anonymous
  • anonymous
I Will Medal And Fan! I need explanation AND answer! First, rewrite 9/20 and 7/15 so that they have a common denominator. Then, use <, =, or > to order 9/20 and 7/15 9/20 = ? ; 7/15 = ? 9/20 <,>, or = 7/15
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{ 9 }{ 20 } = ? ; \frac{ 7 }{ 15 } = ?\]
anonymous
  • anonymous
\[\frac{ 9 }{ 20 } <,>, or =, \frac{ 7 }{ 15 }\]
mathstudent55
  • mathstudent55
Can you think of a number that you can divide by both 15 and 20 without remainder?

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anonymous
  • anonymous
5?
mathstudent55
  • mathstudent55
No. You misunderstood me. You found a number that you can divide 15 by and 20 by with no remainder. 15/5 = 3, and 20/5 = 4. No remainder. That's not what we need. We need a number greater than 15 and 20. Call that number x. The number must be such that x/15 and x/20 have no remainder. Here's a way of finding such a number. Multiply 15 by 1, 2, 3, 4, 5, and write down the numbers. Then multiply 20 by 1, 2, 3, 4, 5, and write down the numbers. The smallest number in both lists is the number we need.
anonymous
  • anonymous
60?
mathstudent55
  • mathstudent55
Excellent. 60 is the least common multiple of 15 and 20. That means 60 is the smallest number that you can divide by both 15 and 20 with no remainder.
mathstudent55
  • mathstudent55
We are comparing these two fractions with denominators 15 and 20. |dw:1440013066669:dw|
mathstudent55
  • mathstudent55
Now that we know that 60 is the least common denominator, we need to change both fractions to a denominator of 60.
mathstudent55
  • mathstudent55
To change a fraction to an equivalent fraction, we must multiply the numerator and denominator by the same number.
mathstudent55
  • mathstudent55
|dw:1440013188915:dw|
anonymous
  • anonymous
3
mathstudent55
  • mathstudent55
Good.
mathstudent55
  • mathstudent55
|dw:1440013291109:dw|
mathstudent55
  • mathstudent55
Now we do the same to 7/15.
mathstudent55
  • mathstudent55
|dw:1440013338011:dw|
anonymous
  • anonymous
4
mathstudent55
  • mathstudent55
Good.
mathstudent55
  • mathstudent55
|dw:1440013457711:dw|
mathstudent55
  • mathstudent55
Now that we have equivalent fractions with the same denominator, 60, we can compare them with <, =, or >.
anonymous
  • anonymous
mathstudent55
  • mathstudent55
|dw:1440013525798:dw|
mathstudent55
  • mathstudent55
Wow, you answer my question before I even ask.
mathstudent55
  • mathstudent55
|dw:1440013619290:dw|
mathstudent55
  • mathstudent55
Since we use < in the equivalent fractions below, we use < also in the original fractions.
anonymous
  • anonymous
ty

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