To add 1/2 and 3/4, the fractions must first be changed to the least common denominator of...what?

Update:

Is the answer 2, 4, 6 or 8?

24 Answers

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  • Anonymous
    2 years ago

    4. 1/2 = 2/4

    2/4 + 3/4 = 5/4

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  • 2 years ago

    not "least common denominator",but

    "least common MULTIPLE OF denominatorS"(LCM in popular parlance)

    easier way would be to multiply all denominators.

    and follow the method listed below

    (a/b)+(c/d)+(e/f)

    ([a*d*f]/bdf)+([c*b*f]/bdf)+([e*b*d]/bdf)

    try this for practice. (1/3)+(4/7)+(5/9)

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  • 2 years ago

    What you have to do is multiply the fractions with the other denominator so you multiply 1 and 2 by 4 which is 4/8 and then multiply 3 and 4 by 2 which is 6/8 after you add it tho you must convert it into an mixed number the final answer would be 1 2/8 if you want to put it to simplest form it would be 1 1/4

    • Trevor H
      Lv 7
      2 years agoReport

      NO - LCM - L stands for LOWEST - which is 4
      Change 1/2 to 2/4 then 2/4 + 3/4 = 5/4 = 1 1/4 or 1.25

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  • 2 years ago

    When you have fractions having different denominators, and you're adding or subtracting, you first need to find a common denominator. This way, you're dealing with apples-to-apples rather than apples-to-oranges. And yes, most textbooks and teachers will have you find the lowest common denominator. And then convert each fraction into it, then add or subtract to get your final answer.

    However, I've taught students to find ANY common denominator they happen to see. Or if you cannot find one, just multiply the denominators together to get a common one. This technique sometimes allows you to at least get an answer. And then you can reduce it down to its lowest terms.

    With 1/2 and 3/4, most can easily see that a common denominator is 4. So we'd need to convert halves to fourths. 1/2 would become 2/4 by multiplying both numerator and denominator by 2. Once this is done, we'd add 2/4 and 3/4 to get our final answer of 5/4. And if your answer needs to be a mixed fraction, it would be 1 1/4.

    But what if you didn't know 4 was the lowest common denominator? You could have just multiplied the two denominators together to get a common one. IN this case that would give you 8. And then convert each fraction to eights. 1/2 would become 4/8 because we'd multiply top and bottom by 4. And 3/4 would become 6/8 because we'd multiply top and bottom by 2. Adding 4/8 and 6/8 together would give us 10/8.

    Both numerator and denominator are divisible by 2. So we can reduce this down to 5/4. That matches the answer we got earlier on. So either way, you can arrive at the final answer. It's just a matter of whether you first find the lowest common denominator or ANY, then reduce afterwards. Depending upon the numbers, I find this alternate strategy sometimes is helpful.

    Source(s): I've taught math on the college-level and when subbing in the public schools.
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  • 2 years ago

    Least common multiple of denominator.

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  • 2 years ago

    The least common denominator of.1/2 and 3/4 is 4.

    1/2 + 3/4

    = 2/4 + 3/4

    = 5/4

    = 1 1/4

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  • 2 years ago

    1/2 = 2/4

    2/4 + 3/4 =

    5/4 =

    1 1/4

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  • Anonymous
    2 years ago

    7.

    Source(s): Wikipedia
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  • RR
    Lv 7
    2 years ago

    It means the lowest number that is divisible by both of them:

    2 is divisible by 2 but not divisible by 4

    6 is divisible by 2 but not divisible by 4

    8 is divisible by 2 and also divisible by 4. It would work but it's not the lowest

    4 is divisible by 2 and also divisible by 4. It's the lowest number that works.

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  • Laurie
    Lv 7
    2 years ago

    What you say is not quite right. In order to add fractions, they must have the SAME (common) denominator... but that does not necessarily have to be the least common denominator.

    For example,

    1/2 = 2/4 = 4/8 = 6/12 = 12/24, and

    3/4, 3/4 = 6/8 = 9/12 = 18/24

    You can add them with any like denominator

    2/4 + 3/4 = 5/4, which simplifies to 1 1/4

    4/8 + 6/8 = 10/8, which simplifies to 1 2/8 = 1 1/4

    6/12 + 9/12 = 15/12, which simplifies to 1 3/12 = 1 1/4

    12/24 + 18/24 = 30/24, which simplifies to 1 6/24 = 1 1/4

    "Least" common denominator simply refers to the smallest number that will work as a denominator for this purpose... but you can use ANY common denominator to add them.

    However, if you do use the LCD, that makes simplification of the final answer easier.

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