2 BASIC MATH A. BASIC ARITHMETIC Foundation of modern day life. Simplest form of mathematics.Four Basic Operations :Addition plus signSubtraction minus signMultiplication multiplication signDivision division signxEqual or Even Valuesequal sign
3 1. Beginning Terminology Numbers - Symbol or word used to express value or quantity.NumbersArabic number system - 0,1,2,3,4,5,6,7,8,9Digits - Name given to place or position of each numeral.DigitsNumber Sequence2. Kinds of numbersWhole Numbers - Complete units , no fractional parts. (43)Whole NumbersMay be written in form of words. (forty-three)Fraction - Part of a whole unit or quantity. (1/2)Fraction
4 2. Kinds of numbers (con’t) Decimal Numbers - Fraction written on one line as whole no.Decimal NumbersPosition of period determines power of decimal.
5 B. WHOLE NUMBERS 1. Addition Number Line - Shows numerals in order of valueNumber LineAdding on the Number Line (2 + 3 = 5)Adding on the Number LineAdding with picturesAdding with pictures
6 1. Addition (con’t) Adding in columns - Uses no equal sign 5+ 510897+ 3681265Answer is called “sum”.SimpleComplexTable of Digits
8 2. SubtractionNumber Line - Can show subtraction.Number LineNumber LineSubtraction with picturesPosition larger numbers above smaller numbers.If subtracting larger digits from smaller digits, borrow from next column.45 3 81141
11 3. Checking Addition and Subtraction 2+ 810- 85+ 38- 373+ 48121- 48Result should produce other added number.Check Addition - Subtract one of added numbers from sum.Check Addition927318426183To AddTo CheckCheck Three or more #sCheck Three or more #s - Add from bottom to top.5- 41+ 462- 3725+ 37103- 8716+ 87Check Subtraction - Add subtracted number back.Check Subtraction
12 Check these answers using the method discussed. CHECKING ADDITION & SUBTRACTION PRACTICE EXERCISES1. a+ 8b+ 5c+ 18d+ 236131426335a. 87- 87b- 192c- 212d- 51995524a. 34+ 12b1381+ 14c. 871381+ 14d- 8346104195746a- 16b- 361c22Check these answers using the method discussed.
14 4. Multiplication Learn “Times” Table In Arithmetic - Indicated by “times” sign (x).In ArithmeticLearn “Times” Table6 x 8 = 48
15 4. Multiplication (con’t) Complex Multiplication - Carry result to next column.Complex MultiplicationProblem: x 2348X 234+ 248X 23144+ 248X 23144+ 1648X 23144+ 19601104Same process is used when multiplyingthree or four-digit problems.
18 5. DivisionFinding out how many times a divider “goes into” a whole number.Finding out how many times a divider “goes into” a whole number.= 3= 5
19 So, 5040 divided by 48 = 105 w/no remainder. 5. Division (con’t)Shown by using a straight bar “ “ or “ “ sign.1548 “goes into” 50 one time.48504048 goes into 24 zero times.48 goes into 240, five times481 times 48 = 482450 minus 48 = 2 & bring down the 4240Bring down other 0.5 times 48 = 240240 minus 240 = 0 remainderSo, 5040 divided by 48 = 105 w/no remainder.Or it can be stated:48 “goes into” 5040, “105 times”
20 DIVISION PRACTICE EXERCISES 92 211 62 1. a. 48 5040 7 434 c. 9 828 b.7434c.982813310101a.9117b.123720c.101010256687a.235888b.56384729867a.989604b.1387150123a.502500b.78997047Let's check our answers.
21 DIVISION PRACTICE EXERCISES (con’t) 79000a.21147b.32700061101a.321952b.88888867 r 19858 r 13a.875848b.151288312 r 95522 r 329a.99412883b.3528073Let's check our answers.
