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12.1.IP-8 Ignacio is an artist who hand weaves traditional Mexican Saltillo serapes. What fraction of the rows woven on Wednesday were neither yellow nor black? Click the icon to view a figure and explanation of the rows. The fraction of the rows that were neither yellow nor black is \( \square \) . (Type a whole number or a fraction.) More Info \( \frac{4}{15} \) of the rows woven on Wednesday were yellow. \( \frac{1}{3} \) of the rows woven on Wednesday were black. Print Done

Ask by Watkins Watkins. in the United States
Mar 11,2025

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Tutor-Verified Answer

Answer

The fraction of rows that were neither yellow nor black is \( \frac{2}{5} \).

Solution

1. Calculate the total fraction of rows that were yellow or black: \[ \frac{4}{15} + \frac{1}{3} \] 2. Convert \(\frac{1}{3}\) to a fraction with denominator 15: \[ \frac{1}{3} = \frac{5}{15} \] 3. Add the fractions: \[ \frac{4}{15} + \frac{5}{15} = \frac{9}{15} \] 4. Simplify the fraction: \[ \frac{9}{15} = \frac{3}{5} \] 5. Subtract this result from 1 (which represents all the rows) to find the fraction of rows that were neither yellow nor black: \[ 1 - \frac{3}{5} = \frac{2}{5} \] The fraction of the rows woven on Wednesday that were neither yellow nor black is \( \frac{2}{5} \).

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The Deep Dive

To find the fraction of the rows that were neither yellow nor black, we first need to determine the total fraction that was either yellow or black. Given that \( \frac{4}{15} \) of the rows were yellow and \( \frac{1}{3} \) were black, let's convert \( \frac{1}{3} \) into a fraction with a denominator of 15 for easy addition: \[ \frac{1}{3} = \frac{5}{15} \] Now, we can add the fractions together: \[ \frac{4}{15} + \frac{5}{15} = \frac{9}{15} \] To find the fraction that was neither yellow nor black, we subtract the total fraction of yellow and black from 1 (considering 1 as the whole): \[ 1 - \frac{9}{15} = \frac{15}{15} - \frac{9}{15} = \frac{6}{15} \] This fraction can be simplified to: \[ \frac{6}{15} = \frac{2}{5} \] Therefore, the fraction of the rows woven on Wednesday that were neither yellow nor black is \( \frac{2}{5} \).

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