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MATH OPERATIONSWhy is it important to know the basic math operations?What kind of problems are solved using basic mathoperations? Fractions Decimals Percents Algebra Geometry
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WHAT ARE THE 4 BASIC MATH OPERATIONS? Addition Multiplication Subtraction DivisionIt doesn’t matter what kind of math problems are beingsolved. These are the only Math operations used.
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DEFINITIONS: BASIC OPERATIONSAddition (+) Adding two or more numbers together.Subtraction (-) Finding the difference between numbers.Multiplication (x) is repeated addition. 5 x 3 is the same as 5+5+5 or 3 sets of 5 = 15 3 x 5 is the same as 3 + 3 + 3 + 3 + 3 or 5 sets of 3 = 15Division (divide ÷) Splitting into equal groups or parts; theresult of sharing. There are 12 chocolates, and 3 friends want to share them, how do are the chocolates divided? 4 each
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SYMBOLS FOR BASIC OPERATIONSMultiplication: There are four ways to write a multiplicationproblem. • An “ x ” - 3 x 4 • A dot - 3 • 4 • Parenthesis - (3)4 or (3)(4) or 3(4) • Algebraic expression - 5n = (5 x n)Division: There are three ways to write a division problem. Using a division bracket 5 25 The division sign “÷ ” 25÷ 5 A fraction 25 5
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KEY WORDS Addition Multiplication Add Subtraction Sum Multiply Division Subtract Product Total Divide Difference Total Altogether Each Compare Times Combine Average Minus TwiceIncreased by Split Less than Per In all Share More than Decreased by
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PLACE VALUEBefore any numbers can be added, subtracted,multiplied or divided, the place value of numbers mustbe understood.Each place has a given value, therefore each digithas a given value.Hundred Ten Thousands Hundreds Tens OnesThousands Thousands 1 2 7 8 5 4 Written: 127,854
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WHAT IS PLACE VALUE?Place value is the basis of our entire number system.A place value system is one in which the position of adigit in a number determines its value.In the standard system, called base ten, each placerepresents ten times the value of the place to its right.Think of this as making groups of ten of the smallerunit and combining them to make a new unit.
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Think of this:1 x 10 = 10 The tens place has ten times the value of the ones place10 x 10 = 100 The hundreds place has 10 X the value of the tens place100 x 10 = 1,000 The thousands place has 10 X the value of the hundreds place1000 x 10= 10,000 The ten thousands place has 10 X the value of the thousands place10,000 x 10 = 100,000 The hundred thousands place has 10 X the value of the ten thousands place
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In the number 456, each digit has a specific value. 4 5 6 hundreds tens ones 4 x 100 5 x 10 6 x 1 The value for each number is as follows: 400 + 50 + 6 456
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GUIDED PRACTICE: PLACE VALUEWrite the value for the underlined number below. 1. 478 ___________ 2. 985 ___________ 3. 225 ___________ 4. 761 ___________
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GUIDED PRACTICE: PLACE VALUEWrite the value for the underlined numberbelow. 1. 478 8 ones ___________ 9 hundreds 2. 985 ___________ 3. 225 2 tens ___________ 4. 761 7 hundreds _____________
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PLACE VALUEA comma is used to separate the thousandsplace from the hundreds place. Hundreds Thousands Tens Ten thousands Ones Hundred thousands 127,854 comma
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PLACE VALUEWhen there is no digit to represent a place,a zero (0) is used as a place holder. 1 2 3,4 0 0 hundred thousands ones tens thousands thousands tens hundreds
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Zeros used as a place holder 107, 804No ten thousands digit No tens digit place holder
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GUIDED PRACTICE: PLACE VALUE Write the place value for the underlined digit.1. 16,780 ________________2. 5078 __________________3. 156,006 _________________4. 209,721 _________________
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Write the place value for the underlined digit. 0 ones1. 16,780 ________________ 5 thousands2. 5078 __________________ 1 hundred thousands3. 156,006 _________________ 0 ten thousands4. 209,721 _________________
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Reading & Writing Whole NumbersWriting whole numbers can be done by following a few rules.1.Some words are compound and need a hyphen: twenty-one2. Do not use AND when writing whole numbers: 1,120 one thousand one hundred twenty3. Place a comma between the digit in the millions and hundred thousands place and the thousands and hundreds 1,0 0 0,0 0 0 place1,000,000. millions thousands
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ADDITION thousands When adding digits, it hundreds thousands doesn’t matter which order tens hundreds the numbers are placed. ones tens ones 4124 + 25 25 + 4124 25 +4124The numbers must be lined up in the correct place value column. Thousands Hundreds Tens Ones 4 1 2 4 + 2 5
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PLACE VALUE OF NUMBERS Each number has a value in the problem. Thousands Hundreds Tens Ones 4 1 2 4 + 2 5When working the problem, the ones column is added first.