22 C. FRACTIONS - A smaller part of a whole number. Written with one number over the other, divided by a line.381116orAny number smaller than 1, must be a fraction.Try thinking of the fraction as “so many of a specified number of parts”.For example: Think of 3/8 as “three of eight parts” or...Think of 11/16 as “eleven of sixteen parts”.1. Changing whole numbers to fractions.Multiply the whole number times the number of parts being considered.Changing the whole number 4 to “sixths”:4 x 662462464 ==or
23 CHANGING WHOLE NUMBERS TO FRACTIONS EXERCISES 73437343to sevenths==or740 x 883208320to eighths==or854 x 994869486to ninths==or927 x 3381381to thirds==or312 x 4448448to fourths==or4130 x 556505650to fifths==or5Let's check our answers.
24 2. Proper and improper fractions. Proper Fraction - Numerator is smaller number than denominator.Improper Fraction - Numerator is greater than or equal to denominator.3/415/93. Mixed numbers.Combination of a whole number and a proper fraction.4. Changing mixed numbers to fractions.Change 3 7/8 into an improper fraction.Change whole number (3) to match fraction (eighths).3 x 8824or3 ==Add both fractions together.=2487+31
25 CHANGING MIXED NUMBERS TO FRACTIONS EXERCISES /2124 x 28=+919 x 161630473117 x 12128411956 x 1414935 x 64643203218 x 4424327/4/16/12/14/64Let's check our answers.
26 Changing improper fractions to whole/mixed numbers. Change 19/3 into whole/mixed number..19/3 = = 6, remainder 1 = 6 1/3 (a mixed number)CHANGING IMPROPER FRACTIONS TO WHOLE/MIXED NUMBERS EXERCISES1. 37/7 =2. 44/4 =3. 23/5 =4. 43/9 =/8 =/6 == = 5, remainder 2 = 5 2/7 (a mixed number)= = 11, no remainder = 11 (a whole number)= = 4, remainder 3 = 4 3/5 (a mixed number)= = 4, remainder 7 = 4 7/9 (a mixed number)= = 30, no remainder = 30 (a whole number)= = 31, remainder 5 = 31 5/6 (a mixed number)Let's check our answers.
27 7. Reducing to Lower Terms 6. Reducing FractionsTerms - The name for numerator and denominator of a fraction.Reducing - Changing to different terms.Reducing does not change value of original fraction.7. Reducing to Lower TermsDivide both numerator and denominator by same number.Example:.= 1= 339=&1Have same value.8. Reducing to Lowest TermsLowest Terms - 1 is only number which evenly divides both numerator and denominator.Example:1632=.= 8= 16a..= 4= 8b..= 2= 4c..= 1= 2d.
28 a. to 4ths = b. to 10ths = c. to 6ths = d. to 9ths = e. to 15ths = f. REDUCING TO LOWER/LOWEST TERMS EXERCISES1. Reduce the following fractions to LOWER terms:.= 3= 415a.20to 4ths=Divide the original denominator (20) by the desired denominator (4) = 5..Then divide both parts of original fraction by that number (5)..= 9= 1036b.to 10ths40=.= 4= 6c.24to 6ths36=.= 3= 9d.1236to 9ths=.= 10= 1530e.45to 15ths=.= 4= 1916f.to 19ths76=Let's check our answers.
29 = = = = = = Let's check our answers. REDUCING TO LOWER/LOWEST TERMS EXERCISES (con’t)2. Reduce the following fractions to LOWEST terms:= 3= 5.a.a.6=10= 1= 3.a.b.3=9= 3= 32.a.c.6=6413d.=Cannot be reduced.32e.32= 16= 32.a.= 8= 16.b.= 1= 2.c.=48f.16= 8= 38.a.= 4= 19.b.76=Let's check our answers.
30 10. Least Common Denominator (LCD) Two or more fractions with the same denominator.18267When denominators are not the same, a common denominator is found by multiplying each denominator together.16382951218724366 x 8 x 9 x 12 x 18 x 24 x 36 = 80,621,56880,621,568 is only one possible common denominator ...but certainly not the best, or easiest to work with.10. Least Common Denominator (LCD)Smallest number into which denominators of a group of two or more fractions will divide evenly.
