Two Times Intro

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Number format: you can choose a specific font for the numbers. There are standard fonts, but also school fonts. Select the one that's closest to the one used at school. The result is a (mixed) fraction reduced to it’s simplest form. Also a table with the result fraction converted in to decimals an percent is shown. Some people have a different interpretation. And while it’s not the correct answer today, it would have been regarded as the correct answer 100 years ago. Some people may have learned this other interpretation more recently too, but this is not the way calculators would evaluate the expression today. Game mode: random or increasing. When you don't know your table very well, we advise you to start with the "increasing" mode. As soon as you feel more comfortable, try the "random" mode, which is a little more difficult but will help you memorize all the multiplications in the 2 times table.

If you type 8÷2(4) into a calculator, the input has to be parsed and then computed. Most calculators will convert the parentheses into an implied multiplication, so we get I also think the appeal to authority is interesting in this problem. It’s like everyone forgot Paul Erdos said Monty Hall was 1/2, or that Leibniz (co-inventor of calculus) thought thought that two dice will have a sum of 12 the same as 11. See: https://www.oreilly.com/library/view/classic-problems-of/9781118314333/chapter15.html as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below. Suppose it was 1917 and you saw 8÷2(4) in a textbook. What would you think the author was trying to write?People often ask how I make the videos. Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared--animation is time consuming and software can be expensive! I’m so happy people think of me for these kinds of questions. And I’m proud of everyone that takes the time to explain PEMDAS/BODMAS and why 16 is the correct answer. Along the way I have had the chance to help people clear up common sources of confusion.

When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction 3For years I’ve heard from people/math professors how this problem is a waste of time, and that no mathematician would talk about it. Now these same people are trying to tell everyone what the right answer is. I wish they would have researched the problem and its history carefully like I did. Please do share my videos with them–many times they realize their mistake. Here the list starts at 2x1 and ends at 2x12. One way to memorize your table is to recite it aloud in this way:

This indicates that the divisor is the entire product on the right of the symbol. In other words, the problem is evaluated: In a Multiplication Chart, the results are displayed in a table (with columns and rows), whereas in a Times table Chart they are displayed as a list of increasing multiplications. An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers. Multiples of 2: 2, 4, 6, 8 10, 12

When multiplying decimals, say, 0.2 0.2 0.2 and 1.25 1.25 1.25, we can begin by forgetting the dots. That means that to find 0.2 × 1.25 0.2 \times 1.25 0.2 × 1.25, we start by finding 2 × 125 2 \times 125 2 × 125, which is 250 250 250. Then we count how many digits to the right of the dots we had in total in the numbers we started with (in this case, it's three: one in 0.2 0.2 0.2 and two in 1.25 1.25 1.25). We then write the dot that many digits from the right in what we obtained. For us, this translates to putting the dot to the left of 2 2 2, which gives 0.250 = 0.25 0.250 = 0.25 0.250 = 0.25 (we write 0 0 0 if we have no number in front of the dot). To someone that says that, I would ask, “what is the sum of angles in a triangle?” If they say 180 degrees, I would point out that answer is only true in plane geometry (Euclidean geometry). In other geometries the answer can be different from 180 degrees. But no one would say “what is the sum of angles in a triangle” is not a well-defined question–we most often work in the plane, or we would specify otherwise.