Chapter 4.1 - 4.5 Flashcards
complex fraction
A complex fraction is a fraction in which the numerator or the denominator contains a fraction.
equivalent fractions
Equivalent fractions are two or more fractions that have the same value.
fraction
A fraction is written. In a fraction,is the numerator andis the denominator. A fraction represents parts of a whole. The denominatoris the number of equal parts the whole has been divided into, and the numerator indicates how many parts are included.
least common denominator (LCD)
The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.
mixed number
A mixed number consists of a whole numberand a fractionwhere. It is written as, where c does not equal zero.
proper and improper fractions
The fraction “a/b” is proper if “a is less than b” and improper if “a is greater than b”.
reciprocal
lThe reciprocal of the fraction “a/b” is “b/a” where “a is less than 0” and “b is less than zero”.
simplified fraction
A fraction is considered simplified if there are no common factors in the numerator and denominator.
Property of One
Any number, except zero, divided by itself is one. a/a = 1, where a does not equal 0.
mixed number
A mixed number consists of a whole number “a” and a fraction “ b/c”, where c does not equal 0. It is written as follows: “a b/c”, where c does not equal 0.
Proper and Improper Fractions
The fraction “a/b” is a proper fraction if “a is less than b”, and an improper fraction is “a is greater than or equal to b”.
Convert an improper fraction to a mixed number.
Step 1. Divide the denominator into the numerator. Step 2. identify the quotient, remainder, and divisor., Step 3. Write the mixed number as “quotient + remainder/divisor”.
Convert a mixed number to an improper fraction
Step 1. Multiply the whole number by the denominator. Step 2. Add the numerator to the product found in Step 1. Step 3. Write the final sum over the original denominator.
Equivalent Fractions Property
If a, b, and c are numbers where “b does not equal 0”, “c does not equal 0”, then “a/b = (a x c)/(b x c)”.
Equivalent Fractions Property
If a, b, c are numbers where “b does not equal 0”, “c does not equal 0”, then “(a/b) = (a x c)/(b x c)” and “(a x c)/(b x c) = a/b”.
Simplify a fraction.
Step 1. Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers. Step 2. simplify, using the equivalent fractions property, by removing common factors. Multiply any remaining factors.
Fraction Multplication
If a,b,c and d are numbers where “b does not equal 0” and “d does not equal 0”, then “(a/b) x (c/d)” = “(ac/bd)”.
reciprocal
A number and its reciprocal have a product of 1. “a/b” x “b/a” = 1.
Opposite
Has opposite sign.
Absolute Value
Is never negative.
reciprocal
Has same sign, fraction inverts.
Fraction Division
To divide fractions, multiply the first fraction by the reciprocal of the second. If a,b,c and d are numbers where “b does not equal 0”, “c does not equal 0” and “d does not equal 0”, then “(a/b)” / “(c/d)” = “(a/b)” x “(d/c)”.
Multiply or Divide Mixed Numbers
Step 1. Convert the mixed numbers to improper fractions. Step 2. Follow the rules for fraction multiplication or division. Step 3. Simplify if possible.
Simplify a Complex Fraction
Step 1. Rewrite the complex fraction as a division problem. Step 2. Follow the rules for dividing fractions. Step 3. simplify if possible.