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If labels are given with the numbers, add themto the answer after the problem is solved.5 miles + 3 miles 5 +3 8 miles 8 Labels must be carried to the answer
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GUIDED PRACTICESolve the following problems. Rewrite each problemusing the column form. 6051. 605 + 32 = + 32 6372. 334 + 52 =3. 456 quarts + 233 quart =4. 2546 + 151 =
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CARRYING WITH ADDITION• Be sure the numbers are lined up in thecorrect place value column.•Addition starts with the digits in the ONEScolumn hundreds tens ones 558 +145
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hundreds1.Add the two numbers in tens ones the ones column. 558 +145 8+5= 13 tens2.If the sum of the numbers in the ones column is greater (>) than 1 9, the number in the tens 558 column is carried over. +145 3
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3. In this case the 3 1 is placed in the 558 ones column and +145 the 1 is stacked 3 on the 5 in the 8+5= 13tens column. 1 14. The next set of numbers which 5 5 8 are in the tens +1 4 5column are now 0 3added together. 5 + 4 + 1= 10
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1 1 5 5 8 +1 4 5 0 3 6. The digits in thehundreds column are added together 1 1and the total is written 5 5 8down in the hundreds +1 4 5 7 0 3column. 5 + 1 + 1= 7ANSWER: 703
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GUIDED PRACTICEUse the correct steps to solve each problem. Rewrite eachproblem in column form.1. 7,170 + 342 =2. 254 + 676 =3. 5,667 feet + 654 feet =4. 1,678 + 435
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Use the correct steps to solve each problem. Rewrite eachproblem in column form. 1 7,1 7 01. 7,170 + 342 = 7,512 + 342 7512 1 1 2542. 254 + 676 = 930 +676 9 30
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KEY WORDS:IMPORTANT VOCABULARY FOR WORD PROBLEMS Subtraction Division Subtract Addition Difference Multiplication Divide Compare Each Add Average Sum Minus Multiply Split Total Less than Product Share Altogether More than Total Combine Decreased by TimesIncreased by Twice In all Per
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Addition Addition Add Sum Addition problems do not have Total the “+” symbol in written Altogether problems. CombineIncreased by Know the key words that apply In all to help solve problems.
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STEPS FOR SOLVING WORD PROBLEMSStep 1: What is the question being asked?Step 2: What information is necessary to solve the problem?Step 3: Decide what information in the question is NOT necessary.Step 4: What math operations will be needed to solve the problem?Step 5: Does the answer make sense?
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The first step to answer any word problem isto find key words.In the following word problems, identify the KEYWORDS used in ADDITION and write on a piece ofpaper1. At rush hour, the Busy Bee Café has 4waitresses, 1 dishwasher, 2 cooks, 2 busboys,and 1 manager. How many people in all work at the Busy Bee Café during rush hour?
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How many people in all work at the BusyBee Café during rush hour?Key words: In all
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2. Zack bought a cheesecake for $ 8.15 and acoffeecake for $6.98 and tax was $1.20. What was the total cost?
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In order to understand any wordproblem, it must be broken down intosteps. The problem may require a student toread and re-read the problem tounderstand what information innecessary to answer the questioncorrectly.
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Kathryn goes out to lunch with Mia and Fran.Each girl orders the $5 lunch special.Kathryn wants to treat her friends to lunch.The tax is 9% and a 25% tip will add $3.75.Not counting the tax and tip, how much willKathryn have to pay?
