Mixed fractions are another form of representing an improper fraction composed of a whole number and a proper fraction. Subtracting mixed fractions is the subtraction operation performed between any two mixed fractions. We will be studying different methods and rules to understand subtracting mixed fractions in this article. Show
Subtracting Mixed Fractions with Like DenominatorsTwo or more fractions having a common denominator are known as like fractions. Hence, mixed fractions with like denominators will have the same denominators such as \(3\dfrac{2}{7}\) and \(2\dfrac{1}{7}\). Look at the following points to be kept in mind while subtracting mixed fractions.
Now let us understand the steps of subtracting mixed fractions with like denominators. Example: Subtract the mixed fraction \(2\dfrac{1}{3}\) from \(4\dfrac{2}{3}\). We have to perform \(4\dfrac{2}{3}\) - \(2\dfrac{1}{3}\). Let's look into the steps.
Hence the value of \(4\dfrac{2}{3}\) - \(2\dfrac{1}{3}\) is \(2\dfrac{1}{3}\). Subtracting Mixed Fractions with Unlike DenominatorsFractions with unequal denominators are known as unlike fractions. Thus, some examples of mixed fractions with unlike denominators are \(5\dfrac{2}{3}\) and \(1\dfrac{2}{5}\). Let us take an example to understand the steps of subtracting mixed fractions with unlike denominators. Example: Subtract \(3\dfrac{1}{6}\) from \(5\dfrac{2}{3}\). We have to perform \(5\dfrac{2}{3}\) - \(3\dfrac{1}{6}\). We have two ways to perform the subtraction. Method I: By subtracting the whole numbers separately and the fractions separately by making their denominators equal.
Method II: By converting them into improper fractions, followed by subtracting them by making their denominators equal.
Hence the value of \(5\dfrac{2}{3}\) - \(3\dfrac{1}{6}\) is equal to \(2\dfrac{1}{2}\). Subtracting Mixed Fractions with RegroupingWhile subtracting mixed fractions, there might arise a situation wherein the fraction to be subtracted is greater than the fraction from which it is being subtracted. In such cases, we will use the concept of regrouping. Let's now understand subtracting mixed fractions with regrouping by taking an example. Example: Subtract \(7\dfrac{2}{3}\) from \(10\dfrac{4}{9}\). We have to perform \(10\dfrac{4}{9}\) - \(7\dfrac{2}{3}\).
Related Articles on Subtracting Mixed FractionsCheck these articles related to the concept of subtracting mixed fractions.
FAQs on Subtracting Mixed FractionsHow to Solve Subtracting Mixed Fractions?Subtracting mixed fractions can be done in two ways. For like denominators, the whole numbers can simply be subtracted and the fractional part of the mixed fractions can also be subtracted and the two results are combined to get the result. The other way to do it is, by converting the mixed fractions to improper fractions and subtracting them. For unlike denominators, they can be first converted to like denominators by finding the LCM and the same steps can be followed as subtracting mixed fractions with like denominators. How to Borrow when Subtracting Mixed Fractions?While subtracting mixed fractions, if the proper fractional part of the mixed fraction from which the other mixed fraction is getting subtracted is smaller, then the whole number gives a borrow to the proper fraction to make it larger. For example, to perform \(3\dfrac{1}{3}\) - \(1\dfrac{2}{3}\) we see that 2/3 > 1/3. Thus, 1/3 will borrow 1 whole from 3. 1 whole can be written as 3/3. The whole number 3 after giving a borrow of 1 becomes 3 - 1 = 2 and the fraction 1/3 becomes (1/3) + (3/3) = 4/3. Thus, the new modified mixed fraction after borrowing is \(2\dfrac{4}{3}\). Now, the subtraction will be \(2\dfrac{4}{3}\) - \(1\dfrac{2}{3}\) = \(1\dfrac{2}{3}\). How to Regroup when Subtracting Mixed Fractions?Regrouping is done when a greater fraction is subtracted from a smaller fraction. For example, let's perform \(8\dfrac{4}{9}\) - \(5\dfrac{2}{3}\) . We will be making the denominators of 4/9 and 2/3 equal to compare them. The fraction 2/3 can also be written as 6/9. But 6/9 > 4/9. We cannot subtract a larger fraction from a smaller fraction. Thus, 4/9 has to be made larger. To do so, 4/9 borrows a 1 from 8. 1 whole can also be written as 9/9. Now, the whole number 8 becomes 8 - 1 = 7 and the fraction 4/9 becomes (4/9) + (9/9) = 13/9. Thus, the new fraction will be \(7\dfrac{13}{9}\). Thus, now the subtraction is as follows: \(7\dfrac{13}{9}\) - \(5\dfrac{6}{9}\) = \(2\dfrac{7}{9}\). How to Subtract Mixed Fractions with Same Denominators?Subtracting mixed fractions with the same denominators is done by subtracting the whole number part and fractional part of the mixed fractions separately followed by combining them to get the result. On simplifying we get, How to Subtract Mixed Fractions with Different Denominators?Subtracting mixed fractions with different denominators can be done by converting them into an improper fraction followed by converting them into like denominators by taking their LCM and finally subtracting their numerators. The final result is then converted back to a mixed fraction. How to Subtract Mixed Fractions from Whole Numbers?The whole numbers can be modified and be written as a mixed fraction. Once the whole number is written in the form of a mixed fraction, the general steps of subtracting the mixed fractions can be followed. How to do Adding and Subtracting Mixed Fractions?Mixed fractions will be subtracted from mixed fractions by first converting them into improper fractions and subtracting their numerators if they have the same denominator. If they have different denominators, then they are first
converted into the same denominators by taking their LCM followed by subtracting their numerators. The final result will be converted back to a mixed fraction. The steps to add mixed fractions also remain the same. The only difference is we add the numerators instead of subtracting. How do you subtract mixed fractions when the first numerator is smaller?Change the mixed number (with 1 as the whole number) into an improper fraction. Subtract the whole number of the smaller mixed number from the whole number of the new larger mixed number. If the proper fractions have similar denominators, subtract the numerators directly and remain the denominator as it is.
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