## anonymous one year ago 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

1. anonymous

$\frac{ 9 }{ 20 } = ? ; \frac{ 7 }{ 15 } = ?$

2. anonymous

$\frac{ 9 }{ 20 } <,>, or =, \frac{ 7 }{ 15 }$

3. mathstudent55

Can you think of a number that you can divide by both 15 and 20 without remainder?

4. anonymous

5?

5. 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.

6. anonymous

60?

7. 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.

8. mathstudent55

We are comparing these two fractions with denominators 15 and 20. |dw:1440013066669:dw|

9. mathstudent55

Now that we know that 60 is the least common denominator, we need to change both fractions to a denominator of 60.

10. mathstudent55

To change a fraction to an equivalent fraction, we must multiply the numerator and denominator by the same number.

11. mathstudent55

|dw:1440013188915:dw|

12. anonymous

3

13. mathstudent55

Good.

14. mathstudent55

|dw:1440013291109:dw|

15. mathstudent55

Now we do the same to 7/15.

16. mathstudent55

|dw:1440013338011:dw|

17. anonymous

4

18. mathstudent55

Good.

19. mathstudent55

|dw:1440013457711:dw|

20. mathstudent55

Now that we have equivalent fractions with the same denominator, 60, we can compare them with <, =, or >.

21. anonymous

<?

22. mathstudent55

|dw:1440013525798:dw|

23. mathstudent55

24. mathstudent55

|dw:1440013619290:dw|

25. mathstudent55

Since we use < in the equivalent fractions below, we use < also in the original fractions.

26. anonymous

ty