Chapter 2 Objectives Write part-to-whole relationships in fractional form Use the terminology of fractions Find common denominators Create equivalent fractions Order fractions Reduce or simplify fractions Use cancellation to reduce larger fractions Add fractions with like and unlike denominators Subtract fractions, including using borrowing, with like and unlike denominators Multiply fractions and mixed numbers Divide fractions and mixed numbers Complete word problems that have fractions Convert between Celsius and Fahrenheit degrees Reduce/simplify and solve complex fraction problems Complete measurement conversions with fractions Read a ruler

Fractions are important to know because they appear in medication dosages, measurements, sizes of instruments, work assignments, & time units. Fractions Fraction skills are needed in all health care situations. The students need to be assured that understanding fractions is a foundational skill necessary for making conversions among systems and is applicable to measurements and dosing. Pages 36 – 69

Part-to-Whole Relationships Pages 33 – 34 Part-to-Whole Relationships Fraction = a number that has two components: a part and a whole. A minute is 1 part of 60 minutes in a whole hour. This relationship of a part to whole can be shown in a fraction: Take another common part-to-whole relationship. Many people sleep an average of 8 hours a night. The relationship of sleeping hours to total hours in a day is 8 to 24 or 8/24, or a reduced fraction of 1/3. 1 60 ← numerator (the part) ← denominator (the whole) Fractions are important to understand because you will come across them many times in health care occupations. Reading fractions on drug labels is a workplace necessity. **** Skip practice 1 it’s stupid

Identifying Fractions Page 34 Identifying Fractions Proper or common fractions = fractions with a numerator less than the number of the denominator: 3/7, 24/47, 9/11. The value of any proper or common fraction will be less than 1. Mixed numbers = fractions that include both a whole number & a proper fraction: 33/4, 129/11, 10113/22. Improper fraction = fractions where the numerator is equal to or larger than the denominator: 17/12, 33/11, 9/9. Improper fractions are equal to or larger than 1. These fractions are used to in the multiplication & division of fractions. Answers that appear as improper fractions need to be reduced so that the answer is a mixed number.

Equivalent Fractions Pages 34 – 35 Understanding equivalent fractions is important in making measurement decisions. These fractions represent the same relationship of part to whole, but there are more pieces or parts involved. Making equal fractions is easy using multiplication or division. REMEMBER: Whatever you do to the top must also be done to the bottom. The skill of making equivalent fractions will be used in adding, subtracting & comparing fractions. **** Example – page 35 – practice 2: even Group Work – page 35 – practice 2: odds

Reducing to Lowest or Simplest Terms Page 35 Reducing to Lowest or Simplest Terms As in making fractions equivalent, reducing fractions to their lowest or simplest terms is another important fraction skill. Lowest terms = the fraction is the lowest proper fraction possible and can be reduced no further. Two methods will help you to get to the lowest terms: Multiplication and Division Method After each calculation of addition, subtraction, multiplication, or division, you will need to reduce the answer to its lowest terms. Most tests & practical applications of fractions require that answers be in the lowest terms.

Multiplication Method Page 36 Multiplication Method Look at the numbers in the fraction. Find a number that divides into both the numerator and the denominator evenly. Write out the multiplication for the numerator and the denominator. Cross out the two identical numbers in the multiplication problems. What is left is the reduced fraction. Continue to next slide 2 16 2 x 1 8 x 2 1 8 = =

Division Method Page 36 8 24 8 ÷ 4 24 ÷ 4 2 6 = = Not reduced! 2 6 Look at the numerator and the denominator numbers. Choose a number that divides into both the numerator and the denominator. Divide the by that number. Check to ensure that the resulting fraction is in its lowest form. Continue to next slide 8 24 8 ÷ 4 24 ÷ 4 2 6 = = Not reduced! 2 6 2 ÷ 2 6 ÷ 2 1 3 = =

Rules for divisibility Page 386 Short cut Questions Rules for divisibility Example If it is an even number (has a 0, 2, 4, 6, or 8 in the ones place) 4586 is divisible by 2 because an even number 6 is in the ones place. Divide by 2 If the sum of the digits is divisible by 3 762 is divisible by 3 because 7 + 6 + 2 = 15, which is divisible by 3. Divide by 3 If the number contains a 5 or 0 in the ones place 495 is divisible by 5 because the last digit is a 5 Divide by 5 If the number has a 0 in the ones place 3,490 is divisible by 10 because the ones place has a 0. Divide by 10 How do you decide on the best method to use? Choose your strongest skill – multiplication or division – and use it to reduce fractions. You will make fewer errors if you select one method and use it consistently. When working with a mixed number, set aside the whole number. Handle the fraction portion of the number and then place it beside the whole number. **** Example – pages 36-38 – practice 3-5: even Group Work – pages 36-38 – practice 3-5: odds

1 Improper Fractions Page 38 Recall: An improper fraction is a fraction that has a larger numerator than a denominator. Simply divide the denominator into the numerator. 1 3 8 1 11 8 → 8 11 Improper fractions are either whole numbers or mixed numbers Improper fractions are use in multiplication & division of fractions **** Example – page 39 – practice 6: even Group Work – page 39 – practice 6: odds –8 3

Adding Fractions with like Denominators Page 39 Adding Fractions with like Denominators Addition of fractions with the same denominators is straightforward. Follow the two steps below: Line up the fractions vertically, add the numerators, and place the sum over the common, or like, denominator. Reduce, if necessary. Check your work to ensure accuracy. **** Example – page 40-41 – practice 7: even Group Work – page 40-41 – practice 7: odds