31 10. Least Common Denominator (LCD) con’t. To find the LCD, find the “lowest prime factors” of each denominator.38295121872413662 x 32 x 2 x 23 x 32 x 3 x 22 x 3 x 33 x 2 x 2 x 22 x 2 x 3 x 3The most number of times any single factors appears in a set is multiplied by the most number of time any other factor appears.(2 x 2 x 2) x (3 x 3) = 72Remember: If a denominator is a “prime number”, it can’t be factored except by itself and 1.LCD Exercises (Find the LCD’s)1681211216243104157202 x 32 x 2 x 22 x 3 x 22 x 2 x32 x 2 x 2 x 23 x 2 x 2 x 22 x 53 x 52 x 2 x 52 x 2 x 2 x 3 = 242 x 2 x 2 x 2 x 3 = 482 x 2 x 3 x 5 = 60Let's check our answers.
32 11. Reducing to LCDReducing to LCD can only be done after the LCD itself is known.38295121872413662 x 32 x 2 x 23 x 32 x 3 x 22 x 3 x 33 x 2 x 2 x 22 x 2 x 3 x 3LCD = 72Divide the LCD by each of the other denominators, then multiply both the numerator and denominator of the fraction by that result.16= 12.1 x 12 = 126 x 12 = 7238= 9.3 x 9 = 278 x 9 = 7229= 8.2 x 8 = 169 x 8 = 72512= 6.5 x 6 = 3012 x 6 = 72Remaining fractions are handled in same way.
33 Reducing to LCD Exercises Reduce each set of fractions to their LCD.1681211216243104157202 x 32 x 2 x 22 x 3 x 22 x 2 x 2 x 3 = 242 x 2 x 2 x 2 x 3 = 482 x 2 x32 x 2 x 2 x 23 x 2 x 2 x 22 x 53 x 52 x 2 x 52 x 2 x 3 x 5 = 6016= 4.1 x 4 = 46 x 4 = 248= 31 x 3 = 38 x 3 = 2412= 21 x 2 = 212 x 2 = 24112= 4.1 x 4 = 412 x 4 = 4816= 31 x 3 = 316 x 3 = 4824= 21 x 2 = 224 x 2 = 48310= 6.3 x 6 = 1810 x 6 = 60415= 44 x 4 = 1615 x 4 = 60720= 37 x 3 = 2120 x 3 = 60Let's check our answers.
34 13. Addition of Mixed Numbers 12. Addition of FractionsAll fractions must have same denominator.Determine common denominator according to previous process.Then add fractions.1423=6+Always reduce to lowest terms.13. Addition of Mixed NumbersMixed number consists of a whole number and a fraction. (3 1/3)Whole numbers are added together first.Then determine LCD for fractions.Reduce fractions to their LCD.Add numerators together and reduce answer to lowest terms.Add sum of fractions to the sum of whole numbers.
35 + + + + 1 + + 1 + 1 6 7 Let's check our answers. Adding Fractions and Mixed Numbers ExercisesAdd the following fractions and mixed numbers, reducing answers to lowest terms.1.=34+2.710+25==12644107+1=113.1516+932=14.34+25=393230+9=715 + 1 = 682015+=233167Let's check our answers.
36 14. Subtraction of Fractions Similar to adding, in that a common denominator must be found first.Then subtract one numerator from the other.202414-=6To subtract fractions with different denominators: ( )51614-Find the LCD...51614-2 x 2 x 2 x 22 x 22 x 2 x 2 x 2 = 16Change the fractions to the LCD...5164-Subtract the numerators...5164-=1
37 15. Subtraction of Mixed Numbers Subtract the fractions first. (Determine LCD)12310-43 x 2 = 6 (LCD)Divide the LCD by denominator of each fraction.= 2= 3.2Multiply numerator and denominator by their respective numbers.3x=461Subtract the fractions.364-=1Subtract the whole numbers.= 6Add whole number and fraction together to form complete answer.6 +16=
38 15. Subtraction of Mixed Numbers (con’t) BorrowingSubtract the fractions first. (Determine LCD)381165-(LCD) = 16becomes6Six-sixteenths cannot be subtracted from one-sixteenth, so1 unit ( ) is borrowed from the 5 units, leaving 4.16Add to and problem becomes:1616174-3Subtract the fractions.61617-=11Subtract the whole numbers.4 - 3 = 1Add whole number and fraction together to form complete answer.1 +1116=1
39 Subtracting Fractions and Mixed Numbers Exercises Subtract the following fractions and mixed numbers, reducing answers to lowest terms.1.=13-254.1-23315=35115-56=1415=6-5332032172.5-35.1-5715=101=416812924-615=38516=15-41015720100432-3.47281=536.143-105=412115=5-6472819=512-91410413Let's check our answers.
