Find the L.C.D. of each of the following groups of fractions and then express the fractions of each group in terms of the L.C.D. of the group.
1/3, 3/5, 21/25, 13/15
Is the LCD 75? Then
1/3 = ?/75 =
Here is the way you convert. Divide 75 by 3 and multiply by 1. so ?/75 = 25/75. You can check to see that you are correct by dividing both 25 and 75 by 3 to obtain 1/3. The others are done the same way. We shall be happy to check your answers if you post them. Post your work if you get stuck.
To find the least common denominator (LCD) of a group of fractions, you need to find the smallest number that is divisible by all the denominators in the group.
1) Start by listing the denominators: 3, 5, 25, and 15.
2) Look for the smallest number that is divisible by all of them. In this case, the number 75 is the smallest number that fulfills this condition.
3) Now that we have the LCD, we need to express each fraction in terms of this common denominator.
To express a fraction in terms of the LCD, you need to multiply the numerator and denominator of each fraction by the same number so that the denominator becomes the LCD. Let's do it for each fraction:
1/3: Multiply numerator and denominator by 25 (75/225)
3/5: Multiply numerator and denominator by 15 (45/75)
21/25: Multiply numerator and denominator by 3 (63/75)
13/15: Multiply numerator and denominator by 5 (65/75)
Hence, the fractions in terms of the LCD (75) are:
75/225, 45/75, 63/75, and 65/75.