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: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 5

1장, 문제 5

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

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.