40 16. MULTIPLYING FRACTIONS Common denominator not required for multiplication.4163X1. First, multiply the numerators.4163X=122. Then, multiply the denominators.4163X=12643. Reduce answer to its lowest terms.41264=316.
41 17. Multiplying Fractions & Whole/Mixed Numbers Change to an improper fraction before multiplication.34X1. First, the whole number (4) is changed to improper fraction.412. Then, multiply the numerators and denominators.413X=123. Reduce answer to its lowest terms.412=31.
42 18. CancellationMakes multiplying fractions easier.If numerator of one of fractions and denominator of other fraction can be evenly divided by the same number, they can be reduced, or cancelled.Example:51683X=51683X=125213X=6Cancellation can be done on both parts of a fraction.3241221X=17214
43 1 26 2 3 1 1 5 25 Multiplying Fractions and Mixed Numbers Exercises 3 Multiply the following fraction, whole & mixed numbers. Reduce to lowest terms.3431611.2.X=26X=1416264253.15X3=4.92X=5533549327505.X=16.X=435105177727.X=8.251033612X=3117725239.5X=15Let's check our answers.
44 20. Division of Fractions and Whole/Mixed Numbers Actually done by multiplication, by inverting divisors.The sign “ “ means “divided by” and the fraction to the right of the sign is always the divisor.Example:1534becomesX=1520. Division of Fractions and Whole/Mixed NumbersWhole and mixed numbers must be changed to improper fractions.Example:18becomes31623 +=51andX8 +17X5116178Inverts to=123DoubleCancellation132X=
45 8 25 18 144 15 Dividing Fractions,Whole/Mixed Numbers Exercises 51 3 1 Divide the following fraction, whole & mixed numbers. Reduce to lowest terms.5131281.5314==2.86168173.18=14457254.15812=147235.=34
46 D. DECIMAL NUMBERS1. Decimal SystemSystem of numbers based on ten (10).Decimal fraction has a denominator of 10, 100, 1000, etc.Written on one line as a whole number, with a period (decimal point) in front.510=.5100.051000.0053 digits.999 is the same as9991000( same number of zerosas digits in numerator)
47 5 is written 5.7 55 is written 55.07 555 is written 555.077 2. Reading and Writing Decimals7105is written5.7Whole NumberDecimal Fraction (Tenths)710055is written55.07Whole NumberDecimal Fraction (Hundredths)Decimal Fraction (Tenths)771000555is writtenWhole NumberDecimal Fraction (Tenths)Decimal Fraction (Hundredths)Decimal Fraction (Thousandths)
48 2. Reading and Writing Decimals (con’t) Decimals are read to the right of the decimal point..63 is read as “sixty-three hundredths.”.136 is read as “one hundred thirty-six thousandths.”.5625 is read as “five thousand six hundred twenty-fiveten-thousandths.”3.5 is read “three and five tenths.”Whole numbers and decimals are abbreviated.6.625 is spoken as “six, point six two five.”One place .0 tenthsTwo places .00 hundredthsThree places .000 thousandthsFour places ten-thousandthsFive places hundred-thousandths
49 3. Addition of DecimalsAddition of decimals is same as addition of whole numbers except for the location of the decimal point.AddAlign numbers so all decimal points are in a vertical column.Add each column same as regular addition of whole numbers.Place decimal point in same column as it appears with each number..8651.3000“Add zeros to help eliminate errors.”0000“Then, add each column.”
