Which choice shows the correct way to write 1624\frac{16}{24} in lowest terms?A. 1624=8+88+16=816=12A.\text{ }\frac{16}{24}=\frac{8+8}{8+16}=\frac{8}{16}=\frac12B. 1624=4⋅44⋅6=46B.\text{ }\frac{16}{24}=\frac{4\cdot4}{4\cdot6}=\frac46C. 1624=8⋅28⋅3=23C.\text{ }\frac{16}{24}=\frac{8\cdot2}{8\cdot3}=\frac{2}{3}

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 5

Chapter 1, Problem 5

Which choice shows the correct way to write $16 over 24$ in lowest terms?
$A . \frac{16}{24} = \frac{8 + 8}{8 + 16} = \frac{8}{16} = \frac{1}{2}$
$B . \frac{16}{24} = \frac{4 \cdot 4}{4 \cdot 6} = \frac{4}{6}$
$C . \frac{16}{24} = \frac{8 \cdot 2}{8 \cdot 3} = \frac{2}{3}$

Verified step by step guidance

To write a fraction in lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator.

Identify the numerator and denominator: numerator = 16, denominator = 24.

Find the GCD of 16 and 24. The factors of 16 are 1, 2, 4, 8, 16; the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest common factor is 8.

Divide both the numerator and denominator by the GCD (8): $\frac{16}{24} = \frac{16 \div 8}{24 \div 8} = \frac{2}{3}$.

Compare this simplified fraction to the choices given to determine which one correctly shows the fraction in 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:

Was this helpful?

Key Concepts

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

Simplifying Fractions

Simplifying fractions involves reducing the numerator and denominator to their smallest whole numbers while keeping the same value. This is done by dividing both by their greatest common divisor (GCD). For example, 16/24 can be simplified by dividing both by 8, resulting in 2/3.

Greatest Common Divisor (GCD)

The GCD of two numbers is the largest number that divides both without leaving a remainder. Finding the GCD is essential for simplifying fractions correctly. For 16 and 24, the GCD is 8, which helps reduce 16/24 to 2/3.

Correct Fraction Reduction Steps

Proper fraction reduction requires factoring numerator and denominator, identifying the GCD, and dividing both by it. Incorrect steps, like adding terms or dividing by a non-common factor, lead to wrong simplifications. The correct method ensures the fraction remains equivalent but in lowest terms.

Recommended video:

Guided course

05:45

Radical Expressions with Fractions

Related Practice

Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. -3x^-1/3

views

Textbook Question

Determine whether each statement is true or false. If false, correct the right side of the equation. (2/3)^-2 = (3/2)²

views

Textbook Question

Perform the indicated operation, and write each answer in lowest terms. 2x/5 ∙ 10/x²

views

Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. 3x^-1/3

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. In the expression 6³, 6 is the ____ , and 3 is the ____ .

views

Textbook Question

Identify the set { 1,1/3, 1/9 ,1/27, ....} as finite or infinite.

views