A mixed number is a combination of a whole number and a fraction. For example, if you have two whole apples and one half apple, you could describe this as 2 + 1/2 apples, or 21/2 apples. Show Writing Mixed Numbers as FractionsThis mixed number can also be expressed as a fraction. Each whole apple contains two half apples. Your two whole apples are also four half apples. Four half apples plus one half apple is five half apples. So you have 5/2 apples. To put this another way: to turn a mixed number into a fraction, multiply the whole number by the denominator (the bottom part), and add the result to the numerator (the top part). 21/2 = ? Another ExampleLet's try another example: 52/3 = ? Proper and Improper FractionsA fraction in which the numerator is smaller than the denominator, like 1/3 or 2/5 is called a proper fraction. A fraction in which the numerator is larger than or equal to the denominator, like 5/2, 17/3, or 6/6 is called an improper fraction. (To put it another way, a fraction with a value less than 1 is a proper fraction. A fraction with a value greater than or equal to 1 is an improper fraction.) As we have shown above, mixed numbers can be written as improper fractions. Similarly, improper fractions can be written as mixed numbers. Writing Improper Fractions as Mixed NumbersTo write an improper fraction as a mixed number, divide the numerator (top part) by the denominator (bottom part). The quotient is the whole number, and the remainder is the numerator. How would you express 17/4 as a mixed number? Two More ExamplesLet's try another couple of examples: 14/9 = ? If there is no remainder, just take the quotient as the whole number: 20/5 = ?Lowest Common Multiples Multiplying Fractions and Mixed Numbers .com/ipa/0/9/3/3/4/5/A0933459.html
Analysis: This problem is asking: How many halves are in three and one-half? Step 1: Let's use shapes to represent the mixed number three and one-half. Step 2: Solution: In example 1, we used shapes to help us solve the problem. Let's look at example 2. Example 2: A school bell rings every half-hour. If it just rang, then how many times will it ring in in the next nine and one-half hours? Analysis: Using shapes to solve this problem would not be practical. We need to find another method. Recall that a mixed number consists of a whole-number part and a fractional part. For example: Procedure: To write a mixed number as an improper fraction:
Let's use the procedure above to solve the problem from example 2. Example 2: A school bell rings every half-hour. If it just rang, then how many times will it ring in in the next nine and one-half hours? Analysis: Step 1: Step 2: Solution: The school bell will ring 19 times in the next nine and one-half hours. Let's look at some more examples of writing a mixed number as an improper fraction. Example 3: Write two and three-fourths as an improper fraction. Analysis: Step 1: Step 2: Solution: Example 4: Write six and two-thirds as an improper fraction. Analysis: Step 1: Step 2: Solution: Here is a summary of examples 1 to 4. Do you see a pattern? Do you see an easier way to write a mixed number as an improper fraction? There is a shortcut we can take for writing a mixed number as an improper fraction: If you multiply the denominator by the whole-number part, then add the numerator, the result gives you the numerator of the improper fraction. This is shown below for the mixed number two and three-fourths. Recapping examples 1 to 4, we get: Let's look at some more examples of writing a mixed number as an improper fraction using this shortcut. Example 5: Write eleven and three-fifths as an improper fraction. Analysis: Step 1: Solution: Example 6: Write fourteen and one-third as an improper fraction. Analysis: Step 1: Solution: This shortcut uses only one step, and makes it easier to convert large mixed numbers into improper fractions. Summary: There are several methods for converting a mixed number into an improper fraction. Use the one that is appropriate for the given problem. ExercisesIn Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the improper fraction five-thirds, enter 5/3 into the form.
Sign Up For Our FREE Newsletter!Sign Up For Our FREE Newsletter!What is 3/4 as a mixed number?3/4 = 34 = 0.75
Spelled result in words is three quarters.
What is 7/4 as a mixed number?Answer: 7/4 as a mixed number can be written as 1 3/4.
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