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PRESENTATION 5 Common Fractions

PRESENTATION 5 Common Fractions. COMMON FRACTIONS. A fraction is a value that shows the number of equal parts taken of a whole quantity The symbol used to indicate a fraction is the slash (/) or bar (—) A fraction indicates division. COMMON FRACTIONS.

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PRESENTATION 5 Common Fractions

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  1. PRESENTATION 5Common Fractions

  2. COMMON FRACTIONS • A fraction is a value that shows the number of equal parts taken of a whole quantity • The symbol used to indicate a fraction is the slash (/) or bar (—) • A fraction indicates division

  3. COMMON FRACTIONS • There are two parts to a fraction, called terms: • The numerator is the top number and shows how many equal parts of the whole are taken • The denominator is the bottom number and shows how many equal parts are in the whole quantity

  4. COMMON FRACTIONS • A proper fraction is a number less than 1 • For example: 3/4, 5/8, 99/100 written with the slash or written with the bar: • An improper fraction is a number greater than 1 • For example:

  5. FRACTION IN LOWEST TERMS • Fractions can be expressed in lowest terms by dividing both the numerator and denominator by the same number without changing the value. • For example: • To reduce to lowest terms, divide both the numerator and denominator by 2:

  6. FRACTION IN LOWEST TERMS • The fraction is still not in lowest terms, so find another common factor in the numerator and the denominator. In this case, divide by the factor of 2: • A fraction is in lowest terms when the numerator and denominator do not contain a common factor

  7. MIXED NUMBERS AS FRACTIONS • A mixed number is a whole number plus a fraction • To express a mixed number as an improper fraction: • Find the number of fractional parts contained in the whole number • Add the fractional part to the whole number equivalent

  8. MIXED NUMBERS AS FRACTIONS • Find the number of fractional parts contained in the whole number • Add the fractional part

  9. FRACTIONS AS MIXED NUMBERS • To convert fractions into mixed numbers, divide and place the remainder over the denominator

  10. FRACTIONS AS MIXED NUMBERS • Example: • Divide and place the remainder over the denominator • Reduce to lowest terms

  11. ADDITION OF FRACTIONS • Fractions cannot be added unless they have a common denominator (the denominator of each fraction is the same) • The lowest common denominator (LCD) is the smallest number that all denominators divide into evenly • For example, the lowest common denominator of 4 & 2 is 4 since 4 is the smallest number evenly divisible by both 2 and 4

  12. COMPARING VALUES OF FRACTIONS • To compare values of fractions with like denominators, compare the numerators • The fraction with the larger numerator is the larger fraction • To compare fractions with unlike denominators, express the fractions as equivalent fractions with a common denominator and compare numerators

  13. ADDITION OF FRACTIONS • To add fractions, express using the lowest common denominator • Add the numerators and write their sum over the LCD • Example:

  14. ADDITION OF FRACTIONS, MIXED NUMBERS, AND WHOLE NUMBERS • To add fractions, mixed numbers, and whole numbers: • Express the fractional parts of the number using a common denominator • Add the whole numbers • Add the fractions • Combine the whole number and the fraction and express in lowest terms

  15. SUBTRACTION OF FRACTIONS • To subtract common fractions, express the fractions as equivalent fractions with a common denominator • Subtract the numerators • Reduce to lowest terms

  16. SUBTRACTION OF FRACTIONS • Example:

  17. SUBTRACTION OF FRACTIONS • Express the fractions as equivalent fractions with 60 as the denominator • Finally, subtract the numerators of the fractions:

  18. MULTIPLICATION OF FRACTIONS • Multiplication and division of fractions do not require a common denominator • To multiply simple fractions, multiply the numerators and multiply the denominators • Mixed numbers must be changed to improper fractions before multiplying

  19. MULTIPLICATION OF FRACTIONS • Example: • Multiply the numerators and denominators

  20. MULTIPLICATION OF FRACTIONS • Example: • Multiply numerators and denominators • Express as mixed number in lowest terms

  21. DIVIDING BY COMMON FACTORS • Problems involving multiplication of fractions are generally solved more quickly if a numerator and denominator are divided by any common factors before the fractions are multiplied • This process is called cancellation

  22. DIVIDING BY COMMON FACTORS • Example: • The factor 3 is common to both the numerator 3 and the denominator 9, so divide • The factor 4 is common to both the numerator 4 and the denominator 8, so divide • Multiply the numerators and denominators

  23. DIVISION OF FRACTIONS • Division is the inverse of multiplication • To divide fractions, invert the divisor, change to the inverse operation (multiplication), and multiply

  24. DIVISION OF FRACTIONS • Example: • Invert the divisor, multiply, and reduce

  25. DIVISION OF FRACTIONS • To divide any combination of fractions, mixed numbers, and whole numbers: • Write mixed numbers as fractions • Write whole numbers over the denominator of 1 • Invert the divisor • Change to the inverse operation • Multiply

  26. DIVISION OF FRACTIONS • Example: • Write • Invert the divisor • Change to the inverse operation and multiply

  27. ORDER OF OPERATIONS • As with any arithmetic expression, the order of operations must be followed. The operations are: • Parentheses • Exponents and roots • Multiplication and division from left to right • Addition and subtraction from left to right

  28. ORDER OF OPERATIONS • Example: • First, add the fractions in ( ) • Next, multiply and divide • Finally, subtract

  29. PRACTICAL PROBLEMS • A baker prepares a cake mix that weighs 100 pounds. • The cake mix consists of shortening and other ingredients. • The weights of the other ingredients are 20 1/2 pounds flour, 29 3/4 pounds of sugar, 18 1/8 pounds of milk, 16 pounds of whole eggs, and a total of 5 1/4 pounds of flavoring, salt, and baking powder. • How many pounds of shortening are used in the mix?

  30. PRACTICAL PROBLEMS • Add all the ingredients

  31. PRACTICAL PROBLEMS • Subtract from the total weight of the cake mix • There are pounds of shortening in the mix

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