Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 75
Chapter 1, Problem 75

Add or subtract as indicated. Write answers in lowest terms as needed. 829−4238\(\frac{2}{9}\) - 4\(\frac{2}{3}\)

Verified step by step guidance
1
First, rewrite the expression clearly: \(8 \left( \frac{2}{9} \right) - 4 \left( \frac{2}{3} \right)\).
Multiply the whole numbers by the fractions separately: calculate \(8 \times \frac{2}{9}\) and \(4 \times \frac{2}{3}\).
For each multiplication, multiply the numerator by the whole number and keep the denominator the same: \(\frac{8 \times 2}{9}\) and \(\frac{4 \times 2}{3}\).
Simplify each fraction if possible by dividing numerator and denominator by their greatest common divisor (GCD).
Subtract the second fraction from the first by finding a common denominator, rewriting both fractions with this denominator, then subtracting the numerators. Finally, simplify the resulting fraction to lowest terms.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiplication of Whole Numbers and Fractions

Multiplying a whole number by a fraction involves multiplying the whole number by the numerator of the fraction and then dividing by the denominator. For example, 8 × (2/9) means 8 times 2 divided by 9, which simplifies the expression before further operations.
Recommended video:
05:02
Multiplying Complex Numbers

Subtraction of Fractions

To subtract fractions, they must have a common denominator. If denominators differ, find the least common denominator (LCD), convert each fraction, then subtract the numerators while keeping the denominator the same.
Recommended video:
Guided course
05:45
Radical Expressions with Fractions

Simplifying Fractions to Lowest Terms

After performing operations, fractions should be simplified by dividing numerator and denominator by their greatest common divisor (GCD). This ensures the answer is expressed in simplest form, making it easier to interpret and compare.
Recommended video:
Guided course
05:45
Radical Expressions with Fractions
Related Practice
Textbook Question

Factor each polynomial. See Examples 5 and 6. 125x3-27

Textbook Question

Determine whether each statement is true or false. {3, 5, 9, 10} ∩ ∅ = {3, 5, 9, 10}

Textbook Question

Find each product. Assume all variables represent positive real numbers. (x+x1/2)(x-x1/2)

1
views
Textbook Question

Simplify each radical. Assume all variables represent positive real numbers. - ∜243

1
views
Textbook Question

Simplify each complex fraction. [ 1 + 1/(1-b) ] / [ 1 - 1/(1+b) ]

2
views
Textbook Question

Determine whether each statement is true or false. {3, 5, 9, 10} ∪ ∅ = {3, 5, 9, 10}

1
views