Question 1202919
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Kira had a roll of blue paper and a roll of red paper. The length of the roll of blue paper is 1/2 the length of the roll of red paper. She cut the roll of blue paper into equal parts of length 9 cm and on each part she drew 3 star shapes. After that, she cut the roll of red paper into equal parts of length 7 cm and on each part she drew 5 heart shapes. What fraction of the shapes Kira drew were star shapes?

Let length of blue paper be B
Then length of red paper = 2B
Cutting the blue roll into 9-cm equal lengths means that there were {{{B/9}}} blue parts.
Since he drew 3 stars on each part, he drew {{{matrix(1,3, (B/9)3, "=", B/3)}}} stars
Likewise, cutting the red roll into 7-cm equal lengths means that there were {{{2B/7}}} red parts.
Since he drew 5 hearts on each red part, he drew {{{matrix(1,3, (2B/7)5, "=", 10B/7)}}} hearts 
Total shapes (stars and hearts) drawn: {{{matrix(1,5, B/3 + 10B/7, "=", (7B + 30B)/21, "=", 37B/21)}}}
Fraction of total shapes drawn that were stars: {{{highlight_green(matrix(1,7, (B/3)/(37B/21), "=", (B/3)(21/(37B)), "=", (cross(B)/cross(3))(7cross(21)/(37cross(B))), "=", highlight(7/37)))}}}</pre>