"$$p = \\frac{7}{3}q$","points":2},{"id":"f9dba4e0-151f-4d49-acc2-96de654e740e","cardType":"cloze","front":"If $A:B=5:2$, it is a common mistake to write $A = \\frac{2}{5}B$; the correct linear relationship is $\\text{[...]}$.","back":"If $A:B=5:2$, it is a common mistake to write $A = \\frac{2}{5}B$; the correct linear relationship is $\\boxed{A = \\frac{5}{2}B}$.","points":null},{"id":"a25ee46d-a11b-4c86-9e41-39494eda572b","cardType":"basic","front":"When combining $a:b=2:5$ and $b:c=3:4$, what is the first step?","back":"Find the lowest common multiple (LCM) of the shared quantity $b$.","points":1},{"id":"5b2e6b22-5df5-4de5-8e10-28f3bd6f08a5","cardType":"basic","front":"If $a:b=2:5$ and $b:c=3:4$, what value should the $b$ parts be scaled to?","back":"15 (the LCM of 5 and 3).","points":1},{"id":"b3713b45-b457-4990-8aee-b2e928478f05","cardType":"cloze","front":"The combined ratio of $a:b=2:5$ and $b:c=3:4$ is $a:b:c = $ [ ].","back":"The combined ratio of $a:b=2:5$ and $b:c=3:4$ is $a:b:c = $ 6:15:20.","points":null},{"id":"03d3e8a5-b5db-42fd-9140-01bd953d4ca0","cardType":"basic","front":"What is a common multiplier ($k$) used for in ratio problems?","back":"To convert ratio parts into real/actual amounts.","points":1},{"id":"33fea08e-e914-4c82-ba99-b89fd1731e03","cardType":"basic","front":"If $D:E:F = 15:6:20$ and Finn ($F$) has 14 more counters than Dylan ($D$), how many parts represent 14 counters?","back":"5 parts (since $20 - 15 = 5$).","points":2},{"id":"1c9420e3-2b17-4463-a794-107c7d8053ed","cardType":"cloze","front":"When a question involves items like people or sweets, the final answer must be a [ ].","back":"When a question involves items like people or sweets, the final answer must be a whole number.","points":null},{"id":"594359d8-5a26-45c5-a310-727f536e0f20","cardType":"basic","front":"In the ratio \"red to not red = 3:7\", how many parts are in the total?","back":"10 parts ($3 + 7 = 10$).","points":1},{"id":"53b32947-dbef-4b63-a70b-5143961e7d2b","cardType":"basic","front":"If won to not won is 5:3, what fraction of the games were won?","back":"$$\\frac{5}{8}$","points":1},{"id":"2a2bf5d0-f165-4157-982a-4b3175072c38","cardType":"basic","front":"Red:not red is 3:7 and Green:not green is 2:3. What total number of parts works for both to compare them?","back":"10 parts (the LCM of 10 and 5).","points":2},{"id":"b3271620-f67d-4ccb-b8a3-514e922fd35d","cardType":"cloze","front":"If Red is $\\frac{3}{10}$ of a total and Green is $\\frac{4}{10}$ of a total, the remaining Blue parts make up $\\text{[...]}$ of the total.","back":"If Red is $\\frac{3}{10}$ of a total and Green is $\\frac{4}{10}$ of a total, the remaining Blue parts make up $\\boxed{\\frac{3}{10}}$ of the total.","points":null},{"id":"e3a03d03-fdc7-4809-8cef-aa27f5799bf4","cardType":"basic","front":"Points $A, B, C, D$ lie in order on a line. Write segment $BD$ as the sum of two smaller segments.","back":"$$BC + CD$","points":1},{"id":"033f7db8-216e-410a-913e-2befcf9830f0","cardType":"basic","front":"Points $A, B, C, D$ lie in order. Write segment $AC$ as the sum of two smaller segments.","back":"$$AB + BC$","points":1},{"id":"8a3e9df6-3eb9-464b-aac2-2b40a7a8372a","cardType":"cloze","front":"If $AB:BD = 1:4$ and we let $AB = x$, then the sum of the segments $BC + CD$ must equal $\\text{[...]}$.","back":"If $AB:BD = 1:4$ and we let $AB = x$, then the sum of the segments $BC + CD$ must equal $\\boxed{4x}$.","points":null},{"id":"02efc612-8d1e-4db4-b271-9ed66dd8f8d2","cardType":"basic","front":"If $(x+y):z = 3:5$, how can this be written as an equation?","back":"$$5(x+y) = 3z$","points":2},{"id":"ad88c6e1-e5a3-4e1e-b96f-bd1c3e1a2799","cardType":"cloze","front":"In the ratio $A:B = 4:7$, $B$ in terms of $A$ is $\\text{[...

Writing a Ratio as a Fraction or Linear Function Flashcards

Writing a Ratio as a Fraction or Linear Function Flashcards

Writing a Ratio as a Fraction or Linear Function Flashcards

Writing a Ratio as a Fraction or Linear Function Flashcards