50 4. Subtraction of Decimals Subtraction of decimals is same as subtraction of whole numbers except for the location of the decimal point.Solve:Write the numbers so the decimal points are under each other.Subtract each column same as regular subtraction of whole numbers.Place decimal point in same column as it appears with each number.“Add zeros to help eliminate errors.”“Then, subtract each column.”
51 5. Multiplication of Decimals Rules For Multiplying DecimalsMultiply the same as whole numbers.Count the number of decimal places to the right of the decimalpoint in both numbers.Position the decimal point in the answer by starting at theextreme right digit and counting as many places to the left asthere are in the total number of decimal places found in both numbers.Solve: X 2.08Decimal point 3 places over.xDecimal point 2 places over.“Add zeros to help eliminate errors.”.“Then, add the numbers.”Place decimal point 5 places over from right.
52 6. Division of Decimals Rules For Dividing Decimals Place number to be divided (dividend) inside the division box.Place divisor outside.Move decimal point in divisor to extreme right. (Becomes whole number)Move decimal point same number of places in dividend. (NOTE: zerosare added in dividend if it has fewer digits than divisor).Mark position of decimal point in answer (quotient) directly above decimalpoint in dividend.Divide as whole numbers - place each figure in quotient directly abovedigit involved in dividend.Add zeros after the decimal point in the dividend if it cannot be dividedevenly by the divisor.Continue division until quotient has as many places as required for theanswer.Solve:
53 6. Division of Decimals.8993137 4....35 0 49 1 8remainder
54 Decimal Number Practice Exercises “WORK ALL 4 SECTIONS (+, , X, )1. Add the following decimals.4.7====410.832. Subtract the following decimals.0.6685======9.0560.07960.21===0.46798.8470.340.7Let's check our answers.
55 Decimal Number Practice Exercises 3. Multiply the following decimals.3.01x 6.20bx 1.2cx 1.618.66225.562.56dxex 1.2fx1.968gxhxix42.113Let's check our answers.
56 Decimal Number Practice Exercises 4. Divide the following decimals.3 0.55.7875ab5 1 7cd10 0eLet's check our answers.
57 E. CHANGING FRACTIONS TO DECIMALS A fraction can be changed to a decimal by dividing the numerator by the denominator..7534Change to a decimal.Decimal Number Practice ExercisesWrite the following fractions and mixed numbers as decimals.a.610b.35c.4d.1e.2f.820g.7h.15i.25j.12k.17l.4950m.9n.o..18.104.22.168.22.214.171.124.126.96.36.1991.91.046.6Let's check our answers.
58 F. PERCENTAGES or 1. Percents Used to show how many parts of a total are taken out.Short way of saying “by the hundred or hundredths part of the whole”.The symbol % is used to indicate percent.Often displayed as diagrams.1/44/4 = 100%25/100 = 25%100 Equal Squares = 100%25% or 25/100orTo change a decimal to a %, move decimal point two places to right and write percent sign..15 = 15%.55 = 55%.853 = 85.3%1.02 = 102%“Zeros may be needed to hold place”..8 = 80%
59 Percents Practice Exercises Write as a decimal.35% = _________14% = _________58.5% = _________17.45% = __________5% = _________Write as a percent..75 = ______%0.40 = _____%0.4 =_______%.4 = _______%.35.14.585.1745.0575404040Let's check our answers.
