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Ones group Thousands group Millions group Billions group Trillions group Three- Digit Groups (separated by commas) 3 4 5 5 7 6 4 0 2 8 9 7 4 1 5 CHAPTER 1 REVIEW SECTION 1.1 A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,….} The set of whole numbers is {0,1,2,3,4,5,…} Whole numbers are used for counting objects (such as money!) However, they do not include fractions or decimals. The digits in a whole number have place value. Expanded Notation: When a number’s digits are written with their place value names. 30,542 = 30 thousands + 5 hundreds + 4 tens + 2 ones Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don’t use the word “and”.) Standard Notation uses only digits (0 through 9) and commas to state the number. 16 million = 16,000,000 Data comparisons can be shown in tables or graphs Rounding Whole Numbers: Step 1: Locate the “rounding digit”, which is the digit at the place value you are rounding to. Step 2: Look at the digit directly to the right of the rounding digit. This is the test digit. If the test digit is < 5 (less than 5), keep the rounding digit the same and change all digits to the right of it to 0. If the test digit is ≥5 (greater than or equal to 5), then increase the rounding digit by 1 and change all the digits to the right of it to 0.

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SECTIONS 1.2 and 1.3 Addition Terms: The numbers being added are called addends. Subtraction Terms: The number you are taking away is the subtrahend, the number you are subtracting from is the minuend, and the answer is the difference. Multiplication Terms: The numbers being multiplied together are the factors. The result of the multiplication is the product. Division Terms: The number you are dividing by is the divisor. The number you are dividing into is the dividend. The answer to the division problem is the quotient. The amount over if the dividend is not exactly divisible by the divisor is the remainder. 1. Subtraction is the inverse of addition: If a - b = c, then c + b = a So if 10 - 3 = 7, then 7 + 3 = 10 Check subtraction by adding your difference answer to the subtrahend. Your new answer should be the minuend. 2. Division is the inverse of multiplication: If a ÷ b=c, then c x b = a So if 8 ÷ 2=4, then 4 x 2 = 8 Check division like this: Quotient X Divisor + Remainder = Dividend. Multiply your answer to the division problem by the number you are dividing by, then add the remainder. Your answer should equal the number you divided into. 3. Addition and multiplication follow the commutative properties: a + b = b + a, so 8 + 3 = 3 + 8 a x b = b x a, so 5 x 2 = 2 x 5 Check division like this: Quotient X Divisor + Remainder = Dividend. Multiply your answer to the division problem by the number you are dividing by, then add the remainder. Your answer should equal the number you divided into. The perimeter of a rectangle or a square is the distance around it. This is found by adding up the lengths of all its sides. P = length + length + width + width The area of a rectangle or square is is the amount of material needed to "cover" it completely. This is found by the product of its length and width: A = l x w.

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SECTION 1.4 Prime Factors and Exponents A prime number is a whole number, greater, greater then 1, that has only 1 and itself as factors. Whole numbers greater than 1 that are not prime are called composite numbers. Whole numbers Divisible by 2 are EVEN numbers. Whole numbers not divisible by 2 are ODD numbers. The prime factorization of a whole number is the product of its prime factors. This is found by starting with any two factors of the number and then factoring each of those numbers until you have nothing left but prime numbers at the bottom “roots” of the factorization “tree”. Example: The prime factorization of 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5 = 2 2 ● 3 2 ● 5 2 27 100 93 33 10 25 25 2700

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SECTION 1.5 ORDER OF OPERATIONS P lease : do all operations within parentheses and other grouping symbols (such as [ ], or operations in numerators and denominators of fractions) from innermost outward. E xcuse : calculate exponents M y,D ear : do all multiplications and divisions as they occur from left to right A unt,S ally : do all additions and subtractions as they occur from left to right. Example: 20 – 2 + 3(8 - 6) 2 Expression in parentheses gets calculated first = 20 – 2 + 3(2) 2 Next comes all items with exponents = 20 – 2 + 3(4) Next in order comes multiplication. Multiplication and Division always come before addition or division, even if to the right. = 20 – 2 + 12 Now when choosing between when to do addition and when to do subtraction, always go from left to right, so do 20-2 first, because the subtraction is to the left of the addition. = 18 + 12 Now finally we can do the addition. = 30 SECTION 1.6 An equation is a statement that two expressions are equal. A variable is a letter that stands for a number. Two equations with exactly the same solutions are called equivalent equations. To solve an equation, isolate the variable on one side of the equation by “undoing” the operation performed on it. If the same number is added to (or subtracted from) both sides of an equation, an equivalent equation results. Example: x – 5 = 2 gives the same solution as x – 5+ 5 = 2 + 5 which is x + 0 = 7, or x = 7. Check by substituting the result for x into the original equation and seeing if it is true. 7-5 = 2 ? Yes. Problem-Solving Strategy: 1.Analyze the problem. What are you trying to find? What’s the given info? 2.Form an equation. Let a variable = what you’re trying to find. Use this variable in your equation using the given information. 3.Solve the equation by getting the variable by itself on one side. 4.Check the result by substituting the result for the variable into the original equation and seeing if the equation is true.

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