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d. Grandma gave Kendra recipes for cranberry cookies and cranberry bread. One recipe calls for (2)/(3) cup cranberries, and the other recipe calls for 1(3)/(4) cup. How many cups of cranberries will Kendra need to make both recipes?

d. Grandma gave Kendra recipes for cranberry cookies and cranberry bread. One recipe calls for 23 \frac{2}{3} cup cranberries, and the other recipe calls for 134 1 \frac{3}{4} cup. How many cups of cranberries will Kendra need to make both recipes?

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Q. d. Grandma gave Kendra recipes for cranberry cookies and cranberry bread. One recipe calls for 23 \frac{2}{3} cup cranberries, and the other recipe calls for 134 1 \frac{3}{4} cup. How many cups of cranberries will Kendra need to make both recipes?
  1. Identify amounts needed: Identify the amounts needed for each recipe. The first recipe needs 23\frac{2}{3} cup and the second needs 1341\frac{3}{4} cups.
  2. Convert to improper fraction: Convert the mixed number to an improper fraction for easier addition. 1(34)1\left(\frac{3}{4}\right) is the same as (44)+(34)\left(\frac{4}{4}\right) + \left(\frac{3}{4}\right), which equals (74)\left(\frac{7}{4}\right) cups.
  3. Add fractions with common denominator: Add the two fractions (23)(\frac{2}{3}) cup + (74)(\frac{7}{4}) cups. To add fractions, find a common denominator. The least common multiple of 33 and 44 is 1212.
  4. Convert to twelfths: Convert (23)(\frac{2}{3}) into twelfths by multiplying the numerator and denominator by 44, getting (812)(\frac{8}{12}). Convert (74)(\frac{7}{4}) into twelfths by multiplying the numerator and denominator by 33, getting (2112)(\frac{21}{12}).
  5. Add fractions with common denominator: Add the two fractions now that they have a common denominator: (812)+(2112)(\frac{8}{12}) + (\frac{21}{12}) equals (2912)(\frac{29}{12}).
  6. Convert back to mixed number: Convert the improper fraction (29)/(12)(29)/(12) back to a mixed number. 1212 goes into 2929 twice with a remainder of 55, so the mixed number is 25122\frac{5}{12} cups.

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