A number is called "mixed" when it contains both an integer value and a proper fraction (a fraction where the numerator is less than the denominator). For example, if you are cooking a cake and need to use 2 ½ ounces of flour, you are working with a mixed number. You can convert it to an improper fraction, in which the numerator is greater than the denominator, by using an elementary formula. Such a transformation facilitates the process of calculating and manipulating numbers in an equation or could help you figure out if the solution you have found makes sense.
Steps
Part 1 of 2: Converting a Mixed Number into an Improper Fraction
Step 1. Learn the basic formula
If a mixed number is expressed in the form a b / c, it follows that the equation to convert it into an improper fraction is: (ac + b) / c. In this formula:
- "a" is the internal number;
- "b" is the numerator (the upper part of the fraction);
- "c" is the denominator (the number below the fraction line).
Step 2. Remember the order of operations
The acronym PEDMAS dictates that you first tackle the numbers in brackets. Since multiplications and divisions take precedence over the sum, first calculate the product B. C; later, you can add b, since it is enclosed in parentheses. In the end you can divide the result by c or leave the number c same as the denominator of the improper fraction.
The acronym PEDMAS stands for: parentesi, Andprominent, dvision, moltiplication, todiction e sobtaining.
Step 3. Multiply the integer part of the mixed number by the denominator
Consider the number 1 ⅔, therefore: a = 1, b = 2 And c = 3. Multiply B. C and you get 3 x 1 = 3.
Step 4. Add the numerator to the product you just found
You know what the product is ac = 3, you must then go to the sum of b = 2: 3 + 2 = 5. The total is 5 and represents the new numerator of the improper fraction.
Step 5. Rewrite the fraction with the new numerator
Remember that the denominator of the original fraction (c = 3) remains unchanged and that the new numerator is 5. The improper fraction obtained from the conversion of the mixed number is 5/3.
Step 6. Check the calculations
To be sure of the work, always check the math steps and numbers or check the solution with an online calculator.
Step 7. Simplify the fraction if necessary
The simplified form is the easiest and most direct way to represent a fractional number. To proceed, determine if the numerator and denominator have common factors; if the answer is yes, divide both by the greatest common factor.
- For example, in the fraction 9/42, the greatest common factor is 3.
- Divide both the numerator and the denominator by this value and then simplify the fraction to the lowest terms: 9 ÷ 3/42 ÷ 3 = 3/14.
Part 2 of 2: Converting an Improper Fraction into a Mixed Number
Step 1. Remember the mixed number formula
Once you have learned how to turn a mixed number into an improper fraction, you can also proceed with the inverse calculation. Use the formula a b / c for the mixed number, the denominator remains that of the fraction.
For example, when you convert 7/5 in a mixed number, c = 5.
Step 2. Divide the numerator of the improper fraction by the denominator
Proceed with a division by column or a simple calculation to determine "how many times the denominator is in the numerator" (in other words, do not consider the decimal places). The quotient represents the integer part of the mixed number (the value to).
Dividing 7/5 you get 1, 4 where a = 1.
Step 3. Determine the rest
This represents the new numerator of the fractional portion of the mixed number. When you divide 7/5 you get 1 with the remainder of 2, where b = 2. Now you have all the elements to define the mixed number; the improper fraction 7/5 can be converted to mixed number 1 ⅖.
