Comparing negative numbers
John is making pasta dough. To make the dough, he mixed 3/2 cups wheat flour with 3/4 cups regular flour in some water. Write an inequality to express the relationship between the wheat flour and the regular flour. He mixed 3/2 cups of wheat flour. 3/2 is the exact same thing as 1 and 1/2, if we were to write it as a mixed number. So it's more than 1 cup of wheat flour. And he mixes his that with 3/4 cups of regular flour. Well, 3/4 is less than 1, so 3/2 is definitely greater than 3/4. And we can just pick greater than right over there. 3/2 is greater than 3/4. Let's do a couple more of these. One of the deepest points in the Indian Ocean, the Diamantina trench, is at negative 8 kilometers. We say it is negative 8 kilometers because it is 8 kilometers below sea level. The deepest part of the Bering Strait is at negative 5 and 4/9 kilometers. Write an inequality to show the relationship between these two points, and determine which point is deeper. Let's see. We have a greater than sign here. So we want to write whichever quantity is greater on the left-hand side. We look right over here. This number, negative 5 and 4/9, it is less negative. So it's actually going to be greater value. It's not as deep. We can write negative 5 and 4/9 kilometers is greater than negative 8 kilometers. And so if we're thinking about which point is deeper, it's going to be the one that's more negative, because that tells us how far below sea level we are. So the negative 8 kilometer point is further below sea level. Let's see. Negative 8 kilometers. The Diamantina trench at negative 8 kilometers is the deeper point. This is fun, because in some of these questions you actually learn things. I always thought that the deepest part of the Bering Sea-- well, anyway. We can talk about that another time. Negative 8 kilometers, so the Diamantina trench is deeper. Let's do one more. John is making noodles. To make the batter, he mixes 11/16 cups tapioca flour with 3/8 rice flour and some water. Write an inequality to express the relationship between the tapioca flour and rice flour. So we're really comparing 11/16 cups of tapioca to 3/8 cups rice flour. So we're really comparing these two fractions. And at first it might seem hard to compare. You have different denominators. But 3/8 could easily be converted to a fraction with 16 as the denominator. What would you do? Well, if you doubled both the 3 and the 8-- you have to do the same thing to the numerator and the denominator-- this fraction 3/8 is equivalent to 6/16. And then you would have the same denominator. You could compare 11/16 to 6/16. Well, if you have the same denominator and this numerator is greater, 11 is greater than 6, 11/16 is going to be greater than 6/16, which is the same thing as 3/8. And we got it right.