Fundamentals of Mathematics for Nursing Testbank

PART A BASIC MATH REVIEW The following section serves as a review of basic math principles and allows students to identify any areas that will require further study. Students who find they need further development in basic math should refer to the table of math resources on page 5. Answers for practice problems are located in Part G, beginning on page 48. I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 The basic form is to place the larger numerals to the left and add other numerals. XXXIII = 33 (30 + 3 = 33) There is an exception to the basic form. If smaller numeral precedes a larger numeral, the smaller should be subtracted from the larger. IX = 9 (1 - 10 = 9) If there seems to be several ways of writing a number - use the shorter form. XVVI - incorrect XXI - correct (10 + 10 + 1 = 21) Only one smaller numeral is allowed to precede a larger numeral. XCV = 95 - correct IXCV - incorrect (10 - 100 = 90 + 5 = 95) Numerals may be written as lower case letters and the number one may have a line and/or a dot over it. . .. iv = 4 1 = 1 xv11 = 17 1 - 5 = 4 10 + 5 + 2 = 17 1. Roman Numerals 12 2. Fractions Numerator Denominator 2 = Proper fraction = numerator is smaller than denominator. 3 3 = Improper faction = numerator is larger than denominator. 2 1 1 = Mixed fraction = whole number and a fraction. 2 To change an improper fraction to a mixed number: a. Dividethenumeratorbythedenominator. b. Place remainder over denominator. To change a mixed number to an improper fraction: a. Multiplydenominatorbythewholenumber. b. Add numerator. c. Placesumoverthedenominator. 13=23 5 5 31=7 2 2 To reduce a fraction to its lowest denominator: a. Dividenumeratoranddenominatorbythegreatestcommondivisor. b. The value of the fraction does not change. EXAMPLE: Reduce 12 60 12 divides evenly into both numerator and denominator 12 ) 12 = 1 12 = 1 60 ) 12 = 5 60 5 EXAMPLE: Reduce 9 12 3 divides evenly into both 9 )3=3 12 )3 = 4 9=3 12 4 13 EXAMPLE: Reduce 30 45 15 divides evenly into both 30 ) 15 = 2 45 ) 15 = 3 30 = 2 45 3 You can multiply or divide when denominators are NOT alike. You CANNOT add or subtract unless the fractions have the same denominator. Addition of fractions: a. Musthavecommondenominator. b. Add numerators. 1+ 2 = (change 2 to 1 ) = 1 + 1 = 2 = 1 48 Subtraction of fractions: a. Musthavecommondenominator. b. Subtract numerators. 6 - 3 = (change 6 to 3 ) = 3 - 3 = 0 84 8444 Multiplication of fractions: a. b. To multiply a fraction by a whole number, multiply numerator by the whole number and place product over denominator. 4 x 3 = 12 = 1 4 = 1 1 8882 To multiply a fraction by another fraction, multiply numerators and denominators. 5 x 3 = 15 = 5 6 4 24 8 Division of fractions: a. Inverttermsofdivisor. b. Then multiply. EXAMPLE 1: 2 ) 4 35 2 x 5 = 10 5 3 4 12 Reduced to lowest terms = 6 14 EXAMPLE 2: 4 ) 5 6 4x6=24 =44 555 3. Decimals Decimal ________________ To the left Point To the right Reading from right to left, each place is 10 times larger in value. For example, 100 is 10 times larger than 10 and 1.0 is 10 times larger than 0.1. Changing decimals to fractions: a. b. c. Express the decimal in words. Write the words as a fraction Reduce to lowest terms. EXAMPLE 1: 0.3 a. three tenths b. 3 10 c. already reduced to lowest terms b. 84 c. 21 EXAMPLE 2: 0.84 a. eighty-four hundredths 100 25 15 millions hundred thousands ten thousands (10,000) thousands (1000) hundreds (100) tens (1) ones (1) tenths (0.1) hundredths (0.01) thousandths (0.001) ten thousandths hundred thousandths millionths Changing fractions to decimals: Divide the numerator by the denominator. .75 EXAMPLE 1: 3 4 *3.00 so 3 = 0.75 4 28 4 20 20 0 .2 EXAMPLE2: 8 40*8.0 so 8 =0.2 40 80 40 0 Addition and Subtraction of decimals: Use the decimal point as a guide and line up the numbers by their decimal place so that all the ones places are lined up under each other, all the tens places lined up and so on. ADDITION EXAMPLE 1: 7.4 +12.39 19.79 ADDITION EXAMPLE 2: .003 2.4 .15 + .02157 2.57457 SUBTRACTION EXAMPLE 2: 6.079 -.85 5.229 SUBTRACTION EXAMPLE 1: 86.4 - 3.817 82.583 Multiplication of decimals: a. Multiplythenumbersasiftheywerewholenumbers. b. Count the total number of decimal places to the right of the decimal point for each of the numbers. c. Usethattotaltocountdecimalplacesintheanswer. a. 17.3 17.3 x 0.45 x 0.45 865 692 7785 = 7.785 b. 17.3 has 1 decimal place past the decimal point. .45 has 2 decimal places past the decimal point 3 total c. Count 3 places for decimal in answer - 7.785 16 Division of decimals: To divide a decimal by a whole number, the decimal is placed directly above the decimal in the dividend. Quotient Divisor *Dividend 1.37 5 *6.85 5 18 15 35 35 0 Shift the decimal of the divisor enough places to make it a whole number. The decimal in the dividend is moved the same number of places as the divisor. Decimal point of quotient is placed directly above the new place of the decimal in the dividend. To divide a decimal by a decimal: EXAMPLE 1: EXAMPLE 2: . 5. .6 *3.0 . 1.3 *22.36 6 *30.0 30 0 17.2 13 *223.6 13 93 91 26 26 Rounding off decimals: Decide how far the number is to be rounded, such as to the tenths place or the hundredths place. Mark that place by putting a line under it. If the digit to the right of that place is less than 5, drop that digit and any others to the right. If the digit to the right of the place to be rounded to is 5 or greater, increase the number in the place by 1 and drop the digits to the right. EXAMPLE 1: 7. 7.42 Rounded to nearest hundredth 17 EXAMPLE 2: 87.852 87.9 Rounded to nearest tenth Rules for rounding off for nursing math tests: 1. At the end of each step round the answer to the nearest hundredths before proceeding to the next step. 2. If the final answer is less than one, the answer should be rounded off to hundredths, Example .6666 .67 3. If the final answer is greater than one, the answer should be rounded to tenths, Example 1.812 1.8 4. In IV problems, round to the nearest whole number. Therefore, you must round the final answer up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be rounded to the nearest hundredth. 18 4. Practice Problems 1. xvi= 2. CDXII = 3. XLVII = 4. XXi= 5. XLIV = 6. MCXX = 7. 54= 8. 29= 9. 83= 10. 2 1 = 2 ANSWERS: Page 60 1. 15= 2 2. 13= 6 3. 7= 4 4. 11= 3 5. 15= 8 6. 37= 5 Practice #2 Fractions Basic Math Practice Practice #1 Roman Numerals 19 7. 4= 6 8. 3= 9 9. 15= 60 10. 1+ 4+ 3= 16 5 4 11. 5+2= 95 12. 2+1+9 = 7 2 14 13. 1-1= 23 14. 9 -3= 12 4 15. 6-2= 73 16. 7x2= 83 17. 11x3= 24 18.12x1 = 25 100 19. 2)1= 82 20. 12)1= 33 21. 21)1= 26 22. 2)1= 92 ANSWERS: Page 60 20 Change fractions to decimals 1. 6= 8 2. 5 = 10 3. 3= 8 4. 2= 3 Change decimals to fractions 5. 0.54 = 6. 0.154 = 7. 0.60 = 8. 0.2= Add decimals 9. 1.64+0.6= 10. 0.02+1.0= 11. 2.63+.01= 12. 1.54+0.3= Subtract decimals 13. 1.23-0.6= 14. 0.02 - 0.01 = 15. 2.45 - 0.03 = 16. 0.45 - 0.02 = Multiply decimals 17. 0.23 x 1.63 = 18. .03 x 0.123 = Practice # 3 Decimals 21