How to Change Mixed Numbers to Improper Fractions
Learn the basic equation., Remember the order of operations., Multiply the whole number and the denominator., Add the numerator to the product., Rewrite the improper fraction with the new numerator., Check your work., Reduce the fraction to its...
Step-by-Step Guide
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Step 1: Learn the basic equation.
If a mixed number is a b/c then the equation used to convert it to an improper fraction is (ac+b)/c.In this equation:
A is the whole number.
B is the numerator (the top portion of the fraction).
C is the denominator (the bottom portion of the fraction). -
Step 2: Remember the order of operations.
BEDMAS or PEDMAS dictates that you must first address the numbers in parentheses.
Since multiplication and division come first, you will first multiply ac.
You will then add b, since that figure is also within parentheses.
Finally, you will divide by c, or use c as the new denominator.
P/BEDMAS stands for parentheses/brackets, exponents, multiply or divide, and add or subtract. , Take the mixed number 1 ⅔ for example: a = 1, b = 2, and c =
3.
Multiply ac, which in this example is 3 x 1 =
3., You now know the product of ac = 3, so now it's time to add b = 2: 3 + 2 =
5.This sum, 5, is the new numerator of your improper fraction. , Remember that the denominator (c = 3) remains the same from the original fraction, and the new numerator is
5.
The improper fraction converted from the original mixed number, therefore, is 5/3. , To be certain, you can always double check your math by running the numbers again, or verifying the answer using an online calculator. , The simplest form is the smallest and easiest way to represent a fraction.
To reduce a fraction to its simplest form, determine if the numerator and denominator have common factors.
If they do, select the highest one and divide the numerator and denominator by that number.For instance, in the fraction 9/42, the greatest common factor is
3.
Divide both the numerator and denominator by the greatest common factor to get the fraction's simplest form: 9 ÷ 3 / 42 ÷ 3 = 3/14 , Just as you can convert a mixed number into an improper fraction, so too can you convert going the other way.
Like before, use the formula a b/c for your mixed number.
The denominator from your improper fraction will be the same denominator in your mixed number.
For instance, when converting the improper fraction 7/5 into a mixed number, c =
5. , Use long division or a simple calculation to determine how many times the denominator will fully go into the numerator (don't worry about any decimals).
That number will be the mixed number’s whole number (the a value).
Dividing 7/5 gives you
1.4, where a =
1. , The remainder is your new numerator.
When you divide 7/5 you get 1 with a remainder of 2, where b =
2.
You now have all the components of your mixed number: the improper fraction 7/5 gives you the mixed number 1 ⅖. -
Step 3: Multiply the whole number and the denominator.
-
Step 4: Add the numerator to the product.
-
Step 5: Rewrite the improper fraction with the new numerator.
-
Step 6: Check your work.
-
Step 7: Reduce the fraction to its simplest form if necessary.
-
Step 8: Remember the mixed number formula.
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Step 9: Divide the improper fraction’s numerator by its denominator.
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Step 10: Determine the remainder.
Detailed Guide
If a mixed number is a b/c then the equation used to convert it to an improper fraction is (ac+b)/c.In this equation:
A is the whole number.
B is the numerator (the top portion of the fraction).
C is the denominator (the bottom portion of the fraction).
BEDMAS or PEDMAS dictates that you must first address the numbers in parentheses.
Since multiplication and division come first, you will first multiply ac.
You will then add b, since that figure is also within parentheses.
Finally, you will divide by c, or use c as the new denominator.
P/BEDMAS stands for parentheses/brackets, exponents, multiply or divide, and add or subtract. , Take the mixed number 1 ⅔ for example: a = 1, b = 2, and c =
3.
Multiply ac, which in this example is 3 x 1 =
3., You now know the product of ac = 3, so now it's time to add b = 2: 3 + 2 =
5.This sum, 5, is the new numerator of your improper fraction. , Remember that the denominator (c = 3) remains the same from the original fraction, and the new numerator is
5.
The improper fraction converted from the original mixed number, therefore, is 5/3. , To be certain, you can always double check your math by running the numbers again, or verifying the answer using an online calculator. , The simplest form is the smallest and easiest way to represent a fraction.
To reduce a fraction to its simplest form, determine if the numerator and denominator have common factors.
If they do, select the highest one and divide the numerator and denominator by that number.For instance, in the fraction 9/42, the greatest common factor is
3.
Divide both the numerator and denominator by the greatest common factor to get the fraction's simplest form: 9 ÷ 3 / 42 ÷ 3 = 3/14 , Just as you can convert a mixed number into an improper fraction, so too can you convert going the other way.
Like before, use the formula a b/c for your mixed number.
The denominator from your improper fraction will be the same denominator in your mixed number.
For instance, when converting the improper fraction 7/5 into a mixed number, c =
5. , Use long division or a simple calculation to determine how many times the denominator will fully go into the numerator (don't worry about any decimals).
That number will be the mixed number’s whole number (the a value).
Dividing 7/5 gives you
1.4, where a =
1. , The remainder is your new numerator.
When you divide 7/5 you get 1 with a remainder of 2, where b =
2.
You now have all the components of your mixed number: the improper fraction 7/5 gives you the mixed number 1 ⅖.
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Janice Henderson
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