How do I solve this problem step by step: 21/2 + 42/3?


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Mike J Profile
Mike J answered

You want a step-by-step answer, so I'll give you a thorough, organized answer to your question. :)

When answering a question like this in which you have to add fractions that do not have common denominators, you first need to make both fractions have the same denominator. In this problem, your denominators are different, as you have 2 and 3. You need to find the least common denominator for both fractions.

Least common denominator is similar to least common multiple. In order to find this, list multiples of both numbers until both numbers have a denominator in common. This number will be used as your least common denominator.

So, find the least common denominator of 2 and 3.

  • 2: 2, 4, 6
  • 3: 3, 6
This one didn't take too long, as you already have a common denominator of 6. So now that you have the common denominator, you need to change both fractions so they both have that denominator.
  • I want to change 21/2 to have a denominator of 6. In order to make the denominator 6, you have to multiply 2 by 3. What you do to the denominator, you must do to the numerator. So, multiply the numerator (21) by 3 as well. Now you have 63/6 as your new fraction. Keep this in mind, as you'll need it later.
  • Now, I want to also change 42/3 to have a denominator of 6. To do this, multiply the denominator, which is 3, by 2, and then you'll get a denominator of 6. Again, do the same to the numerator. Multiply 42 by 2. Your numerator is 84, so your fraction is 84/6.
Now that we have our fractions with common denominators, it's really easy from here. Just add the numerators, and keep the denominator the same.
63/6 + 84/6 = 147/6.
Your answer turns out to be 147/6, however you need to reduce the fraction into lowest terms (simplest form). To do this, divide both the numerator and denominator by 3 (this is known as your greatest common factor, which is the largest factor that both numbers have in common). Your new, and final answer, is 49/2.
Hope this helps you out!

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