0 is still undefined. Learning about limits isn’t typically taught in the third-grade, yet, however.
The basic division test: As you would do with a result like 15/5 = 3 where you can multiply the result by the denominator to get the numerator (in this case 3 * 5 = 15), with 1/0 what number do you multiply the denominator by to get 1? In other words what number, times zero is 1? Answer: there isn’t one!
Here’s an intertaining YouTube video:
This video, while very well done, it’s depressing that someone actually had to make it.
Consider other videos where people are asked on the street what is 2 x 2 x 2 and cannot answer correctly. Or when asked “what is 15/3”. Nope, lots got that wrong also. When asked what time it is at a quarter after 6, many answer 6:25. “How many dimes in a dollar?” ….
With an estimated 40% of students unable to read by some reports, having a teacher who is teaching math but does not know basic math that he or she is teaching is a flashing red light — yet another one — that our educational system in the US is beyond broken.
In other news … what about the college student at the University of Connecticut that graduated from High School but can neither read nor write? This student was not “functionally” illiterate, but actually illiterate.
In Summary:
1/0 is undefined.
0/1 is zero.
Food for thought
0/0 is another special case (also not zero or 1). Zero divided by zero is undefined in standard arithmetic. This one is easy to prove also. —
When politicians or advertisers claim something is offered at a “500% discount,” it’s mathematically impossible (NOT POSSIBLE!). A discount reduces the price, from the original price. A discount more than 100% doesn’t make sense.
Understanding Percentages (review):
A percentage is a part of 100. A 100% discount means you get the full value of an item for free. If something costs $100, a 100% discount brings the price to $0. A 20% discount on that same $100 item brings the price to $80.
So, what Does 500% Mean?
A 500% discount means the discount is five times the original price. If an item costs $100, a 500% discount would mean you’re paid $400 to take the item. This situation is impossible—prices can’t go below zero, and no one is going to pay you to buy something.
Politicians or advertisers often use exaggerated claims to make what they’re saying “sound” more appealing. They often make the same bogus mathematical claims over and over to try to legitimize what they’re saying (or, sadly, they actually believe what they’re saying is true).
But a “500% discount” is not only misleading but simply wrong. Such a stated discount grabs attention, but the claim doesn’t hold up with even 6th grade math. If the discount were actually 500%, we would get a discount percentage larger than 1 — see Example 2 below.
A discount percentage larger than 100% (1) is economically meaningless as a pure discount, because it would require the seller to pay the buyer.
Let’s look at a couple examples to better understand.
Example 1 below is a normal situation we encounter.
Example 2 below would never happen, but is the exact situation politicians and others say with a straight face over and over is what “would” happen.
Example 1: A Simple Discount Calculation(Normal Situation)
Let’s say a car that normally costs $30,000 is at a 15% discount. What do we actually end up paying in this case?
Step 2: Calculate the discount: 0.15 × $30,000 = $4,500. ($4,500 is the discounted amount “off” the price)
Step 3: Calculate the final price (full price minus discount): $30,000 – $4,500 = $25,500.
Example 2: What Would a 500% Discount Look Like? (Fictional and Absurd — You make money!)
Let’s imagine, just for fun, that a car is offered at a 500% discount. Hurray! This “discount” matches the absurd political language you actually hear on TV over and over.
Below we use the same three steps as in the above example.
Step 1: Convert 500% to a number we can use to multiply. As above divide the percent by 100. So, 500% = 500/100 = 5. (Wow, this discount is greater than 1!)
Step 2: Calculate the discount: 5 × $30,000 = $150,000. Notice that the discount is now five times the sales price!
Step 3: Calculate the final price: $30,000 – $150,000 = – $120,000.
So, $120,000 means the dealer would pay you $120,000 to take the car, which is clearly impossible and would never happen.
The first 100% is the total cost of the car, or $30,000. The next 400% is four times the sales price or 4 * 30,000 = $120,000. So, in this case, $120,000 is what the dealer would PAY YOU!
Graphs:
To help clarify, the two graphs below demonstrate each case from the two examples above.
Graph: Impact of Discount Percentage on Price.
The graph below shows that as the price drops by 100%, the cost is zero and cannot go further. Simple … 6th grade math.
Graph below showing MONEY TO YOU when discount > 100%.
Sidebar: When Do Students Learn About Percentages?
Students usually start learning about percentages in grades 4 or 5 (ages 9-11). By middle school (grades 6-8), they should be able to calculate percentages and apply them to real-world situations like discounts.
By high school, students understand that a 100% discount means an item is free, and any discount above 100% is impossible, as it would imply a negative price.
Unfortunately, many students are not getting the math skills they need. Studies show over half of U.S. adults (57%) read at or below an 8th-grade level, and critical thinking in education is often overlooked and undervalued. This educational erosion (some say collapse) makes it harder to for citizens to do basic math, basic reasoning, or critical thinking.
A “500% discount” (or any discount > 100%) is mathematically impossible. Any “discount” greater than 100% would be money paid to you! Anyone who claims a discount > 100% is possible either does not understand middleschool math or is lying to you.
It could be argued that such spouted mathematical incompetence is either intentional and meant to distract from other issues or to say rather than having an actual plan for what’s being discussed.
