Today’s Wonder of the Day was inspired by Hunter. Hunter Wonders, “Why cant computers and calcultors find out what zero dived by zero is.” Thanks for WONDERing with us, Hunter!
If you’ve been WONDERing with us for a while, you may already know a thing or two about math. Maybe you’ve read about infinity or the number zero. You may have even learned about division. Would you believe that today’s Wonder of the Day combines all these topics?
You’ve probably learned in school that math follows certain rules. Multiplying two negative numbers will always return a positive. Dividing any number by itself will always result in the number one. Any number multiplied by zero equals zero.
The rule we’re learning about today might sound like the opposite of that last one: You can’t divide any number by zero.
Why not? Like many math concepts, this one is sometimes easier to understand through a real-world example. Imagine you and three family members are enjoying a delicious pizza for dinner. The pizza has eight slices, and there are four of you. How many slices of pizza can each of you have?
If you said two, you’re right! That’s how division works—it’s all about splitting numbers into equal groups. What if there were only two people sharing the pizza? Eight slices divided by two . . . you each get four slices. And if you were the only person at dinner? Congratulations, all eight slices are yours!
Now, imagine dividing eight slices of pizza among zero people. How many pieces would each person get? If you’re scratching your head in confusion, you’re not alone. It’s impossible to divide a pizza among zero people. There’s no way to split up those eight slices among zero equal groups. It just doesn’t make sense!
Just like in this example, there’s no way to divide a number by zero in math. Or, at least, a way to do so doesn’t currently exist. Mathematicians are always trying to find answers to interesting math problems—and plenty of people have tried to work out how to divide by zero. So far, none have been successful.
Instead, any number divided by zero is undefined. In fact, even zero divided by zero is undefined! That simply means we don’t yet have an answer for the problem. After all, how would you go about dividing zero into zero equal groups?
What does the concept of infinity have to do with this? As you divide a number (the dividend) by other smaller and smaller numbers (divisors), the answer (quotient) becomes increasingly larger. Check out this example:
1 ÷ 1 = 1.
1 ÷ 0.1 = 10.
1 ÷ 0.01 = 100.
1 ÷ 0.000001 = 1,000,000.
In other words, as the divisor gets closer to zero, the quotient approaches infinity. Will mathematicians ever be able to divide by zero? Perhaps! For now though, doing so will always result in an undefined answer.
Standards: CCSS.MATH.CONTENT.6.NS.C.5, CCRA.R.4, CCRA.L.3, CCRA.L.6, CCRA.R.2, CCRA.R.10CCRA.R.1, CCRA.SL.1, CCRA.SL.4 CCRA.SL.2, CCRA.W.4, CCRA.L.2, CCRA.SL.2