60 Rules For Any Equivalent To convert a number to its decimal equivalent, multiply by 0.01Change 6 1/4% to its decimal equivalent.Change the mixed number to an improper fraction, then divide thenumerator by the denominator.6 1/4 = 25/4 = 6.25Now multiply the answer (6.25) times 0.016 .25 x 0.01 =Rules For Finding Any Percent of Any NumberConvert the percent into its decimal equivalent.Multiply the given number by this equivalent.Point off the same number of spaces in answer as in both numbers multiplied.Label answer with appropriate unit measure if applicable.Find 16% of 1028 square inches.16 x .01 = .161028 x 0.16 =Label answer: square inches
61 2. PercentageRefers to value of any percent of a given number.First number is called “base”.Second number called “rate”... Refers to percent taken from base.Third number called “percentage”.Rule: The product of the base, times the rate, equals the percentage.Percentage = Base x Rate or P=BxRNOTE: Rate must always be in decimal form.To find the formula for a desired quantity, cover it and the remaining factors indicate the correct operation.Only three types of percent problems exist.RPB1. Find the amount or rate R=PxB2. Find the percentage.P=RB3. Find the base.B=RP
62 Percents Practice Exercises Determine the rate or amount for each problem A through E for thevalues given.BASEPERCENT-AGE2400 lbs1875gallons148 feet3268.5Squareinches$A.B.C.D.E.80%45%15%4 1/2%19.5%1920 lbs.Gal.22.2 feetsq.in.$170.63The labor and material for renovating a building totaled $25,475. Of this amount,70% went for labor and the balance for materials. Determine: (a) the labor cost,and (b) the material cost.$17, (labor) b. $ (materials)35% of 82 = % of 28 =Sales tax is 9%. Your purchase is $4.50. How much do you owe?You have 165 seconds to finish your task. At what point are you 70% finished?You make $14.00 per hour. You receive a 5% cost of living raise. How much raise per hour did you get? How much per hour are you making now?28.74.32$4.91115.5 seconds$.70 /hr raiseMaking $14.70 /hrLet's check our answers.
63 G. APPLYING MATH TO THE REAL WORLD 18 x 12 = 216240 x 8 = 30= 41.5= 13.5 gallons more1.5 x 0.8 = 1.2 mm5 x .20 = 1 inch2400 divided by 6 = 400 per person400 divided by 5 days = 80 per day per person6 x 200 = 1200 sq. ft. divided by 400 = 3 cans of dye2mm x .97 = 1.94 min mm x 1.03 = 2.06 maxLet's check our answers.
64 H. METRICS 1. Metrication Metric Prefixes: Kilo = 1000 units Denotes process of changing from English weights and measuresto the Metric system.U.S. is only major country not using metrics as standard system.Many industries use metrics and others are changing.Metric Prefixes:Kilo = 1000 unitsHecto = unitsDeka = 10 unitsdeci = 0.1 unit (one-tenth of the unit)centi = 0.01 (one-hundredth of the unit)milli = (one thousandth of the unit)Most commonly used prefixes are Kilo, centi, and milli.
65 A. Advantages of Metric System Based on decimal system.No fractions or mixed numbersEasier to teach.Example 1:Using three pieces of masking tape of the following English measurement lengths:4 1/8 inches, 7 6/16 inches, and 2 3/4 inches, determine the total length of the tape.Step 1: Find the least commondenominator (16). Thisis done because unequalfractions can’t be added.4 1/8 = 4 2/167 9/16 = 7 9/162 3/4 = 2 12/16Step 2: Convert all fractions to theleast common denominator.Step 3: Add to find the sum.13 23/16Step 4: Change sum to nearestwhole number.14 7/16“Now, compare with Example 2 using Metrics”.
66 b. Advantages of Metric System Example 2:Using three pieces of masking tape of the following lengths: 85 mm, 19.4 cm, and 57 mm, determine the total length of the tape.Step 1: Millimeters and centimeterscannot be added, so convertto all mm or cm.Step 2: Add to find the sum.85mm = 85mm19.4cm = 194mm57mm = 57mm85mm = 8.5cm19.4cm = 19.4cm57mm = 5.7cmor336 mm33.6 cm“MUCH EASIER”
67 2. Metric Abbreviations Drawings must contain dimensions. Words like “inches, feet, millimeters, & centimeters take too much space.Abbreviations are necessary.Metric Abbreviations:mm = millimeter = one-thousandth of a metercm = centimeter = one-hundredth of a meterKm = Kilometer = one thousand meters76mm25mm30mmDimensioned DrawingSLIDE BLOCK12mm762530Dimensioned Drawing withNote for Standard UnitsSLIDE BLOCKNOTE: All dimensions are in millimeters.12
68 3. The Metric Scale Based on decimal system. Easy to read. Graduated in millimeters and centimeters.Metric Scales110mm or 11.0cm8.35cm or 83.5mmBoth scales graduated the same... Numbering is different.Always look for the abbreviation when using metric scales.Always place “0” at the starting point and read to end point.
