A mixed number is expressed as the sum of a whole number and a fraction (ex. ). Mixed numbers give a good idea of the size of a number. But when it comes to making calculations, improper fractions are usually easier to work with. If you encounter a mixed number, you'll want to know how to convert it into an improper fraction, and vice versa. Let's go over these steps.
Improper fractions are alternate expressions of mixed numbers. For example, the mixed number can also be written as . But what steps should you take to turn a mixed number into an improper fraction? Let's find out.
Write the mixed number as an improper fraction.
First, we'll write the mixed number as a sum of a whole number and a proper fraction:
Then, we'll write the two parts with a common denominator.
Now, add the fractions.
is the improper fraction equivalent of .
Now that you've learned how to write a mixed number as an improper fraction, let's go over the shortcut method, which can give you the same answer much faster.
Write as an improper fraction.
First, multiply the whole part by the denominator of the fractional part.
Next, add the numerator of the fractional part. This is the numerator of the improper fraction.
Another way to find the numerator is to write the following: .
Keep the same denominator, 4, and you have the improper fraction .
Now, let's try writing the improper fraction as a mixed number.
First, divide the numerator by the denominator.
We have a quotient of 5, and a remainder of 2.
We'll use the quotient as the whole part of the mixed number and the remainder as the numerator of the fractional part. Keep the denominator the same.
a. Write as an improper fraction.
Answer:
b. Write as an improper fraction.
Answer:
c. Write as an improper fraction using the shortcut method.
Numerator: . Denominator: 7.
Answer:
d. Write as a mixed number.
To write as a mixed number, we perform the division:
The quotient is 4 and the remainder is 2. The denominator remains as 3.
So, can be expressed as the sum of the whole number quotient and the fraction with the same denominator:
Therefore, the answer is .
e. Write as a mixed number.
Quotient: 6. Remainder: 5. Denominator: 7.
Answer:
Least Common Denominators (LCDs)
Common Core: 5th Grade Math Flashcards
MAP 5th Grade Math Practice Tests
Common Core: 5th Grade Math Diagnostic Tests
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