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Math Basics: Numeration and Vocabulary

Learn about prime factorization, proportions, fractions, and more in this guide to numerical systems and math terminology.

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Math Basics: Numeration and Vocabulary

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  1. Numeration Vocabulary Ms. Hornbuckle

  2. Base Systems • Our System is the decimal or base 10 system for numbers. • Time is measured in Base 60 (60 minutes in one hour) and is from • the ancient Babaloynians. • There are many types of base systems • Mayan:

  3. Common Denominator • A number into which the denominators divide equally • The common denominator of 1/3 and 1/4 is 12 because 3 and 4 divide equally into 12

  4. Commutative Property of Multiplication • The property states that it doesn’t matter which order you multiply the numbers, the answer is still the same • 4*9=9*4

  5. Convert • Means to change the form, but not the value • ½ = .5 = 50% • 1 inch = 2.54cm • Hello = Hola

  6. Decimal • A part of a number (based on the base 10 system) • Ex. 3.4

  7. Distributive Property • Multiply each term in a set of parentheses by the term outside • 3(x+4) = 3x +12 • Animation Link

  8. Exponential Form • Writing a number with a whole number and an exponent • Exponential Form: 43 • Not Exponential Form: 4*4*4

  9. Exponents • A smaller number placed to the upper-right of a number that shows the number of times the base number is multiplied times itself. • 34 = 3*3*3*3

  10. Factor • A whole number that divides EXACTLY into a number • Example: 1, 2, 3, 4, 6, and 12 are factors of 12.

  11. Greatest Common Factor • The largest numbers that will divide into two are more numbers evenly • Example: The GCF of 9 and 12 is 3

  12. Identity of One • Also known as the identity property of multiplication • When a number is multiplied by one the result is the number itself • 12 * 1 = 12

  13. Identity of Zero • Also known as the identity property of addition. • When zero is added to any number the result is the number itself. • 12 + 0=12

  14. Identity Property of Multiplication • See Identity Property of One • 12 * 1 = 12

  15. Improper Fraction • A fraction that is larger than one • The numerator is larger than the denominator • 12/4

  16. Inequality • Not equal in Size, Amount or Value • Represented by >, <, <, > • 5<7 and 7>3

  17. Integer • Any positive or negative number including zero. • Examples -45, 23, 0, 15, -23

  18. Inverse Operations • Two operations that have the opposite effect. • Addition and Subtraction • Multiplication and Division

  19. Least Common Multiple • The smallest number that is the multiple of 2 or more numbers. • The LCM of 3, 4, and 6 is 12 • 3, 6, 9, 12, 15 • 4, 8, 12, 16 • 6, 12, 18

  20. Mixed Number • Number written as a whole number with a fraction. It is larger than one. • 3 ½ • 4 ¼

  21. Model • To show something visually. Model in math usually includes drawing/pictures.

  22. Multiples • To find a multiple of a number at the number to itself. This can be repeated to find many multiples • 3, 6, 9, 12, 15 • 2, 4, 6, 8, 10 • 11, 22, 33, 44, 55

  23. Order • To place from least to greatest or greatest to least.

  24. Percent • A number out of 100 • 60% is 60 out of 100 • 27% is 27 out of 100

  25. Place Value • The value of a digit based on where it is placed in a number

  26. Powers of Ten • This means 10 raised to any positive (usually) integer. • 103 104 10105

  27. Prime Factorization • Write a number as the product of it’s prime factors • 2*2*2*7 or 23*7

  28. Proportion • A proportion has a constant (equal) ratio. • Usually seen as two ratios with an equal sign in the middle • ½ = 2/4

  29. Ratio • Comparative value of two or more amounts as compared to the total. • Example-> The ratio of boys to girls in a group of 10 is Boys:Girls • 6:4

  30. Rational Numbers • Is a repeating decimal, terminating decimal or an integer. • Examples • 3.4 • 3.75 • 5 • 4.223223223

  31. Real Number System • The real number system includes fractions, whole numbers, and rational numbers. All real numbers can be placed on a number line.

  32. Scientific Notation • A way of writing very large or very small numbers using a number between 1 and 10 and multiplied by a power of 10 • Example 1.56 * 102 = 156

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