5. A certain recipe requires 3 2/7 cups of flour and 2 3/5 cups of sugar. a) If 5/9 of the recipe is to be made, how much sugar is needed? b) If the above ingredients are required for one batch, find the amount of flour needed for a triple batch.

If 1 recipe requires [tex] 2\frac{3}{5} [/tex] cups of Sugar, to find how much of sugar requires for [tex] \frac{5}{9} [/tex] recipe, we need to multiply them as below

[tex] \frac{5}{9} \; recipe \; requires\; \; \frac{5}{9}\; \cdot\; 2\frac{3}{5} \; cups \; of\; sugar\\ \\ \frac{5}{9}\; \cdot\; 2\frac{3}{5}=\frac{5}{9}\; \cdot\; \frac{13}{5}\\\\ Multiply \; numerator \; with \; numerator\; and\; denominator\; with \; denominator \\ \\ \frac{5 \cdot 13 }{9 \cdot 5} \\ \\ Cancel \; common \; factors \; to \; simplify \; the\; fraction\; to\; its\; lowest\; terms\\ \\ \frac{13}{9}\\ \\ Rewrite \; it \; as\; mixed\; fraction\\1\frac{4}{9} [/tex]

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If 1 Batch requires [tex] 3\frac{2}{7} [/tex] cups of Flour, to find how much of Flour requires for triple Batch, we need to multiply them as below:

[tex] Triple \; Batch \; requires\; \; 3 \times 3\frac{2}{7} \; Cups\; \; of\; \; Flour\\ \\ 3 \times 3\frac{2}{7}\\ Convert \; mixed \; fraction\; to\; improper\; fraction\\ \\ 3 \times \frac{23}{7} \\ Rewrite\; 3\; whole\; number\; as\; a\; fraction\\ \\ \frac{3}{1} \times\frac{23}{7} \\ Multiply\; numerator\; with\; numerator\; and\; denominator\; with\; denominator\\ \\ \frac{69}{7} [/tex]

[tex] Rewrite\; the\; above \; mixed\; fraction\; to\; improper\; fraction\\ \\ \frac{69}{7} =9\frac{6}{7} [/tex]

Conclusion:

Part a)

[tex] 1\frac{4}{9} \; cups \; of\; sugar\; required\; to\; make\; 5/9 \; Recipe! [/tex]

Part b)

[tex] 9\frac{6}{7} \; cups \; of\; flour\; required\; to\; make\; 3 \; Batch! [/tex]