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.
Placement of negative sign in a fraction.
For any positive numbers “a” and “b”, “(-a) / (b)” = “(a) / (-b)” = -“(a) / (b)”.
Simplify an expression with a fraction bar
Step 1. Simplify the numerator. Step 2. simplify the donominator. Step 3. Simplify the fraction.
Fraction Addition
To add fractions, add the numerators and place the sum over the common denominator. If a,b,c are numbers where “c does not equal 0”, then “a/c” + “b/c” = “(a+b)”/”c”.
Fraction Subtraction
If a,b, and c are numbers where “c does not equal 0”, then “(a/c)” - “(b/c)” =”( a-b)”/c.
Find the Least Common Denominator (LCD) of two fractions.
Step 1. Factor each denominator into its primes. Step 2. List the primes, matching primes in columns when possible. Step 3. Bring down the columns. Step 4. Multiply the factors, The product if the LCM of the donominators. Step 5. The LCM of the denominators is the LDC of the fractions.
Convert two fractions to equivalent fractions with their LCD as the common denominator.
Step 1. Find the LCD. Step 2. For each fraction, determine the number needed to multiply the denominator to get the LCD. Step 3. Use the Equivalent Fractions Property to multiply the numerator and denominator by the number from Step 2. Step 4. Simplify the numerator and denominator.
Add or subtract fraction with different denominators.
Step 1. Find the LCD. Step 2. Convert ech fraction to an equivalent form with the LCD as the denominator. Step 3. Add or subtract the fractions. Step 4. Write the result in simplified form.
