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26 Cards in this Set
- Front
- Back
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Natural Numbers
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The set of natural numbers consists of the numbers used for counting 1, 2, 3, 4, ...
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Whole Numbers
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The set of whole numbers is 0, 1, 2, 3, 4, .....
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Proper Fraction
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When the numerator is less than the denominator
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Improper fraction
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When the numerator is greater than or equaled to the denominator
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Factor
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The factor of a given number is any number that divides evenly ( without remainder) into a given number
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Product
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Is the answer to a multiplication problem
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To factor a number
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Is to write a number (composite number) as a product of of its prime numbers.
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Prime number
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A natural number (except 1) is prime if it has only 1 and itself as factors
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Composite number
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A natural number greater than 1 that is not prime. A composite number has at least one factor other than itself and 1.
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A fraction is in lowest tems
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When the numerator and denominator have no factors in common ( other than 1)
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How do you reduce fractions to lowest terms
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Use the Basic Principle of Fractions
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The Basic Principal of Fractions
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If the numerator and denominator of a fraction are multiplied or divided by the same non-zero number, the value of the fraction is not changed.
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Writing a fraction in lowest terms
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Step 1 Write the numerator and the denominator as a product of prime factors.
Step 2 Divide the numerator and the denominator by the Greatest Common Factor (GCF), the product of all factor common to both. |
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To check your calculations when simplifying fractions to lowest terms
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a/b = c/d , if a x d = b x c
eg. 4/6 = 2/3 , because 4 x 3 = 2 x 6 |
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Multiplying fractions
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If a/b and c/d are fractions, then a/b x c/d = a x c/ b x d
That is, to multiply two fractions, multiply their numerators and then multiply their denominators. |
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Multiplying Mixed Numbers
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Step 1 Switch to improper fraction
Step 2 Simplify and multiply. Step 3 If improper in the end, switch back to mixed number |
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What is the relationship between multiplication and division
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Division is the opposite ( or inverse of multiplication, you use reciprocals to divide fractions.
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Reciprocal
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Pairs of numbers whose product is 1 are called reciprocals of each other. Two fractions are reciprocals of each other if their product is 1.
eg. 3/4 x 4/3 = 12/12 = 1 |
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Quotient
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The answer to a division problem
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Dividing Fractions
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If a/b and c/d are fractions, then a/b ÷ c/d = a/b = d/c
That is, to divide by a fraction, multiply by its reciprocal |
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Adding fractions with the same denominator
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1. add numerators
2. keep same denominator 3. write in lowest terms |
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Least Common Denominator (LCD)
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Given several denominators, the smallest expression that is divisible by all the denominators
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Finding the Least common Denominator (LCD)
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To add or subtract fractions with different denominators , find the LCD:
1. Factor each denominator 2. For the LCD, use every factor that appears in factored form. If the factor is repeated, use the largest number of repeats in the LCD |
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How to calculate the LCD when adding or subtracting fractions and the denominators have no common factors
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Multiply both denom's to get the LCD
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How to calculate the LCD, for all cases, when adding or subtracting fractions and the denominators have at least one common factor
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1. If all the smaller denom's are factors of the largest, then the largest denom is the LCD
2. If all the smaller factors are not factors of the larger denom, then, -Factor all denom's using exponents for repeating factors. -List all factors once -List factors with the highest exponent -Multiply factors |
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How to calculate the LCD, when the factors are small, when adding or subtracting fractions and the denominators have at least one common factor
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1. Take the largest denom, find a
multiple of it. 2. If the smaller denom is a factor of the multiple, then, you have found the LCD. |