69 Metric Measurement Practice Exercises Using a metric scale, measure the lines and record their length._______ mm_______ cm10981.53.11036.380.510.852391.54.25Let's check our answers.
70 4. Comparisons and Conversions Manufacturing is global business.Metrics are everywhere.Useful to be able to convert.Compare the following:One Yard: About the length between your nose and the endof your right hand with your arm extended.One Meter: About the length between your left ear and theend of your right hand with your arm extended.One Centimeter: About the width of the fingernail on your pinkyfinger.One Inch: About the length between the knuckle and theend of your index finger.
71 U.S. Customary and Metric Comparisons Length:A Kilometer is a little over 1/2 mile miles to be more precise.MileKilometerA centimeter is about 3/8 inch.Weight:A paper clip weighs about one gram.A nickel weighs about five grams.A Kilogram is 2.2 pounds. - Two packsof butter plus about 1 stick.
72 U.S. Customary and Metric Comparisons Capacity:One liter and one quart are approximately the same.There are about 5 milliliters in a teaspoon.1 literPressure is measured in newton meters instead of foot pounds.Equivalent Units:milli ThousandthsKilo Thousandscenti HundredthsHecto Hundredsdeci Tenthsbase unit OnesDeka TensPlace ValueTo change to a smaller unit,move decimal to right.To change to a larger unit,move decimal to left.Prefix
73 Changing to a Smaller Unit milli ThousandthsKilo Thousandscenti HundredthsHecto Hundredsdeci Tenthsbase unit OnesDeka Tens15 liters = ________ milliliters (ml)Count the number of places from the base unitto “milli”. There are 3 places.Move the decimal 3 places to the right.15 liters = liters = 15000ml15000Changing to a Larger Unit150 grams (g) = _____ Kilograms (Kg)Count the number of places from the base unitto “Kilo”. There are 3 places.Move the decimal 3 places to the left.150 grams = grams = Kg.150
74 Comparison and Conversion Practice Exercises 1. 1 liter = _______ mlml = _______ liters3. 10 cm = _______ mmcm = _______ m5. 4 Kg = _______ g6. 55 ml = _______ litersKm = _______ mcm = _______ mmmm = _______ cmcm = _______ mm100061005.04000.055850062.0562750Let's check our answers.
75 5. Conversion Factors Conversion Table for Length Conversion Table for Area
76 5. Conversion Factors Conversion of Volume Volume measures the total space occupied by three-dimensionalobjects or substances.Volume of six-sided spaces is calculated as “length x width x height”.Volume of spheres and cylinders is more complicated.Term “cubic” is used because it is a math function involving 3 factors.2ft x 4ft x 3ft = 24 Cubic FeetEnglish1 cubic inch = 1 cubic inch1 cubic foot = 1728 cubic inches (12 x 12 x 12)1 cubic yard = 27 cubic feet (3 x 3 x 3)Metric1 cubic meter = 1,000,000 cubic centimeters (100 x 100 x 100)1 foot = .305 metersand1 meter = 3.28 feetFactors can be converted before or after initial calculation.
77 5. Conversion Factors (con’t) Conversion Table for PressureConversion Table for Weight
78 5. Conversion Factors (con’t) To convert between Celsius and Fahrenheit:Fahrenheit to Celsius (oF-32) x 5/9 = oCCelsius to Fahrenheit (oC x 9/5) = oFConversion Table for Temperature
79 Metric System Practice Exercises 1. Which one of the following is not a metric measurement?millimetercentimetersquare feetcm2. Milli - is the prefix for which one of the following?100 ones0.001 unitunitunit3. How long are lines A and B in this figure?AA = 53 mm, or 5.3 cmB = 38 mm, or 3.8 cmB4. How long is the line below? (Express in metric units).69 mm5. Convert the following:1 meter = __________millimeters5 cm = ____________millimeters12 mm = ___________centimeters7m = _____________centimeters1000501.2700Let's check our answers.
