1. Radiologic Science for Technologists Mathematics for Radiology

2. Fractions Fraction=x/y=numerator/denominator Is a numerical value expressed by dividing one number by another. To add or subtract fractions, first find a common denominator. To multiply, multiply numerators and denominators. To divide, invert the second fraction and multiply.

3. Examples 2/3 + 3/2 = 4/6 + 9/6 = 13/6 (Improper fraction) 3/2 – 2/3 = 9/6 – 4/6 = 5/6 (Proper fraction) 2/5 x 7/4 = 14/20 = 7/10 5/2 divided by 7/4 = 5/2 x 4/7 = 20/14

4. Converting Fractions to Decimals Decimals-fractions in which the denominator is a power of 10 may easily be converted to decimals 3/10=0.3 If the denominator is not a power of 10, the decimal equivalent can be found by long division or with a calculator.

5. Significant Figures In addition and subtraction, round to the same number of decimal places as the entry with the least number of decimal places to the right of the decimal place. In multiplication and division, round to the same number of digits as the entry with the least number of significant figures.

6. Algebra Algebra Rules of algebra provide definite ways to manipulate fractions and equations to solve for unknown quantities –When an unknown, x, is multiplied by a number divide both sides of the equation by that number. ax=cax/a=c/ax=c/a

7. Algebra When numbers are added to an unknown, x, subtract that number from both sides of the equation. –x+a=b –x+a-a=b-a –x=b-a

8. Algebra When an equation is presented in the form of a proportion, cross-multiply and then solve for unknown, x. x/a=b/cx/a=b/c c/x=abc/x=ab X=ab/cX=ab/c

9. Number Systems The system based on the multiples of ten is the decimal system. In the decimal system, numbers can be represented in four ways: –Fractional form –Decimal form –Exponential form –Logarithmic form

10. Numbers Represented in the Decimal System Frac. Decim. Exp. Log. 10,000 10,000 10 4 4.000 10,000 10,000 10 4 4.000 1000 100010 3 3.000 1000 100010 3 3.000 100 100 10 2 2.000 100 100 10 2 2.000 10 10 10 1 1.000 10 10 10 1 1.000 1 1 10 0 0.000 1 1 10 0 0.000 1/10 0.1 10 -1 -1.000 1/100 0.01 10 -2 -2.000 1/1000 0.001 10 -3 -3.000 1/10,000 0.0001 10 -4 -4.000

11. Rules for Handling Numbers in the Exponential Form Multiply : add the exponents 10 2 x 10 3 = 10 5 Divide : subtract the exponents 10 6 divided by 10 4 = 10 2 Raising to a power : multiply the exponents (10 5 ) 3 = 10 15 Inverse : 10 -3 = 1/10 3 = 1/1000 unity : 10 0 = 1

12. Graphs A graph is a drawing that shows a relationship between two sets of numbers. Most graphs are based on two axes, a horizontal or x axis and a vertical or y axis. Where the two axes meet is called the origin and is labeled 0.

13. Features of a graph

14. Graphs Sometimes the axes of graphs are not labeled x or y but represent specific numerical quantities. If the values extend over a very large range, a logarithmic scale must be used. Semilogarithmic graph paper combines linear on one axis, with logarithmic on the other axis.

16. Example The following data was obtained, showing the amount of lead thickness to reduce x- ray intensity. It can be plotted on a graph and then used to read thicknesses of lead that were not actually measured. Data: Mm lead02468 X-ray intensity330140582511 (mR)

17. Linear and Semilogarithmic graphs Equal lengths of linear scale have equal value The logarithmic scale allows a large range of values to be plotted. How much lead is needed to reduce the intensity to 6 mR?

19. Radiologic Units International SystemSI RoentgenR

20. Radiologic Units R (Gy a )-roentgen a unit of radiation quantity, exposure or intensity. Radiation monitors are calibrated in roentgens mR-the output or x-ray imaging systems. The roentgen only applies to x-rays and gamma rays and their interaction with air. Rad (Gy t )-biologic effects are related to the radiation absorbed dose. Used to describe the quantity of radiation received by a patient. Any type of ionizing radiation and any exposed matter, not just air.

21. Radiologic Units cont. Rem-the unit of occupational radiation exposure expressed as effective dose (E) Curie (Ci) (Bq)-a unit of radioactivity, not the radiation emitted. Radioactivity and the curie have nothing to do with x-rays.