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Ordering Fractions

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Transcript Ordering Fractions

“The water glistens on the cave walls tonight.” “Tank, I think this machine is broken.” “We’ll have to get a new one.” We can help Axel find the best deal on a new karaoke machine by… “Ordering Fractions”. We can compare and order fractions with unlike denominators... by creating equivalent fractions with common denominators. An equivalent fraction is a fraction that has the same value but is represented with a different numerator and denominator. Let’s use three-fourths and five-sixths as an example. First, we rename each fraction with a common denominator. To find the common denominator of fractions, we need to think of a multiple that they share. What is one number that is a multiple of BOTH four and six? Twenty-four. This number becomes the denominator for both fractions. To rename the numerators, we multiply the numerator by the SAME number that we multiplied the original denominator by. In three-fourths, we multiply the denominator, four, by six to make twenty-four, so we will also multiply the numerator by six. What is three times six? Eighteen. Three-fourths is the same as eighteen twenty-fourths. In five-sixths, we multiply the six by four to make twenty-four, so we will multiply the five by four. What is five times four? Twenty. Five-sixths is the same as twenty-twenty-fourths. Once we have like denominators, we can order the fractions from least to greatest by looking at the numerators. Eighteen is less than twenty, so three-fourths is less than five-sixths. Axel sees ads for three stores selling karaoke machines. Each store is running a sale with the machine being a fractional amount off the regular price. If we make equivalent fractions and order them, we’ll determine which store has the biggest discount. We have two-thirds, one-half, and four-fifths. First, think of a multiple that three, two, AND five share. Thirty is a multiple that can be made with all three numbers. Now, rewrite all the denominators as thirty. Next, rename the numerators, by multiplying them by the SAME number that we multiplied the original denominator by. Let’s start with the store with two-thirds off the price. What do we multiply three by to make thirty? Ten… so we will multiply the numerator, two, by ten. What is two times ten? Twenty. Two-thirds and twenty-thirtieths are equivalent. In one-half, what do we multiply two by to make thirty? Fifteen. We will multiply the numerator, one, by fifteen and get fifteen. One-half and fifteen-thirtieths are equivalent. Finally, in four-fifths, what do we multiply five by to make thirty? Six. What is six times, the numerator, four? Twenty-four. Four-fifths and twenty-four thirtieths are equivalent. What do we do next? We compare the numerators and order the fractions from least to greatest. The order of the numerators from least to greatest is fifteen, twenty, and twenty-four, so we order the fractions as one-half is less than two-thirds is less than four-fifths. The store with four-fifths off the price has the biggest discount. As Axel and Tank make their purchase, let’s review. Remember… we can compare and order fractions with unlike denominators by creating equivalent fractions with common denominators. First, we rename each fraction with a common denominator. To rename the numerators, we multiply it by the SAME number that we needed to multiply to make the denominator. Once we have like denominators, we can order the fractions from least to greatest by looking at the numerators. We can write the original fractions as an expression using less than or greater than symbols. “The water glistens on the cave walls tonight.” “No fish can be seen.” singing beautifully] “I’m in an aquarium of solitude…” “ and it appears….I’m the KING!” "Ebb and FLOW, ebb and Flow..." "That's so beautiful!"