Basic Math Fractions, Ratios, Proportions PDF

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Basic Math for Pharm Help...

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Basic Math: Fractions, Ratios, Proportions

Fractions 

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A fraction is a number that is not whole. It is a portion of a number. Example if you have a whole pizza that is made up of 8 slices and you take 1 slice, you took 1/8 of the pizza Top number of the fraction is the numerator and the bottom number of the fraction is the denominator Fractions can be proper, improper, mixed Fractions can be reduced to the lowest term (simplified) Proper fractions = the numerator is always lower than the denominator. Example 2/5 Improper fractions= the numerator is equal to or greater than the denominator. Example 2/2 or 11/2 Mixed Fractions = is an improper fraction that has been simplified and results in a whole number with a fraction. Example 11/2 = 5 ½ We can add, multiply, divide, and subtract fraction To simplify or reduce a fraction you divide the numerator and denominator by the largest number that divides into them equally. Example 5/10 can be simplified by dividing by 5. 5/10 / 5/5 = ½ WE saw in the last slide how to make a mixed number out of a fraction. Now we will do an improper fraction out of mixed number. Example 3 ¼- Multiply the whole number by the denominator 3 * 4 = 12 then you will add the numerator to this number 12 + 1= 13. Our improper fraction will be 13/4 (the denominator will not change)

Add Fractions  

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It can be as simple as just adding the numerators together if you have the same denominator. Example 3/7 + 2/7 = 5/7 or 3/5 + 1/5 = 4/5 Most of the time the denominators will not be the same, so in cases like this we have extra steps to do, and we have to find the lowest common denominator (LCD). The easiest way to find the LCD is to simply find the number that both have in common (remember your multiplication tables). Our problem is 4/5 + 1/6. To get the LCD we will multiply 5 * 6 = 30 The next slide will show how to set this up Ok, so we know our LCD is 30 Step 1: Replace each denominator with 30. We will start with 4/5. 4/5 = x/30. We have to solve for x. We do this by dividing the denominator into 30. 30 / 5 = 6. 6 is x. We will take the 6 and multiply it to the other numerator (4) this will give us 24/30. This will replace 4/5. Now we have to do 1/6. 1/6 = x/30. We will do the same steps. 30 / 6 = 5. 5 is x. We will then take 5 and multiply it to the other numerator (1) this will give us 5/30 Step 2: our new problem is now ready to add. 24/30 + 5/30 = 29/30. We can’t simplify 29/30, so the answer will stay 29/30

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Here is one that is a little different. You know that we want to find the LCD when we go to add our fractions. One way to check this is to remember your multiplication tables. Example look on page 90 in your Pharm book and you will see up at the top they are checking the tables for 5’s and 8’s to make sure they have the LCD. ½ + ¾ is a problem that will be different than the one we did on the last slide. WE will work this one out on the next slide ½ + ¾. To find the LCD let’s look at this. What do each of the denominator’s have in common? The # 4. 2*2 = 4, 4* 1 = 4, so 4 is the LCD. Let’s set up the problem and find our answer. ½ = x/4. We divide the denominator’s 2 / 4 = 2. 2 is x. We will take 2 and multiply it by the other numerator (1) and this gives us 2/4. We do not have to do anything with ¾ because it has the correct denominator. 2/4 + ¾ = 5/4

Subtracting Fractions  

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Subtracting fractions uses the same steps as adding fractions and the same steps to find the LCD. Let’s do 1/3 – 2/7. 21 will be the LCD. You will set this up just as you did the addition problems from the last slides. 1/3 = x/21. WE will divide the denominators 3/21 = 7. Then take this 7 and multiply it by the numerator 1, which will give us 7/21. Then we will do the same formula for 2/7. 2/7 = x/21. Divide the denominators 7/21 = 3. Then take the 3 and multiply it by the numerator 2. 3*2 = 6, so we then have 6/21. Our new problem to solve is 7/21 – 6/21 = 1/21. We cannot simplify 1/21. Subtracting fractions and mixed numbers. First step is to change that mixed number to an improper fraction. 1 ½ - 3/6 = x 1 ½ will become 3/2. Now you follow the steps that you learned in the previous slides. Find the LCD. In this problem 6 will be the LCD. After all the steps you should have 9/6 – 3/6 = 6/6. You will simplify 6/6. Divide 6 / 6 = 1 (the answer)

Multiplying Fractions   

1st multiply your two numerators and then your two denominators and simplify if you can. 2/3 * ¾ = 6/12 = ½ Mixed numbers- you will change the mixed number to an improper fraction. 5 2/10 * 5 = x We first need to change the mixed number to an improper fraction 52/10 and then we need to make 5 an improper fraction by placing the 5 over a 1. 52/10 * 5/1. With this problem you can cancel numerators and denominators if possible. We can cancel the numerator 5 (it will become 1) and the denominator 10 (will become a 2). 52/ 2 * 1/1 = 52/2. This can be simplified by dividing 2 into 52 = 26 (the answer to the problem)

Dividing Fractions 

Dividing fractions can be a little trickier than what we have already worked on. When you divide you must invert the second fraction (reciprocal) for

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example the problem ¾ ÷ ½ will become ¾ ÷ 2/1, then it changes to a multiplication problem! ¾ * 2/1 and cancel out numerators and denominators if you can, in this problem we can. 3/2 * 1/1 = 3/2. With dividing fractions you simplify and change to a mixed number if possible. In our problem 2 divided by 3 = 1 ½ You will have mixed numbered fractions that can be divided, you follow the same steps. Change the mixed number to an improper fraction. Then flip the second fraction, cancel if you can, multiply and simplify.

Decimals 

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Metric measurements are expressed in decimals. Decimal places appear to the right of a whole number that is followed by a decimal point to indicate a number less than 1. if no digit is to the left of the decimal a 0 must be placed to prevent errors. 0.5, not .5 You can convert a proper fraction to a decimal. Divide the numerator by the denominator. 4/5 to a decimal is 4 ÷ 5 = 0.8 Add decimals 64.30 + 0.33 = 64.63. Subtract 64.30 – 0.33 = 63.97 Multiply – 92.3 *4.66 = 430.118. Follow basic multiplication rules when it comes to multiplying decimals.

Ratio and Proportion   

Ratio shows the relationship between two numbers by using a colon to separate the numbers 1:3 (ratio) 2:6 (ration) Proportion shows the relationship between two equal ratios or fractions. 1:3 :: 2:6 (proportion) in the proportion 1 & 6 are extremes. 3 & 2 are means Next slide will show you how to set up problems that will be on the worksheet

Proportion 

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A supply of 500 halibut liver capsules sells for $4.80. what would be the price for 125 capsules? Set this up $4.80/500 = x/125. $4.80/500 = 0.0096. 0.0096 * 125 = $1.20 (answer) A speedboat passes a race checkpoint 52.5 miles past the start of the course 2 hours after the race started. If the entire course is 210 miles long, how much time would you except the speedboat to take to finish? 52.5/2 = 26.25 mph. 210/26.25 = 8 hours

Solve for X     

15/x = 20/4 lets set it up 15 * 4 = x * 12 (you’re cross multiplying) 15 * 4 = 60. x*12 = 12 x 60 /12 = 12x /12 X=5

Solve for X 

80mg:480ml = 60mg:x To set this up you will take your two outer numbers (extreme) 80 mg & x and multiply them. You will then take the two middle

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numbers (means) 480ML & 60mg and multiply. 80mg * x = 80x. 480ml * 60 mg = 28,800. Now we have to get rid of the x and solve x. To get rid of 80x we will divide 80x by 80 = x. 28,800 / 80 = 360 X= 360...