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What is the question: How much will she haveto pay?or the total cost to KathrynWhat is the necessary information need to solve.Total cost of each mealsHow many meals did she buy?What math operations will be needed to solvethe problem?Addition Meal + Meal + Meal
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What is the necessary information need tosolve.Total cost of each meals $5How many meals did she buy? 3What math operations will be needed to solvethe problem?Addition Meal + Meal + Meal 5 + 5 + 5Answer: $15
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What information is not necessary to solve this problem?The tax is 9% and a 25% tip will add $3.75.
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GUIDED PRACTICE: ADDITION 1. Julia teaches a GED class. She has many students that faithfullyattend her class. On the roll, there are 15 men and 13women but only 7 men and 11 women arecurrently attending the GED class. How many students are currentlyattending the class?
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How many students are currentlyattending the class? Key word/ words? How many Answer? 18 11 + 7 1 8
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2. What was the total number of participants in the 2011 Marathon?Key word/ words? TotalAnswer? 6,700 1 1 6525 + 448 6973
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3. In 2010, the NCAA Men’s Basketball Tournament had a viewing audience of 506,000. In 2011, the number viewers increased by 72,000 which was the largest viewing audience since 2005. If 2010 and 2011 viewing audience was combined together, what was the size of the viewing audience for 2011?
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If 2010 and 2011 viewing audience was combined together, what was the size of the viewing audience for 2011?Key word/ words?Combined togetherAnswer? 578,000 5 0 6, 0 0 0 + 7 2, 0 0 0 5 7 8 0 0 0
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What was the sum of the two trackpasses for Buddy? Key Word: Sum Answer: 299 150 +149 299
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5. Frank and Steven rent a condo downtown for $1221 per month. The condo maintenance is anadditional $63 per month. What is the total cost of thecondo rent?
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What is the total cost of the condo rent?Key Word: TotalAnswer: $1284 1221 + 63 12 84
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6 . Amanda is having surprise birthday party for Red. She invited twenty of Red’s friends. Her menu will be hamburgers, hot dogs, chips, a birthday cake and ice cream. She spent $25 for a table cloth, $35balloons, $12 for a centerpiece plus a $144 forgroceries. Altogether how much did Amanda spend for the table cloth and groceries?
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Altogether how much did Amanda spend forthe table cloth and groceries? Key Word: Altogether Answer: $169 144 + 25 16 9
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SubtractionThe process of finding the differencebetween two numbers. Just like addition problems:1. Always line up numbers from right to left.2. Always bring down the labels.
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1. Always line up numbers from right to left starting in the ones column. Hundreds Tens Ones 6 5 9 659 - 1 4 2 -142 In subtraction, the larger number must be placed on top of the smaller number.
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659659-142 -142Remember the place value each digit.In subtraction, start in the ones column. 659 659 -1 4 2 -142 7 ones 9 – 2= 7 tens hundreds
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659 -142 7Next, subtract the digits in the tens column. 659 -142 17 5 – 4= 1
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659 -142 17Last, subtract the numbers in the hundreds column. 659 -142 51 7 6 – 1= 5
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To check the answer- do the opposite operation. 517 517 659 + 142 = 659 +1 4 2 -1 4 2 659 517The answer should be the largest or the topnumber in the problem. Does it work?
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GUIDED PRACTICERemember to drop the comma and label when subtracting.Add back after problem solved.1. 1,356 – 254 =2. 5,654 feet – 654 feet =3. 676 – 254 =4. 678 – 135 =5. 13 5 6 – 12 5 4
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Remember to drop the comma and label when subtracting. Add back after problem solved. 1356 11021. 1,356 – 254 = 1,102 - 254 + 254 1 10 2 1356 50 0 0 56542. 5,654 feet – 654 feet = 5,000 feet + 6 5 4 - 654 5 6 5 4 5 00 0 3. 676 – 254 = 4 2 2 676 422 -254 +254 422 676
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67 8 5 4 34. 678 – 135 = +1 3 5 -13 5 5 4 3 6 7 85. 13 5 6 1254 – 12 5 4 + 102 0 1 0 2 1356 Drop the zero at the front of the number. What is the answer now? 102
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SUBTRACTION Subtraction Key Words to Know Subtract Difference Compare Minus How much more Less than How many more Decreased Take AwayNOTE: words that end in “er” might be keywords. Example: fewer, faster
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SUBTRACTION: WORD PROBLEMS1.The speed limit is posted on the highway 55 What is the difference in Alex’s current speed and the posted speed limit? Key word: difference 55 -34 2 1 mph
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How many more fish did Bubba catch? 17 11 fish - 06 11
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3. John bought a used motorcycle. The cost of the bike was $6,440. He also wanted to buy a jacket and helmet. If he had $7,860 total andsubtracted the cost of the bike, whatwas left to spend on the helmet andjacket?
