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Choose the equation that best matches the illustration.

Choose the equation that best matches the illustration.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Choose the equation that best matches the illustration.** Below are three illustrations labeled a, b, and c. Each one is paired with a mathematical equation. a. \( \dfrac{1}{2} \div \dfrac{1}{4} = 2 \) This illustration shows a square divided into two equal parts, and one of these parts is further divided into half. Each half of the original part is now a quarter of the whole square. The shaded region, which represents \(\dfrac{1}{2}\), is divided by the quarter section, resulting in a total of 2 parts, which matches the equation. b. \( 3 \div \dfrac{3}{4} = 4 \) This illustration displays three columns of equal width, with each column divided into four equal horizontal sections. Three of the columns are entirely filled (shaded) and the last column is partially filled at three-quarters. When dividing 3 whole columns by \(\dfrac{3}{4}\) column widths, the result is 4, as you can fit four \(\dfrac{3}{4}\)-width sections into these three columns plus one more quarter-width from an additional column. c. \( 3 \div \dfrac{2}{3} =4 1/2 \) \( \) In this illustration, three columns of equal width are divided into thirds horizontally. Each column is fully filled except for one unshaded third in the last section of the last column. This visually represents what happens when you divide 3 whole columns by \(\dfrac{2}{3}\) column widths. The outcome, 4 1/2, indicates how many full \(\dfrac{2}{3}\) sections can fit into three filled columns plus an additional half section. Explanation of the Diagrams: - Each diagram visually represents dividing a number (whether whole or fractional) by another fractional number. - The shaded and unshaded parts illustrate how the division yields an integer or mixed number as a result.
Transcribed Image Text:**Choose the equation that best matches the illustration.** Below are three illustrations labeled a, b, and c. Each one is paired with a mathematical equation. a. \( \dfrac{1}{2} \div \dfrac{1}{4} = 2 \) This illustration shows a square divided into two equal parts, and one of these parts is further divided into half. Each half of the original part is now a quarter of the whole square. The shaded region, which represents \(\dfrac{1}{2}\), is divided by the quarter section, resulting in a total of 2 parts, which matches the equation. b. \( 3 \div \dfrac{3}{4} = 4 \) This illustration displays three columns of equal width, with each column divided into four equal horizontal sections. Three of the columns are entirely filled (shaded) and the last column is partially filled at three-quarters. When dividing 3 whole columns by \(\dfrac{3}{4}\) column widths, the result is 4, as you can fit four \(\dfrac{3}{4}\)-width sections into these three columns plus one more quarter-width from an additional column. c. \( 3 \div \dfrac{2}{3} =4 1/2 \) \( \) In this illustration, three columns of equal width are divided into thirds horizontally. Each column is fully filled except for one unshaded third in the last section of the last column. This visually represents what happens when you divide 3 whole columns by \(\dfrac{2}{3}\) column widths. The outcome, 4 1/2, indicates how many full \(\dfrac{2}{3}\) sections can fit into three filled columns plus an additional half section. Explanation of the Diagrams: - Each diagram visually represents dividing a number (whether whole or fractional) by another fractional number. - The shaded and unshaded parts illustrate how the division yields an integer or mixed number as a result.
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