Final answer:
In Tamar's algebraic method to convert the repeating decimal 2.45 to a fraction, after multiplying the decimal by 100, she should subtract the original number from this result to obtain an equation without the repeating decimal, and then solve for 'x' to find the fractional equivalent.
Step-by-step explanation:
Tamar's goal is to convert the repeating decimal 2.45 into a fraction. After establishing that x = 2.45 in Step 1 and computing 100x = 245.45
in Step 2, her next step would be to set up an equation that will allow her to isolate the repeating part.
In Step 3, Tamar should subtract the original number (x) from the result of Step 2, i.e., 100x - x. This subtraction eliminates the repeating decimal portion and gives an equation with integers on both sides: 99x = 243, which can be solved for x.
To find the fraction form of 2.45, Tamar will divide both sides by 99, yielding x = 243/99. Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor will give Tamar the fractional representation of the original decimal.