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 76
Chapter 1, Problem 76

Add or subtract as indicated. Write answers in lowest terms as needed. 7512−4567\(\frac{5}{12}\) - 4\(\frac{5}{6}\)

Verified step by step guidance
1
First, rewrite the expression clearly: \(7 \left( \frac{5}{12} \right) - 4 \left( \frac{5}{6} \right)\).
Multiply the whole numbers by the fractions separately: calculate \(7 \times \frac{5}{12}\) and \(4 \times \frac{5}{6}\).
Express each product as a single fraction: \(\frac{7 \times 5}{12}\) and \(\frac{4 \times 5}{6}\), which simplifies to \(\frac{35}{12}\) and \(\frac{20}{6}\) respectively.
Find a common denominator to subtract the fractions \(\frac{35}{12} - \frac{20}{6}\). Since 12 is a multiple of 6, convert \(\frac{20}{6}\) to an equivalent fraction with denominator 12.
Subtract the numerators over the common denominator and simplify the resulting fraction to its 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 while keeping the denominator the same. For example, 7 × (5/12) means 7 times 5 divided by 12, which can be calculated as (7 × 5)/12.
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 constant.
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 reduces the fraction to its simplest form, making the answer clearer and more standard.
Recommended video:
Guided course
05:45
Radical Expressions with Fractions
Related Practice
Textbook Question

Simplify each complex fraction. [ 2 + 2/(1+x) ] / [ 2 - 2/(1-x) ]

6
views
Textbook Question

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

1
views
Textbook Question

Determine whether each statement is true or false. {1, 2, 4} ∪ {1, 2, 4} = {1, 2, 4}

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
Textbook Question

Find each product or quotient where possible. 1213−43\(\frac{\frac{12}{13}\)}{-\(\frac\)43}