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# Operations with rational numbers

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### Operations with rational numbers

1. 2. <ul><li>Any number that can be made by dividing one integer by another. The word comes from &quot;ratio&quot;. </li></ul><ul><li>This means that rational numbers include positive and negative numbers, whole numbers, fractions and decimals. </li></ul>
2. 3. <ul><li>Two fractions that stand for the same number </li></ul>
3. 4. Mixed Numbers Improper Fractions
4. 5. <ul><li>The sum of a whole number and a fraction </li></ul>
5. 6. & These are examples of mixed numbers
6. 7. <ul><li>A fraction with a numerator greater then the denominator </li></ul>NUMERATOR denominator
7. 8. <ul><li>These are examples of improper fractions </li></ul>&
8. 9. = =
9. 10. =
10. 11. = =
11. 12. = =
12. 14. Adding Fractions Subtracting Fractions Multiplying Fractions Dividing Fractions
13. 15. Adding fractions requires a common denominator To find the common denominator between fractions simply multiply the denominators and this is the common denominator. this number may be large so try and find a number that all denominators will divide into evenly.
14. 16. <ul><li>However this number may be large so try and find a number that all denominators will divide into evenly. </li></ul>Adding fractions requires a common denominator To find the common denominator between fractions simply multiply the denominators and this is the common denominator.
15. 17. <ul><li>We need to find a C.D. in order to add these fractions. </li></ul><ul><li>If we multiply the denominators </li></ul><ul><li>that is a big number…but both 6 and 12 divide evenly (without a remainder) into 12. </li></ul><ul><li>The first fraction already has a denominator of 12 so we leave it alone but what do we have to multiple the second denominator by in order to change it to 12? </li></ul><ul><li>If you said 2…you are right! </li></ul>
16. 18. <ul><li>If you multiply the denominator by 2 you MUST multiply the numerator by two also! </li></ul><ul><li>Remember: whatever you do to the bottom you must do to the top. </li></ul><ul><li>Once you have common denominators…add the numerator and KEEP the Common Denominator. </li></ul>
17. 20. Same rule…you have to get a common denominator before you subtract the numerators!
18. 23. Multiplying fractions is easy Multiple the numerators Multiple the denominators
19. 26. Dividing fractions requires one more step Keep the first fraction the same Change the multiple to divide And FLIP the second fraction
20. 27. When the fraction is “flipped” it is called the INVERSE
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