Math Learning Center Directed Learning Activity: Math Skills for Photography Student s Name: Student s ID: CRN (5-digits): Introduction: This Directed Learning Activity reviews and strengthens your knowledge of the basic math skills that you will be required to know going into Photography 0. It will assist you in multiplying and dividing fractions. It will also help you become a little more familiar with terminology that you will see in your Photography 0 class. Objective: The goal is to understand multiplying and dividing fractions and, more specifically, to understand the meaning of halving and doubling with regards to shutter speeds and aperture settings. Objective a: Multiplying Fractions Multiplying fractions can be as simple as multiplying regular numbers. Listed below are the three steps to multiplying any two fractions:. Multiply the top numbers (the numerators).. Multiply the bottom numbers (the denominators).. Simplify/reduce the fraction, if possible and necessary. This means to divide the numerator (top) and denominator (bottom) by the largest number that can divide both numbers exactly. Example: Multiply and 6. 7 6 6 6 6 7 7 4 4 7. 5 9. 4 7
Objective b: Multiplying Fractions in Photography In photography, shutter speeds are very important. They change the amount of light that enters the camera by a factor of from one setting to the next. That is, they are either letting half the amount of light in. the amount of light in or double () Example: From a /5 shutter speed setting, if we wanted half the amount of light to enter, what setting should we change to? From a /5 setting, if we wanted half the light to enter, we would multiply the /5 by /, for half. So the answer would be /50. What this means is that a setting of /50 is letting in half the amount of light as a setting of /5. 5 5 50 Example: From a /60 shutter speed setting, if we wanted twice the amount of light to enter, what setting should we change to? From a setting of /60 and wanting twice the light to enter, we would multiply the /60 by, to double it. So the answer would be /0. What this means is that a setting of /0 is letting in twice the amount of light as a setting of /60. To apply the procedure for multiplying fractions, the number needs to be converted to a fraction. To convert ANY whole number, such as, to a fraction, simply put it over. 60 60 60 60 60 0. From a /000 shutter speed setting, if we wanted twice the amount of light to enter, what setting should we change to?. From a /4 shutter speed, if we wanted half the amount of light to enter, what setting should we change to?. From a /000 shutter speed setting, if we wanted four times the amount of light to enter, what setting should we change to? Hint: When we wanted twice the amount, what number did we multiply by? So now that we want four times the amount, we should multiply by what number?
Objective : Dividing in half In photography, you will be asked to mount images. To correctly mount the image, you will have to understand how to divide fractions in half. When we say divide in half, what we really mean is multiply by. Example: What is half of 4? Example: What is half of 7 8? 4 4 8 7 7 7 8 8 6 Often times, you may run into situations involving mixed numbers. An example of a mixed number would be the number. To take half of that, you would need to first convert the mixed number to an improper fraction. To 4 do that, you ll have to take these steps:. Multiply the denominator with the whole number.. Add that product to the numerator.. Take that result and put it over the original denominator. 5 Example: What is half of? Answer: 8 6 The first step is to convert the mixed number to an improper fraction. 5 (8) 5 9 8 8 8 Next, you will multiply the result by. 9 9 9 8 8 6 If the result is again an improper fraction, as in this case, we might want to convert it back to a mixed number. For that, we do long division. 6 9 9-6 Therefore,. 6 6. What is half of 5?. What is half of 7?. What is half of 4? 6 8
Objective : Shutter Speeds Shutter speeds are one of two settings that will allow you to control the amount of light that enters a camera. Listed below is the range for shutter-speed setting in seconds: / /4 /8 /5 /0 /60 /5 /50 /500 /000 /000 /4000 /8000 On the list above, each time you move one setting to the left, the amount of light that enters a camera is doubled. Conversely, each time you move one setting to the right, the amount of light that enters a camera is halved. Example: From a /5 setting to a /0 setting, are we letting in more or less light and by what factor? From /5 to /0, we moved one setting to the right. That means we let less light in, halving once, so it would be half (/) as much. Example: From a /50 setting to a /0 setting, are we letting in more or less light and by what factor? From /50 to /0, we moved three settings to the left. That means we let more light in, doubling three times, so it would be eight times more. 8. From a /8 setting to a /500 setting, are we letting in more or less light and by what factor?. From a /000 setting to a /4 setting, are we letting in more or less light and by what factor?. From a /5 setting to a /50 setting, are we letting in more or less light and by what factor? 4
Objective 4: Aperture Settings (f-stops) Aperture setting, or f-stop, is the other thing that you can use to control the amount of light that enters the camera. Listed below is the range for f-stops: f/ f/.4 f/ f/.8 f/4 f/5.6 f/8 f/ f/6 f/ f/ The smaller the number, the more light enters the camera. On the list above, each time you move one setting to the left, the amount of light that enters a camera is doubled. Each time you move one setting to the right, the amount of light that enters a camera is halved. Example: From an f/5.6 setting to an f/ setting, are we letting in more or less light and by what factor? From f/5.6 to f/, we moved four settings to the right, so we let less light in and it would be onesixteenth (/6) as much. 4 6 Example: From an f/ setting to an f/5.6 setting, are we letting in more or less light and by what factor? From f/ to f/5.6, we moved two settings to the left, so we let more light in and it would be four times more. 4. From an f/8 setting to an f/.4 setting, are we letting in more or less light and by what factor?. From an f/.4 setting to an f/8 setting, are we letting in more or less light and by what factor? 5
Objective 5: Equivalent Exposure Settings (Combining Shutter Speeds and Aperture) It is very important to know the correct combination of shutter speed and aperture to keep the same desired exposure. You can change one setting and still keep the exposure the same as long as you change the other setting the same amount in the opposite direction. Shutter Speed: / /4 /8 /5 /0 /60 /5 /50 /500 /000 /000 /4000 /8000 Aperture: f/ f/.4 f/ f/.8 f/4 f/5.6 f/8 f/ f/6 f/ f/ Example: /60 second @ f/4 = /500 second @ f/. We went from a /60 second shutter speed setting to a /500 second shutter speed second, moving three settings to the right. So we need to change the aperture the same amount of settings, but in the opposite direction in order for the new combination of shutter speed and aperture setting to produce an equivalent exposure. From f/4, we move three settings to the left and end up at f/.4. So the answer would be..4.. Example: /5 second @ f/6 = second @ f/. We went from an f/6 aperture setting to an f/ aperture setting. We moved six settings to the left so to find the equivalent aperture setting, we need to move the same amount of settings in the opposite direction for the shutter speed setting to get an equivalent exposure. From /5 second, we move six settings to the right and end up at /000. So the answer would be./000... /8 second @ f/5.6 = /5 second @ f/.. /0 second @ f/8 = second @ f/.. /000 second @ f/ = second @ f/. 6
4. /5 second @ f/6 = /500 second @ f/. 5. /60 second @ f/ = /000 second @ f/. 6. /5 second @ f/5.6 = second @ f/. Consultation Instructions (Tutor): The tutor should check over the student s answers and review with the student how to solve any problems he/she did not do correctly. Make sure that the student understands the concept of halving and doubling for the above exercises. If the student is having a hard time visualizing the concept of halving and doubling, use the fraction tiles to physically show him/her why for example, 6 is half of, etc. Note to the tutor: When finished, please direct the student to complete the digital DLA survey. Also, the tutor should complete and submit the electronic DLA form; date, score and stamp the DLA with the official MLC seal; and then release the DLA to the student. 7