3 1 factors, multiples and divisibility
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The document discusses factors, multiples, and divisibility of numbers. It defines a number as being divisible by another if the quotient is a whole number with no remainder. A multiple is the product of a number and any whole number greater than zero. A factor is a number that divides another number with no remainder. It provides examples showing 20 is divisible by 4 and 4 is a factor of 20. It also states 15 is a multiple of 3 and 5. Divisibility rules are outlined for numbers being divisible by 2, 3, 4, 5, 6, 9, and 10.
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FIBONACC1 N DIVISIBILITY. The explanation of Fibonacci sequence and the diagr...NORAFIZAHMOHDNOORIPG
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Decimal point rules pdf
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This document provides instructions for comparing decimals, multiplying decimals, and dividing decimals. It explains that when comparing decimals, you should line up the decimal points and compare place values from right to left. It also outlines the steps for multiplying decimals, which include ignoring the decimal points, counting total decimal places, and placing the decimal point in the product based on the number of decimal places. For dividing decimals, it describes how to handle situations when the decimal is in the dividend or divisor, such as moving decimal points and placing the decimal point in the quotient above the dividend's decimal point.Formulas Perimeter and Area 10 7,8,10,11
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The document provides formulas for calculating perimeter, area, circumference, and circle area. It defines perimeter as the distance around a shape and area as the surface covered within a perimeter. Formulas are given for calculating the perimeter and area of squares, rectangles, parallelograms, triangles, and circles. The circumference of a circle is defined as the distance around it and can be calculated using C=πd or C=2πr, where π is approximately 3.14.Understanding Integers
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The document discusses different types of numbers:
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2) Integers include whole numbers and their opposites, as well as zero. They can be ordered and compared on a number line.
3) Rules for operating on integers include adding like signs and subtracting unlike signs, as well as products and quotients of the same or different signs being positive or negative.
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This document discusses properties of operations in mathematics including addition and multiplication. It defines the commutative, associative, identity, and zero properties of addition and multiplication. The commutative property states that the order of numbers being added or multiplied does not change the sum or product. The associative property states that the grouping of numbers being added or multiplied does not change the sum or product. The identity properties state that adding or multiplying any number by zero or one, respectively, does not change the number. The zero property of multiplication states that multiplying any number by zero equals zero. Examples are provided to illustrate these properties.2 11 scientific notation
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Scientific notation is a way of writing numbers that are too large or too small in standard form. A number is written as the product of a number between 1 and 10 and a power of 10. For example, 350 written in scientific notation is 3.50 x 102. To convert a number to scientific notation, the decimal point is moved to make the number between 1 and 10, and the power of 10 indicates how many places the decimal was moved. This form is useful in science for large and small measurements like distances between planets.2 10 mult and div by powers of ten
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This document discusses multiplying and dividing by powers of ten. It explains that the exponent tells how many times the base of 10 is multiplied by itself. Positive exponents move the decimal point right when multiplying and left when dividing. Negative exponents move the decimal point in the opposite direction - left when multiplying and right when dividing. Examples are provided to illustrate multiplying and dividing numbers by positive and negative powers of ten.3.2 prime and composite numbers
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A prime number is a whole number greater than 1 that is only divisible by 1 and itself, while a composite number can be divided by other numbers besides 1 or itself. All even numbers greater than 2 and numbers greater than 5 that end in 5 are composite. The prime factorization of a number expresses it as the product of its prime factors by finding all prime numbers that divide into the original number from least to greatest in exponential form.2 5 adding and sub whole num and decimals
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This document provides instructions for adding and subtracting decimals. It emphasizes that decimals should be aligned by their place values when performing calculations by lining up the decimal points. It also recommends annexing zeros to the right of non-zero digits in decimals to maintain alignment and avoid confusion. An example calculation demonstrates these techniques and shows how to check subtraction problems by adding the residue back to the subtrahend.2 6 mult whole num and decimals
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To multiply decimals, count the decimal places in each factor and add them to determine the decimal places in the product. The decimal point is placed in the product by moving left by the total number of decimal places. Adding zeros to the left of the product may be necessary to position the decimal point correctly. The product of two numbers less than one is always less than either factor.1 10 mental math using...
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The document discusses the distributive property of multiplication over addition and subtraction. It explains that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products. It provides examples of using the distributive property to mentally calculate products by breaking numbers apart and distributing the multiplier. Vocabulary terms like distributive property and breaking apart are defined. Steps for using the distributive property with PEMDAS order of operations are outlined. Practice problems are provided to find missing numbers using the distributive property.3 1 factors, multiples and divisibility
- 1. 3-1 FACTORS MULTIPLES AND CHAPTER 3 DIVISIBILITY DIVISIBLE A number is divisible by another if its QUOTIENT is a WHOLE NUMBER and the REMINDER IS ZERO. MULTIPLE A multiple of a number is the PRODUCT of that number and a whole number greater than zero. FACTOR A number that divides another number without a remainder DIVISOR The number used to divide another number.
- 2. EXAMPLE 20 is DIVISIBLE by 4 WHY? Because 20 can be divided by 4 with no remainder (0). 4 is a FACTOR of 20 WHY? Because 20 ÷ 4 = 5 The 4 divides 20 with no remainder 20 is a MULTIPLE of 4 WHY? Because the product of 4 × 5 = 20
- 3. AMULTIPLE of a given number is theproduct of that number and a wholenumber greater than 0. 15 is a multiple of 3. 15 is a multiple of 5. A whole number isDIVISIBLE by another whole number whenthequotient is a whole number and the remainder is 0. 15 isdivisible by 3. 15 is divisible by 5 When a number is divided by any of its factors, or divisors, the remainder is 0. 3 and 5 are factors of 15. 3 and 5 are divisors of 15.
- 4. Divisibility Rules A whole number is divisible by 2 if the ones digit is 0, 2, 4, 6, or 8. 3 if the sum of the digits of the number is divisible by 3. 4 if the last two digits of the number are divisible by 4. 5 if the ones digit is 0 or 5. 6 if the number is divisible by both 2 and 3. 9 if the sum of the digits of the number is divisible by 9. 10 if the ones digit is 0.