Algebraic Expressions with Fraction Bars

When solving an algebraic expressions that include fraction bars, it is important to consider these bars as grouping symbols, similar to parentheses. Some key points to use while solving algebraic expressions with fraction bars are:

Invisible Parentheses

Both the numerator and the denominator of a fraction can be considered to have invisible parentheses around them. Suppose, in an algebraic expression [Tex]\frac{3 + 3}{4 \times 1}[/Tex] there is no visible parentheses. Hence, while solving the fraction, first all operations of the numerator and the denominator should be solved separately.

Like in the fraction given above,

numerator = 3 +3 = 6

denominator = 4 × 1 = 4

The new fraction becomes 6/4

Now, as the invisible parentheses of numberator and denominator are solved, we can solve the new fraction as a whole,

6/4 = 3/2

Order of Operations- PEMDAS

PEMDAS expands to parentheses, exponents, multiplication, division, addition and subtraction. Order of operations means, solving the algebraic expression using PEMDAS rule starting with operation P for parentheses then E, M, D, A, and S.

Suppose in an algebraic equation 3+4×2-5, we have to use PEMDAS rule.

• P (parentheses): The expression has no parentheses.
• E (exponents): The expression has no exponents.
• M (multiplication): The expression has 4×2, therefore on solving this first we get 8. and the new expression becomes 3+8-5.
• D (division): the expression has no division sign.
• A (addition): The expression has 3+8, therefor on solving this operation we get, 11 and the new expression becomes 11-5
• S (subtraction): The last of PEMDAS is subtraction. Hence, 11-5 = 6.

This is how PEMDAS is used to solve an algebraic expressions.

NOTE: If, in an algebraic expression there are more than one brackets or parentheses, then solve the innermost parentheses first.

Parentheses in Numerator or Denominator

If there are actual parentheses within the numerator or denominator, those operations take precedence over the fraction bar. Solve everything inside these parentheses before addressing the fraction.

Parentheses Outside the Fraction

If there are parentheses outside of the fraction, the fraction bar itself takes precedence over the operations inside these outer parentheses.

Example of Algebraic Expressions with Fraction Bars

Example: Given: [Tex]\frac{(3 + 2) \times 4}{(1 + 1) \times 2}[/Tex]

Solution:

First we will simplify the parentheses of numerator and denominator.

[Tex]\frac{5 \times 4}{2 \times 2}[/Tex]

Now perform the operations in numerator and denominator

Numerator= 5 × 4 = 20

Denominator = 2 × 2 = 4

Now on simplifying the fraction, we get:

20/4 = 5

Fraction bars are visual and hands-on tools used to teach and understand fractions. They provide a simple way to see the size of different fractions and how they relate to each other. These are especially helpful in elementary and middle school education for introducing and reinforcing concepts of fractions.

In this article, we will understand fraction bars and solve some questions with fraction bars.