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If he had $7,860 total and subtracted the cost of the bike, what was left to spend on the helmet and jacket?Key Word: subtracted 7860 - 6440Answer: $1,420 1 4 20
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BORROWING WITH SUBTRACTION:To subtract, write the numbers in column form,and begin with the digits in the ones column.The smaller number is always subtracted fromthe larger number.Remember the: place _____ value ____Start from the ones place and move left
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753 – 145= Re-write in column form 753 753 -1 4 5 -145 ones tens hundreds
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What happens when the bottom number can’tbe subtracted from the top number? 753 -145 Cannot subtract 5 from 3
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…need to borrow from the next columnSince the next column is the tens column,one set of ten will be borrowed. Now the 5 can be subtracted from 13 4 1 753 13 – 5= -145 The digit in the tens column (5) is reduced by one set of ten making it 4
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4 1 The operation can be 753 completed. -145 13 – 5 = 8 4 1 7 5 3 Look in the tens column and see if- 1 4 5 the digits can be subtracted. 8 The digit was reduced by 1 set of ten.
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41 Can 4 be subtracted from 4? 753 4 - 4= 0 -145 08 4 1 753 Look in the hundreds column.-145 Can the numbers be subtracted? 608 Can 1 be subtracted from 7? 7 – 1 =6
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Check answerWhat is the opposite operation of subtraction? Addition Add the answer (608) to the smallest number (145) 4 1 1 753 608 -145 +145 6 08 75 3 Does it work?
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SUBTRACTION WORD PROBLEMS Subtraction Key Words to Know Subtract Difference Compare Minus How much more Less than How many more Decreased Take Away NOTE: words that end in “er” might be key words. Example: fewer, faster
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Identify and write the key word in each problem thensolve. Tori loves to play bingo at her grandma’s church. Tonight Tori was excitedbecause she won the big bingoprize of $25. If she spent $9 on a bingo card, how much money did she have after she subtracted the cost of card?
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If she spent $9 on a bingo card,how much money did she haveafter she subtracted the cost ofcard?Key words: subtracted 1 1 25Answer: - 9 $16 16
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GUIDED PRACTICE:1. In 1998, the unemployment rate was at 4%. In 2010,the unemployment rate as 13%. What was the difference in theunemployment rate during the 12 year span?
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What was the difference in theunemployment rate during the 12 year span? Key word: difference Answer: 9% 0 1 13 - 4 09
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2 . Trudy is having a Sunday brunch forEaster with her family. If she serves eggs, sausage, bacon, French Toast, waffles, and orange juice, she estimated her grocery bill will be around $150. She went shopping and her total was $129. What was the difference in the cost and her estimation?
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What was the difference in the cost and estimation? 41Key word: difference 150 -129Answer: $21 02 1
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3. Monte wants to buy a new car that costs $21,620. He is researching how much insurance will cost for the particular model. He received quotes from WeInsureAll Insurance , an online company, and the local Field and Farm Insurance Company. Both companies provided quotes for six months full coverage. WeInsureAll quoted Monte a price of $592 and Farm Insurance Company provided a quote of $635. Assuming the coverage is of equal quality, What is the comparison difference between the two companies?
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Assuming the coverage is of equal quality,What is the comparison difference between the twocompanies?Key words: comparison difference (compare) 5 1 635 Answer: $43 - 592 043
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4.Buckshot had a nickname of “double ought Buckshot” because he drovethe “00” car. On the first pass, Buckshot’s car was clocked at 134 mph. The next driver, I.B. Faster, was clocked at 182 mph. How much faster was I.B. than Buckshot?
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How much faster was I.B. than Buckshot?Key words : How much faster 7 1Answer: 48 mph 182 -134 04 8
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5. Frank and Wendy are planning a vacationand had two options for a week rental of a beachhome. One home rented for $1416 per week on the beach. The other rented for $1122 per week and it was located two blocks from the beach. How much more was the beach home rental that was closest to the beach?
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