A recipe for pie crust calls for 2\/3 cup of water for every 3 cups of flour. If you doubled the recipe, you would need 1 and 1\/3 cups of water for 6 cups of flour. Which proportions involving complex fractions could represent these ratios?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To find the proportion involving complex fractions<\/strong> that represents the given ratios, let\u2019s analyze the information step-by-step.<\/p>\n\n\n\n These are complex fractions<\/strong> because the numerator is a fraction and the denominator is a whole number.<\/p>\n\n\n\n Let\u2019s simplify both complex fractions:<\/p>\n\n\n\n 233=23\u00f73=23\u00d713=29\\frac{\\frac{2}{3}}{3} = \\frac{2}{3} \\div 3 = \\frac{2}{3} \\times \\frac{1}{3} = \\frac{2}{9}<\/p>\n\n\n\n 436=43\u00f76=43\u00d716=418=29\\frac{\\frac{4}{3}}{6} = \\frac{4}{3} \\div 6 = \\frac{4}{3} \\times \\frac{1}{6} = \\frac{4}{18} = \\frac{2}{9}<\/p>\n\n\n\n Since both simplify to 29\\frac{2}{9}<\/strong>, the proportions are equivalent<\/strong>, which means the complex fractions: 233=436\\frac{\\frac{2}{3}}{3} = \\frac{\\frac{4}{3}}{6}<\/p>\n\n\n\n are a valid representation of the ratio of water to flour in the original and doubled recipe.<\/p>\n\n\n\n 233=436\\frac{\\frac{2}{3}}{3} = \\frac{\\frac{4}{3}}{6}<\/p>\n\n\n\n This type of proportion is called a complex fraction<\/strong> because a fraction is divided by a whole number. These proportions are useful when comparing unit rates or scaling recipes.<\/p>\n\n\n\n In this example, the ratio of water to flour remains constant, meaning the recipe scales correctly. So, using complex fractions like: waterflour=233\\frac{\\text{water}}{\\text{flour}} = \\frac{\\frac{2}{3}}{3}<\/p>\n\n\n\n and 436\\frac{\\frac{4}{3}}{6}<\/p>\n\n\n\n ensures that the proportion is preserved whether you are using the original or doubled recipe.<\/p>\n","protected":false},"excerpt":{"rendered":" A recipe for pie crust calls for 2\/3 cup of water for every 3 cups of flour. If you doubled the recipe, you would need 1 and 1\/3 cups of water for 6 cups of flour. Which proportions involving complex fractions could represent these ratios? The correct answer and explanation is: To find the proportion […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26765","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26765"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26765\/revisions"}],"predecessor-version":[{"id":26766,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26765\/revisions\/26766"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nGiven Ratios:<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nStep 1: Write both as ratios (fractions):<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nStep 2: Determine whether they are equivalent:<\/strong><\/h3>\n\n\n\n
Simplify Original:<\/h4>\n\n\n\n
Simplify Doubled:<\/h4>\n\n\n\n
\n\n\n\n\u2705 Correct Answer:<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation:<\/strong><\/h3>\n\n\n\n