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order of operations in fractions


Order of Operations𝅺 in Fractions


The order of⁤ operations in fractions is a ⁤fundamental concept⁤ in mathematics. It helps us solve complex fractions 𝅺by determining the correct sequence ⁤of 𝅺calculations.‍ The‍ order of ‍operations ensures that we obtain the right answer every time, allowing us to⁤ solve a wide range of fraction𝅺 problems with ease.

When working with 𝅺fractions, it’s ​necessary to ‌follow a ⁢specific order of operations to correctly simplify or solve ​any​ expression involving fractions. Let’s break it​ down ‌step ‍by ⁢step:

  1. Parentheses ( ): Start by simplifying any expressions within parentheses first. This applies to​ both fractions and whole‍ numbers.

  2. 𝅺

  3. Exponents​ ^: ‌Evaluate ‍any⁣ exponentiation. If there⁣ are ⁤no​ exponents,⁢ move on to the next​ step.
  4. Multiplication and ⁣Division: Perform ⁣multiplication and division operations from left to right.‍ Remember to convert ‌mixed numbers ​to improper ⁤fractions when necessary.
  5. Addition⁣ and Subtraction: ⁣Finally, perform ⁢addition𝅺 and subtraction ‌from ‌left⁤ to right.⁢ Similar to⁢ the 𝅺previous step, convert ⁢mixed numbers to improper fractions if 𝅺needed.


Let’s illustrate⁤ the order of ​operations in fractions with an ‍example:

Consider the expression: ⁢

4/5 ⁤+ 2/3𝅺 * (7/8 -𝅺 1/2) /​ 3/4

We ‍start‌ by simplifying the expression⁢ within ​the parentheses first:

4/5 + 2/3 *‌ (7/8‌ – 1/2) ​/‌ 3/4 ⁤

This allows ‍us to simplify further:

4/5 ⁤+ 2/3 *⁣ (7/8⁤ – 4/8) /⁣ 3/4 ‌

After subtracting the⁣ fractions within the parentheses:

4/5 + 2/3 ⁢* (3/8) / 3/4

We can‍ then evaluate ​the⁤ multiplication:

4/5‌ + (2/3 *⁢ 3/8) / 3/4

And now,‌ following the division:


4/5 + (1/4)

Lastly, we 𝅺can​ perform the addition:

4/5 +𝅺 1/4‍

To⁤ add these ⁢fractions with different denominators,𝅺 we must first find⁢ the‍ least ​common denominator (LCD), which is𝅺 20 in this case:

16/20 + 5/20 ​= 21/20

⁢ ⁣

This ⁤means the final result of the expression is 21/20.

Understanding and applying ⁣the‍ order of ⁤operations ‌in fractions is ⁤essential‍ for correctly solving complex ​fraction problems. Always ‍remember ‍to follow the𝅺 sequence of ​parentheses, exponents, multiplication ⁣and ‍division, and⁢ finally addition ⁤and subtraction. By‌ using⁣ this method,⁢ you will ensure ⁤accurate results and ​avoid​ common calculation errors.

So⁢ the next time you encounter fractions in a ‌mathematical expression, don’t ‌forget about the⁤ order‌ of‍ operations in ⁤fractions. ⁤It will 𝅺guide you⁣ through the correct steps ‍to achieve the correct⁣ answer.

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