80 H. THE CALCULATOR Functions vary from one manufacturer to the next. Most have same basic functions.More advanced scientific models have complicatedapplications.Solar models powered by sunlight or normal indoorlight.1. Basic Keys:On/Off Key: Turns calculator on or off. Solar unit will not have “off” key..C/AC: Press once ( C ) to clear last entry - Press twice (AC) to clear all functions.Key: Controls the division function.X Key: Controls the multiplication function.Key: Controls the subtraction function.+ Key: Controls the addition function.Key: Controls the square root function.M+ Key: Adds a number or function to the memory register, to be recalled later.M- Key: Subtracts number or function from memory register.MR Key: Memory Recall recalls function stored in register.MC Key: Memory Clear clears or erases all contents from memory.% Key: Controls the percentage functions
81 2. Calculator Functions: Cannot give correct answer if given the wrong information or command.Decimals must be placed properly when entering numbers.Wrong entries can be cleared by using the C/AC button.Calculators usually provide a running total.ADDITIONAdd 3, 8, 9, and 14.Step 1: Press “3” key - number 3 appears on screen..Step 2: Press “+” key - number 3 remains on screen.Step 3: Press “8” key - number 8 appears on screen.Step 4: Press “+” key - running total of “11” appears on screen.Step 5: Press the “9” key - number 9 appears on screen.Step 6: Press “+” key - running total of “20” appears on screen.Step 7: Press “1 & 4” keys - number 14 appears on screen.Step 8: Press the = key - number 34 appears. This is the answer.In step 8, pressing the + key would have displayed the total. Pressing the = key stops the running total function and ends the overall calculation.
82 Calculator Addition Exercise Use the calculator to add the following..06783.49160.76841.02134390641235434=168297Let's check our answers.
83 Calculator Subtraction Exercise SUBTRACT 25 FROM 187.Step 1: Press 1, 8, and 7 keys - number 187 appears on screen..Step 2: Press “-” key - number 187 remains on screen.Step 3: Press 2 & 5 keys- number 25 appears on screen.Step 4: Press “=” key - number 162 appears on screen. This is the answer.In step 4, pressing the - key would have displayed the total.Calculator Subtraction ExerciseUse the calculator to subtract the following..0543=0.00110.0115Let's check our answers.
84 Calculator Multiplication Exercise MULIPLY 342 BY 174.Step 1: Press 3, 4, and 2 keys - number 342 appears on screen..Step 2: Press “X” key - number 342 remains on screen.Step 3: Press 1, 7 & 4 keys- number 174 appears on screen.Step 4: Press “=” key - number appears on screen. This is the answer.Calculator Multiplication ExerciseUse the calculator to multiply the following.2.45xx 19x 43.7 x 12.01=40.641155.2Let's check our answers.
85 Calculator Division Exercise DIVIDE 66 BY 12.3Step 1: Press the 6 key twice - number 66 appears on screen..Step 2: Press “ ” key - number 66 remains on screen.Step 3: Press 1, 2,. (decimal), & 3 keys- number 12.3 appears on screen.Step 4: Press “=” key - number appears on screen. This is the answer.Calculator Division ExerciseUse the calculator to divide the following.=== 0.353Let's check our answers.
86 Calculator Percentages Exercise FIND 1.3% OF 50Step 1: Press the 5 and 0 keys - number 50 appears on screen..Step 2: Press “ x ” key - number 50 remains on screen.Step 3: Press 1, . (decimal), & 3 keys- number 1.3 appears on screen.Step 4: Press “%” key - number .065 appears on screen. This is the answer.Calculator Percentages ExerciseUse the calculator to find the following percentages.Find 5% of:a. 150b. 675c. 100Find 10% of:ab. 871c. 202Find 26% ofa. 260b. 212c= 7.5= 125= 67.6= 33.75= 5= 87.1= 20.2= 55.12=Let's check our answers.
87 That concludes theBasic Math portionof your training.