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Unit 1 Study Guide Vocabulary Words (Quizzes will include vocabulary words) Array- a rectangular arrangement that has an equal number of objects in each row and an equal number of objects in each column. (P. 4) *An array for the #15 can be shown as 3 x 5. There are 3 rows with 5 objects in each row. The array can also be made as 5 x 3. There are 5 rows with 3 objects in each row. Factor pairs- two natural numbers other than zero that are multiplied together to produce another number. (P. 5) List all the factor pairs of 21 __21_ 1 x 21 3x7 Factors- two numbers that when multiplied together equal another number. (P. 5) The #21 has 4 factors 1, 3, 7, 21 CF (Common Factors) 15 and 30: Write out all the factors of 15 and 30. 15______ 1 x 15 3x5 __30__ 1 x 30 2 x 15 3 x 10 5x6 The CF of 15 and 30 are 1,3,5,15 Distinct factors- factors that appear only once in a list. (P. 6) We said the #30 has 8 distinct factors. Each factor is ONLY used once. The #9 has 3 distinct factors. 1,3, 9 The #9 is a square number so we only count 3 one time. ___9__ 1x9 3x3 Commutative Property of Multiplication states that changing the order of two or more factors does not change the product. (P. 5) For any numbers a and b, a x b= b x a 4x7=7x4 Set- a collection of numbers, geometric figures, letters, or other objects that have some characteristic in common. (P. 26) Perfect square- a number multiplied by itself forms a square. (P. 8) (5th grade AKA Square numbers) Example 5 x 5 Multiples- the product of a given whole number and another whole number. (P. 13) The multiples of the #8 is 8, 16, 24, 32, 40, 48 and so on 8x1 8x2 8x3 8x4 8x5 8x6 Venn diagram- a picture that illustrates the relationships between two or more sets. (P. 26) Prime and Composite *0 and 1 are neither prime nor composite. *2, 3, 5, 7, 11, 13, 17, 19 are prime because they have only two factors. The only way to get to the produce by multiplying is 1 times the number. (Example: 19: only way to get to it is 1 X 19). *4 is composite because it has more than 2 factors. You can multiply 1x4 and 2x2. 4 has 3 factors (1, 2, and 4). Prime- a number that has only 2 factors. (P. 32) __7__ 1x7 The #7 has only 2 factors 1 and 7 Composite- a number that has more than two factors. (P. 32) __14__ 1x14 2x7 The #14 has 4 factors 1,2,7,14 Multiplicative Identity- a number that when multiplied by a second number, the product is the second number. Example: 1 x 8 = 8 Divisible- one number is divisible by the second number when the second number divides “evenly” into the first number with no remainder. (P. 14) Divisibility Rules: (P 36-39) Numbers 2 3 5 6 9 10 Rule Digit in the ones column must be a 0, 2, 4, 6, 8 Add the digits together. If the sum is a multiple of 3, the number can be divided by 3. Digit in the ones column must be a 0 or 5 MUST be divisible by both 2 and 3 Add the digits together. If the sum is a multiple of 9, the number can be divided by 9. Digit in the ones column must be a 0 *In fourth grade, students learned about divisibility rules of 2, 5, and 10. These rules apply to the digit in the ONES column. *In fifth grade, students learned about divisibility rules of 3, 6, and 9. The rules of 3 and 9 are very similar. Students need to add the sum of the digits together to determine divisibility. To determine the rule of 6, both 2 and 3 must be divisible by the number.