Finding the Common Denominator Page 41 Finding the Common Denominator Adding and subtracting fractions requires that the denominator be of the same number, also referred to as a common denominator. The lowest common denominator is the smallest number or multiple that both of the denominators of the fractions can go into. Using multiplication, find the smallest number or multiple that the numbers can go into. **** Example – page 42-43 – practice 8-9: even Group Work – page 42-43 – practice 8-9: odds

Difficult Common Denominators Page 43 Difficult Common Denominators Sometimes one must consider a wider range of possible numbers for common denominators. For example, you may have a pair of fractions in which on of the denominators cannot be multiplied by a number to get the other denominator. In this case, it is often easiest to simply multiply the two denominators by each other. The result will be a common denominator. **** Example – page 44-45 – practice 10-12: even Group Work – page 44-45 – practice 10-12: odds

Ordering Fractions Page 46 Different health-care fields require the comparison of fractions. It is useful to be able to determine the size relationships of instruments and place them in order for a surgeon before a surgery. This is accomplished by using the common denominator method. Convert the fractions to give each a common denominator. Order by the numerators now that the fractions have the same denominator. **** Example – page 46 – practice 13: even Group Work – page 46 – practice 13: odds

Subtraction of Fractions Pages 46 – 47 Subtraction of Fractions Subtraction of fractions follows the same basic principles as addition of fractions. The fractions must have common denominators before any subtraction can be done. Make a common denominator if necessary Subtract the numerators and then reduce if necessary. **** Example – page 47-48 – practice 14: even Group Work – page 47-48 – practice 14: odds

Borrowing in Subtraction of Fractions Page 48 Borrowing in Subtraction of Fractions Two specific situations require that a number be borrowed in the subtraction of fractions: Subtraction of fractions from a whole number After a common denominator is established and the top fraction of the problem is less or smaller than the fraction that is being subtracted from it. Recall that the borrowing in whole number? In fractions, the same borrowing concept is used; the format varies only slightly. The difference is that the borrowed number must be put into a fractional form. Step 1: Borrow 1 from the whole number. Convert the 1 into an improper fraction having the same common denominator as the first fraction. Then add the two fractions. Step 2: Rewrite the problem so it incorporates the changes, then subtract the numerator only. Place it over the denominator. Reduce as necessary.

Borrowing in Subtraction Rules Page 49 Borrowing in Subtraction Rules Must have a common denominator To borrow from the whole number, make it a fractional part. Add fractional parts Subtract; reduce if necessary Example – page 49-51 – practice 15-17: even Group Work – page 49-51 – practice 15-17: : odds **** !!!!!Stop HERE for the first fraction day if possible!!!!!!

Multiplication of Fractions Page 51 Multiplication of Fractions To facilitate multiplication and division of fractions, set up the problems horizontally. One of the simplest computations in fractions is to multiply a common fraction. No common denominator is needed. Set up the problem horizontally and multiply the fraction straight across Reduce to the lowest terms, if necessary. Example – page 52 – practice 18: even Group Work – page 52 – practice 18: odds

Multiplying a Fraction by a Whole Number Page 52 Multiplying a Fraction by a Whole Number To multiply a fraction by a whole number, follow these steps: Make the whole number into a fraction by placing a 1 as its denominator. Multiply straight across and then reduce if necessary. Any whole number can become a fraction by placing a 1 as the denominator. ***** Example – page 53 – practice 19: even Group Work – page 53 – practice 19: odds

Reducing before You Multiply as a Timesaver Pages 53 – 54 Reducing before You Multiply as a Timesaver When multiplying, you can expedite the work by reducing before you multiply. (Also called canceling) It saves energy and time: By allowing you to work with smaller numbers At the end of the problem because you won’t have to spend so much time reducing the answer. Example – page 54-55 – practice 20: even Group Work – page 54-55 – practice 20: odds

Multiplication of Mixed Numbers Page 55 Multiplication of Mixed Numbers Mixed numbers are whole numbers with fractions. Multiplication involving mixed numbers requires that the mixed number be changed to an improper fraction. Example – page 56-58 – practice 21-23: even Group Work – page 56-58 – practice 21-23: odds

Division of Fractions Pages 58 – 59 To divide fractions: Change the sign to a x sign Invert the fraction to the right of the ÷ sign. (Also called taking the reciprocal) Follow the steps of multiplication of fractions: Cancel if possible multiply straight across reduce as necessary. Example – page 60-61 – practice 24-25: even Group Work – page 60-61 – practice 24-25: odds

Converting Temperatures Using Fraction Formula Pages 61 – 62 Converting Temperatures Using Fraction Formula Fractions are more accurate than decimals because there is no change in the numbers as a result of rounding the decimals. Follow these two setups: Convert Celsius to Fahrenheit: (oC x 9/5) + 32 = oF Convert Fahrenheit to Celsius: (oF – 32) x 5/9 = oC Example – page 62-63 – practice 26-27: even Group Work – page 62-63 – practice 26-27: odds

Complex Fractions Page 63 These fractions are used to help nurses and pharmacy technicians compute exact dosages. Complex fraction = a fraction within a fraction. They are solved by using rules of division. Example – page 64-65 – practice 28-29: even Group Work – page 64-65 – practice 28-29: odds

Measurement in Fractions Page 66 Measurement in Fractions Fractions are common in the measurement systems we use every day. For example, we use fractions in time such as ½ hour, 7 ½ minutes, and 4 ½ hours. We also use fractions for our household measurements such as 1 ½ cups, ½ teaspoon, and 3 pints as well as in weights in pounds and ounces such as 34 ½ ounces and 12 ½ ounces. Using addition or multiplication, we can convert fractions between these units. Example – page 66-68 – practice 30-31: even Group Work – page 66-68 – practice 30-31: odds