Mixed number is one that contains both a whole number and a proper fraction (a fraction in which the numerator is less than the denominator). For example, if you are baking a cake and need 2 ½ cups of flour, this measurement is a mixed number. This type of number can be converted to improper fractions, that is, a fraction where the numerator is greater than the denominator. This conversion can be done using a basic formula. Then it will be easier to work with the numbers in an equation, or even better understand the result obtained.
Part 1 of 2: Converting a Mixed Number to an Improper Fraction
Step 1. Learn the basic equation
If a mixed number is equal to b/c, so the equation used to convert it to improper fraction is (ac+b)/c. In this equation:
- A is the whole number.
- B is the numerator (the top part of the fraction).
- C is the denominator (the bottom of the fraction).
Step 2. Remember the order of operations
The acronym CEDMAS or PEDMAS dictates that you must first treat the number in parentheses. As multiplication and division come first, you need to multiply first B.C. then disappear B, as it is also in parentheses. Finally, divide the result by ç, or use ç as a new denominator.
P/CEDMAS means parentheses/brackets, exponents, divide or multiply, and add or subtract
Step 3. Multiply the whole number by the denominator
get the mixed number 1 ⅔ for example: a = 1, b = 2 and c = 3. Multiply B.C, which in this example will be 3 x 1 = 3.
Step 4. Add the numerator to the product
Now, you know that the product of ac = 3, so it's time to add b = 2: 3 + 2 = 5. This sum, 5, is the new numerator of the improper fraction.
Step 5. Rewrite the improper fraction with the new numerator
Remember that the denominator (c = 3) remains the same as the original fraction, and the new numerator is equal to 5. Therefore, the improper fraction converted from the original mixed number is 5/3.
Step 6. Check the result
To be sure, check the result by doing the math again or using an online calculator.
Step 7. Reduce the fraction to its simplest form if necessary
The simplest form is the smallest and easiest way to represent a fraction. To do this, determine whether the numerator and denominator have a common factor. If so, select the greatest common factor and divide the numerator and denominator by it.
- For example, in the fraction 9/42, the biggest common factor is 3.
- Divide both the numerator and denominator by the greatest common factor to reduce the fraction to its simplest form. 9 ÷ 3 / 42 ÷ 3 = 3/14.
Part 2 of 2: Changing an Improper Fraction to a Mixed Number
Step 1. Remember the mixed number formula
Just as you can convert a mixed number to an improper fraction, the reverse is also possible. As before, use the formula b/c for the mixed number. The denominator of the improper fraction will be the same denominator of the mixed number.
- For example, when converting the improper fraction 7/5 in mixed numbers, c = 5.
Step 2. Divide the improper fraction numerator by its denominator
Do a hand division or simple calculation to determine how many times the denominator fits "in whole" into the numerator (don't worry about decimals). This number will be the whole number of the mixed number (the value The).
- Splitting 7/5 will result in 1, 4, where a = 1.
Step 3. Get the rest
The rest will be the new numerator. When dividing 7/5, the result is 1 with 2 remaining, where b = 2. Now you have all the components of the mixed number: the improper fraction 7/5 equals the mixed number 1 ⅖.