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Fractions & Decimals

Fractions & Decimals

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Sometimes you'll be asked to convert mixed numbers into improper fractions, and vice versa. Once you get the hang of it, you'll be doing it in your sleep.

Let's start by looking at mixed numbers and improper fractions visually.

This is 2 3/4

diagram of 2 3/4

If we divide each whole circle into fourths, we can count the number of blue fourths. Shazam! There are 11 blue fourths, or 11/4

This is 10/3

diagram of 10/3

As you can see we have 3 wholes and 1 section remaining, or 3 1/3.

You could also think of mixed numbers as sums of whole numbers and their parts. For example 3 1/3 is really 3 + 1/3

3 1/3 = 3 + 1/3

3/1 + 1/3

3/1 x 3/3 + 1/3

9/3 + 1/3

10/3

And try another example...

2 3/ 4 is 2 + 3/4

This time the common denominator is 4.

2 3/4 = 2 + 3/4

2/1 +3/4

2/1 x 4/4 + 3/4

8/4 + 3/4

11/4

How to Change a Mixed Number into an Improper Fraction

  1. Multiply the denominator by the whole number. 
  2. To that, add the numerator. 
  3. Place that number over the original denominator.

Example 1

changing mixed number to improper fraction

Example 2

changing mixed number to improper fraction

Change an Improper Fraction into a Mixed Number

  1. Divide the denominator into the numerator. 
  2. The result will be a whole number with a remainder. The remainder becomes the numerator of the fraction part. The denominator remains the same.
Example 1

19/5

5 goes into 19 three times with four remaining.

19/5

3 is the whole number. 4 is the numerator. 5 is the denominator, which stays the same.


Example 2

19/5

2 goes into 11 five times with one remaining. The denominator stays the same.

19/5

5 is the whole number. 1 is the numerator. The denominator stays the same.


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