Problem 88 - Introductory Algebra for College Students

Question

Find the value of each expression. $$\frac{9}{10}-\left(\frac{1}{4}-\frac{7}{10}\right)$$

Step-by-Step Solution

Answer

The value of the expression is 1.

Step 1: Resolve the Inner Parentheses

Start by resolving the expression inside the parentheses first due to the BIDMAS rule (Brackets, Indices, Division, Multiplication, Addition, Subtraction). Thus perform the subtraction: \( \frac{1}{4} - \frac{7}{10} = \frac{10 - 14}{40} = -\frac{1}{10} \).

Step 2: Subtract the Result from \(\frac{9}{10}\)

Now, subtract the value obtained in step 1 (-1/10) from \(\frac{9}{10}\). The fraction \(\frac{9}{10}\) minus -\(\frac{1}{10}\) is the same as \(\frac{9}{10}\) + \(\frac{1}{10}\). Therefore, \( \frac{9}{10} + \frac{1}{10} = \frac{10}{10}\).

Step 3: Simplify the Fraction

The fraction \(\frac{10}{10}\) can be simplified to 1 because the numerator and denominator are equal.