1. Review of Fractions Addition Common Denominators Reducint Fractions (Factoring) Multiplication Ratios

2. Fractions 1 3 Numerator Denominator 1 3 2 Reduced FormSimple Fraction 7 3 14 6 Units Extracted

3. Fractions How to Add Fractions 1/6 + 1/3 = ? 1/3 + 2/3 = ? To add fractions, they must have a common denominator. Then add the numerators. Sometimes fractions do not have common denominators to start with. So the first step in adding them is to find a common denominator.

4. Fractions 1/6 + 1/3 = ? To find a common denominator, multiply one or both fractions by a form of the number one so that they will have the same denominator. In this case you can multiply 1/3 by 2/2 to turn it into sixths. 1 3 x 2 2 = 2 6 1 6 + 2 6 = 3 6 Then add the fractions with the new common denominator 3 6 = 1 2 Finally, reduce the result. The number one

5. Fractions 2 1/6 + 3 1/3Common denominator to add 2 1/6 + 3 2/6 5 3/6 5 1/2 Reduce

6. Fractions How to Reduce a Fraction Factor the numerator and denominator into prime factors. Cancel all the common factors. What remains is the reduced fraction. 18 30 18 = 3 2 x 2 30 = 5 x 3 x 2 18 = 3 2 x 2 30 = 5 x 3 x 2 3 5

7. Fractions Finding the Lowest Common Denominator (or Least Common Multiple) Factor each number into prime factors. Then take the highest exponent of ALL factors from each number. 9 = 3 2 15 = 3 x 5 3 2 x 5 = 45 Highest exponent

8. Fractions Find the Least Common Denominator Reduce 3/9 + 4/15 9 = 3 2 15 = 3 x 5 (highest number of all factors) 3 2 x 5 = 45 3 9 5 5 15 45 4 15 3 3 12 45 x 15 45 12 45 x + 27 45 3x3x3 3x3x5 3 5 Adding using the Least Common Denominator

9. Fractions 2 1/6 + 3 1/3Common denominator to add 2 1/6 x 3 1/3 Convert to simple fractional form and multiply numerators and denominators Multiplication

10. Fractions In industry most fractional units have to do with measurements of length or mass and are usually decimal if the metric system is used or fractional units of the Old English System (OES). Length: if it is metric it will be decimal divisions. if it is OES it may be decimal or fractional divisions. Mass: if it is metric it will be decimal divisions. If it is OES it will be in separate units. 8.57 cm. 3 3/8 inches 3.3 inches 3 21/64 inches Examples:

11. Fractions 1/2=0.5 1/4=0.25 1/8=0.125 1/16=0.0625 1/32=0.03125 1/64=0.015625 1/128=0.0078125 Fractions Decimal

12. Ratios Rates, amount of change, complex relationships are often governed by ratios: A B C D The units or dimensions on both sides of the equation must be the same

13. Ratios A B C D You can find any one of the variables if you know the other three A = B C D B C D C D A B A C A B D = = =

14. Ratios B C D A B C D A A = B C D B C D A =

15. B C D A B C D A C A B D = D B A C =

16. 1 gallon of water weighs 8 pounds. How much does 360 gallons weigh? 1 gallon 8 pounds 360 gallons ? pounds 360 gallons x 8 pounds 1 gallon 2880 pounds