NAME ____________________________________________ DATE _____________________________ PERIOD _____________
11-7 Study Guide and Intervention
Mixed Expressions and Complex Fractions
!
! ! !
Simplify Mixed Expressions Algebraic expressions such as a + ! and 5 + ! ! ! are called mixed expressions.
Changing mixed expressions to rational expressions is similar to changing mixed numbers to improper fractions.
𝟐
𝟑
Example 1: Simplify 5 + 𝒏.
5+
!
!
! ⋅ !
=
!
+
!
!
! ! !
!
!
=
!! ! !
!
=
=
Add the numerators.
!
Therefore, 5 +
2+
LCD is n.
!
!! ! !
=
Example 2: Simplify 2 + 𝒏 ! 𝟑.
.
=
=
!(! ! !)
! ! ! !! ! !
! ! !
+
+
!
!!!
!
! ! !
!! ! ! ! !
! ! !
!! ! !
! ! !
Therefore, 2 +
!
! ! !
=
!! ! !
! ! !
.
Exercises
Write each mixed expression as a rational expression.
1. 4 +
! 3. 3x –
5. 10 +
7.
!
! – !
2.
!
!
! ! !"
! ! !
+ 𝑦!
Chapter 11
4.
6.
!
!!
!
!!
–3
–2
!
! ! !
8. 4 –
43
+2
! !! ! !
Glencoe Algebra 1
NAME ____________________________________________ DATE _____________________________ PERIOD _____________
11-7 Study Guide and Intervention (continued)
Mixed Expressions and Complex Fractions
Simplify Complex Fractions If a fraction has one or more fractions in the numerator or denominator, it is called a
complex fraction.
Simplifying a
Complex Fraction
Example: Simplify
!
!
!!!
!
!!
!! !"
! !! !!
!(! ! !)
!"
=
=
=
=
!"!!"
!(!!!)
!(! ! !)
!(!!!)
!
!
Any complex fraction
𝟒
𝒂
𝒂 ! 𝟐
𝟑
𝟐!
!
!
!
!
where b ≠ 0, c ≠ 0, and d ≠ 0, can be expressed as
!"
!"
.
.
Find the LCD for the numerator and denominator and rewrite.
Cancel the like denominators.
Factor.
Divide and simplify.
Exercises
Simplify each expression.
1.
4.
!
!
!
! ! !
! ! 2.
!
!
!
! ! !
!
! ! !! ! !"
!
! ! ! !! ! Chapter 11
44
3.
!
! – !
!
!! ! !
5.
!
!
! ! ! ! ! – !
!
!
! ! ! ! ! ! !
Glencoe Algebra 1