Transcript[]
Title text reads, The Mysteries of Life with Tim and Moby
Moby pulls a freshly baked pie out of the oven. Tim walks into the kitchen and notices several other pies cooling on the windowsill.
TIM: Mmmm, are those the pies for the bake sale? I sure like pie!
MOBY: Beep.
TIM: Please?
MOBY: Beep.
TIM: Ohhh…
Tim reads from a typed letter.
TIM: Dear Tim and Moby, I want to know how to add and subtract fractions. From, Joshua. Well, pies are perfect for talking about fractions.
On-screen, Tim pulls a pie off the windowsill. Moby glares.
TIM: As you can see, this is one pie. That's 1 part of 1 whole, or 1 over 1 in fraction form.
On-screen, the pie appears. The fraction, 1 over 1, appears above it.
TIM: If I cut the pie right down the middle, I get 2 pieces.
On-screen, Tim slices the pie into 2 equal pieces.
TIM: Each piece is 1 divided by 2, or one-half of the whole.
On-screen, the fraction, one-half, appears on each half of the pie.
TIM: One-half plus one-half equals 2 halves, or 1 whole.
On-screen, the pie comes back together. The fraction, two-halves, appears. It is reduced to the fraction, 1 over 1. Moby beeps and points at the top and bottom numbers of the fraction.
TIM: In a fraction, the numbers have names. The top number is the numerator, and the bottom number is the denominator.
On-screen, the fraction, one-half, appears. The top half is labeled, numerator, and the bottom half is labeled, denominator.
TIM: The denominator tells us how many pieces make up one whole. The numerator tells us how many of those pieces we’re dealing with.
Moby beeps. The pie is cut in two again, and each piece is labeled, one-half.
TIM: Right, the 2 in this case is a common denominator, shared by both fractions.
On-screen, the 2 on the bottom of each fraction is highlighted. A label reads, common denominator.
TIM: When you add fractions with the same denominator, you add the numerators, while the denominator stays the same.
On-screen, a plus sign appears between the 2 fractions, creating the equation, one-half plus one-half equals two-halves. Tim cuts the pie again, dividing it into 4 quarters. Moby beeps.
TIM: Each of these pieces is 1 divided by 4 or one-fourth of the whole.
On-screen, the pie appears, divided into quarters. The fraction, "one-fourth" appears over each piece.
TIM: We can see that one-fourth plus one-fourth equals two-fourths, or one-half.
On-screen, 2 quarters of the pie join together to form half a pie. The fraction, two-fourths, appears. Two-fourths is reduced to the fraction, one-half.
TIM: So, let's say we want to add one-fourth of this pie to one-half of another one.
On-screen, Tim pulls another pie off the windowsill and cuts it.
TIM: La la la… cutting pie…
On-screen, a quarter pie and a half pie appear. They are labeled with the fractions, one-fourth, and one-half.
TIM: One-fourth and one-half are fractions with different denominators. To add them, we need to find their L-C-D, or lowest common denominator.
A label appears, reading, lowest common denominator, or L-C-D.
TIM: That's basically the lowest common multiple of the fractions' denominators.
On-screen, denominator highlights in the fraction, one-fourth.
TIM: For our denominators, 2 and 4, that number is 4. So we want to write all of our fractions as fractions of 4. One-fourth already is, and as we saw before, one-half and two-fourths are really the same thing.
On-screen, the fraction, one-half changes into, two-fourths.
TIM: Now that we have a common denominator, we can just add the numerators! Two-fourths plus one-fourth equals three-fourths.
On-screen, the quarter pie and half pie come together. An equation reads, two-fourths, plus one-fourth, equals three-fourths. Moby beeps.
TIM: Well, subtraction is the same idea. As long as we have a common denominator, it's just a matter of subtracting the numerators.
On-screen, another pie appears. An equation appears, reading, four-fourths, minus one-fourth, equals three-fourths. A quarter of the pie disappears.
TIM: If we don't have a common denominator, we find the lowest common denominator and rewrite our fractions to match. Here's a good example. Last year, Moby's pies were the highest-selling item in the bake sale; in fact, five-ninths of all the students in our school bought them!
Moby beeps and makes the V for Victory sign with his fingers.
TIM: But the year before, only five-twelfths of the school bought the pies.
Moby frowns.
TIM: C'mon. It was the first year you made them… People didn’t know how good they were yet!
Moby smiles.
TIM: Anyway, to find out what fraction of students bought pies the second year but not the first year, we would subtract five-twelfths from five-ninths.
An equation appears, reading, five-ninths minus five-twelfths.
TIM: Okay, the denominators are 9 and 12. What’s the L-C-D?
Moby beeps, and the number, 36, appears.
TIM: Good, 36! That's the lowest number that both 9 and 12 multiply into evenly.
Two equations appear, reading, 9 times 4 equals 36; and 12 times 3 equals 36.
TIM: So let's rewrite our fractions as fractions of 36. Let’s see… to turn 9 into 36, we need to multiply it by 4, which means we also have to multiply the numerator by 4.
On-screen, both the numerator and denominator of the fraction, five-ninths, are multiplied by 4. This results in the fraction, twenty-thirty-sixths.
TIM: And to turn 12 into 36, we multiply it by 3, which means we also multiply 5 by 3.
On-screen, both the numerator and the denominator of the fraction, five-twelfths, are multiplied by 3. This results in the fraction, fifteen-thirty-sixths.
TIM: Now we can just subtract the numerators to get our answer!
An equation appears, reading, twenty-thirty-sixths, minus fifteen-thirty-sixths, equals five-thirty-sixths.
TIM: So, between last year and the year before, your sales increased by five-thirty-sixths.
On-screen, Tim looks at all the pies on the table.
TIM: Hmmm… all these pies we cut up… they're gonna go bad unless I eat them.
Moby beeps and glares. Time passes, and the table is filled with empty pie plates. Tim sits slumped in his chair, clutching his swollen belly. Tim is very sick because he ate too many pies.
TIM: Oh. Ow.
Moby smiles and beeps.
TIM: This is your fault… for making so many pies… Ugh.