How to add and subtract fractions with whole numbers

Video transcript

Let's add 19 and 3/18 to 18 and 2/3. So I like to separate out the whole number parts from the fraction parts. So 19 and 3/18 is the same thing as 19 plus 3/18. And to that, we are going to add 18 and 2/3, which is the same thing as 18 plus 2/3. Now we can separately add the whole number parts. So we could add the 19 to the 18. So we could do 19 plus 18. And then we can add the fraction parts-- let me do this in green-- plus 3/18 plus 2/3. Now 19/18, pretty straightforward. That is what? Let's see. 19 plus 19 would be 38. So this is going to be 1 less than that. It's going to be 37. So that gives me 37. And then 3/18 plus 2/3, to add them, I need to have the same denominator. And the least common multiple of 18 and 3 is 18. So let's convert 2/3 to something over 18. So 2/3, if I want to write it as something over 18, well, I multiplied the denominator by 6, so I'd also have to multiply the numerator by 6. So it's the same thing as 12/18. So I can rewrite 2/3 as 12/18. And now I can add these two things together. That's going to be-- so I have 37 plus-- it's going to be something over 18-- plus something over 18. 3 plus 12 is 15, plus 15/18. And so expressing this as a mixed number, I get 37 and 15/18. And that's the right number. But we can simplify it even more. We can simplify the 15/18. Both the numerator and the denominator are divisible by 3. So let's divide them both by 3. And we're not changing the value because we're doing the same thing to the numerator and the denominator. And so this gives us, we still have our 37, but the numerator is now 5, and the denominator is now 6. So we get 37 and 5/6. And we're done.

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Subtracting fractions from whole numbers isn't as hard as it looks. There are two main ways to go about it: you can either convert the whole number into a fraction, or subtract 1 from that whole number and convert the 1 into a fraction with the same base as the fraction you're subtracting from it. Once you have two fractions with the same base, you can start to subtract. Both methods will help you.

  1. How to add and subtract fractions with whole numbers

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    Convert the whole number to a fraction.To do this, give the whole number a denominator of 1.[1]

  2. How to add and subtract fractions with whole numbers

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    Convert to fractions of like denominators. The original fraction's denominator is also the least common denominator (LCD) of the two fractions. Multiply the top and bottom of the "whole number fraction" by this number so the fractions have the same denominator.[2]

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  3. How to add and subtract fractions with whole numbers

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    Subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal subtraction problem:[3]

  4. How to add and subtract fractions with whole numbers

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  1. How to add and subtract fractions with whole numbers

    1

    Try this for large whole numbers. Did you see how the method above converts the whole number into a fraction, then converts back to a mixed number at the end? This method lets you skip some of that so the fraction only involves smaller numbers.

  2. How to add and subtract fractions with whole numbers

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  3. How to add and subtract fractions with whole numbers

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    Separate the whole number into 1 and another whole number. For example, rewrite 5 as 4 + 1, or rewrite 22 as 21 + 1.

  4. How to add and subtract fractions with whole numbers

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    Convert the 1 into a fraction. At this point we're using the method above to solve the part of the problem in the form "1 - (fraction)". The other whole number will stay the same for the rest of the problem.

  5. How to add and subtract fractions with whole numbers

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    Multiply to give the fractions like denominators. As described above, multiply the top and bottom of your new fraction so it has the same denominator as the original fraction.

  6. How to add and subtract fractions with whole numbers

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    Combine the two fractions. Subtract the numerators to solve the fraction part of the equation.

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Add New Question

  • Question

    If the whole number is 1, then how am I supposed to make it into a fraction if 1/1 is 1 whole?

    How to add and subtract fractions with whole numbers

    As a simple example, let's say we're subtracting ¾ from 1. Convert 1 to 4/4. 4/4 - ¾ = ¼. If the whole number is something else, let's say 6, and you're subtracting ¾, convert the 6 to 24/4. 24/4 - ¾ = 21/4, or 5¼.

  • Question

    Can you help me with 5 5/6 - 2 2/3 step by step?

    How to add and subtract fractions with whole numbers

    1. 5 5/6 - 2 2/3 = 5 5/6 - 2 4/6 2. 5 5/6 - 2/4/6 = 3 1/6

  • Question

    I'm confused. Can you please give an example?

    How to add and subtract fractions with whole numbers

    Karianna Wood

    Community Answer

    Take 3 - 2/7, for example. What over 7 is 3? 21, because 7 x 3 = 21. So 3 - 2/7 is the same as 21/7 - 2/7. What is 21/7 - 3/7? 21 - 3 = 18. So 21/7 - 3/7 = 18/7. (Optional) Simplify 18/7, which is 2 4/7. Does that help?

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To subtract a fraction from a whole number, start by converting the whole number to a fraction. Do this by giving the whole number a denominator of 1. For instance, if you’re subtracting 4/5 from 8, convert 8 into the fraction 8/1. Next, multiply the new fraction’s numerator and denominator by the denominator of the fraction that you’re subtracting. In our example, you’d multiply 8/1 by 5 to get 40/5. Now you have two like fractions—that is, two fractions that share the same denominator. Carry out the subtraction problem using just the numerators of the two fractions. In this example, 40-4 = 36. Write the difference between the two numerators over the common denominator to get 36/5. If you want to convert the answer to a mixed fraction, divide the numerator by the denominator. The quotient will become the new whole number, while the remainder will become the numerator of the new fraction. In this case, 36/5 = 7 with a remainder of 1, giving you the mixed fraction 7 and 1/5. For a trick to help subtract a fraction from a very large whole number, read on!

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How do you add fractions with a whole number?

Answer: Once again, when adding fractions and whole numbers, first calculate the whole number plus the whole number, and then include the remaining fraction in the answer. For example, 45+2=47, so 4713 is the answer.

How do you add and subtract fractions with different denominators and whole numbers?

Subtracting mixed fractions? You could first convert each to an improper fraction. If they don't have common denominators, then find a common denominator and use it to rewrite each fraction. Then, subtract the fractions and simplify.