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Understanding Fractions: Types, Math Operations & Conversions

Explore what fractions mean and the different types of fractions - proper, improper, and mixed. Learn how to convert between top-heavy fractions and mixed numbers and practice with examples.

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Understanding Fractions: Types, Math Operations & Conversions

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  1. Fractions 1 Click mouse

  2. What does mean? What is a fraction? 7 _____ 10 Seven out of ten 0.7 Seven tenths 70% Seven over ten Seven divided by ten Click mouse

  3. A fraction shows how one part of something compares to the whole. There are two parts to a fraction. Numerator Denominator Click mouse to continue Click mouse

  4. Proper fraction Types of fraction ¾ ½ 3/10 5 8 ¼ Improper fraction 4/3 5/4 8/5 11/7 or “top heavy” 2 3 5 Mixed fraction ½ ¼ ¾ Click mouse

  5. Changing a mixed number to a top heavy fraction The first example will use the fraction 2 1 (two and a third) and change this into a top heavy fraction: 3 1 This is 2 whole ones 2 … and one third of a whole. 3 Q. How many thirds in a whole? One whole A. Three Q. How many thirds in two whole ones? 2 whole ones A. Six Q. How many thirds altogether? … and one third A. Seven 7 How is this written? So you have “seven thirds”. 3 Click mouse

  6. Second example How about 34 ? 5 “Three and four fifths” Q. How many fifths in a whole? A. Five Q. How many fifths in three whole ones? A. Fifteen Then add on the other “four fifths” Q. Total number of fifths? 19 5 A. Nineteen. Click mouse

  7. There must be a quicker way!! Now 34 5 … and there is!! 3 x 5 = 15 Going back to the two previous examples: 19 5 15 + 4 = 19 1 2 3 Q. What is it that you actually find? A. The total number of thirds! Now try 23 4 2 x 4 = 8 + 3 = 11 This can be done as follows: = 11 4 1 This tells us how many thirds there are in two whole ones! 2 2 3 = 6 x 3 Eleven fourths or eleven quarters. 7 Now add the other third to get seven thirds! 3 Click mouse

  8. Questions Change each of the following mixed fractions to top heavy fractions: • 1 1 • 4 5 4 23 7 1 x 4 = 4 4 + 1 = 5 4. 32 7 3 x 7 = 21 21 + 2 = 23 5. 5 1 31 6 2.23 5 13 5 5 x 6 = 30 30 + 1 = 31 2 x 5 = 10 10 + 3 = 13 6 14 3 3.4 2 3 4 x 3 = 12 12 + 2 = 14 Click mouse

  9. Changing a top heavy fraction to a mixed number This is basically the reverse of what you have just been doing: Example: Change 7 into a mixed number. 5 This means seven fifths …… What about? 8 3 = 22 3 Q. How many fifths in one whole? A. Five So you have one whole one and two fifths left over. = 11 4 5 4 Alternatively you can say “how many times does five divide into seven?” – the answer is one remainder two. 9 2 = 41 2 12 5 End Click mouse

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