Divide fractions by whole numbers in recipes

Learning Objectives Translate a recipe-scaling word problem into a mathematical division expression. Apply the multiplicative inverse (reciprocal) to divide a fraction by a whole number. Justify the process of dividing a fraction by a whole number by explaining the 'Keep, Change, Flip' algorithm. Calculate the precise ingredient amount per serving when a fractional quantity is divided among multiple servings. Analyze the result of a division problem to determine if the answer is reasonable within the context of the recipe. Convert mixed numbers to improper fractions before performing division in multi-step recipe problems. Ever tried to share a pan of brownies but only had a recipe for a large group? How do you split 3/4 cup of sugar evenly among 5 smaller batches?...

TermDefinitionExample DividendThe number or quantity that is being divided. In our recipe context, this is the initial fractional amount of an ingredient.In the problem '1/2 cup of flour ÷ 2', the dividend is 1/2. DivisorThe number by which the dividend is divided. In our recipe context, this is the whole number of servings, batches, or portions you are creating.In the problem '1/2 cup of flour ÷ 2', the divisor is 2. QuotientThe result of a division operation. It represents the size of each smaller portion.In '1/2 ÷ 2 = 1/4', the quotient is 1/4, meaning each portion is 1/4 cup. Reciprocal (Multiplicative Inverse)For any non-zero number 'x', its reciprocal is '1/x'. When a number is multiplied by its reciprocal, the product is 1. This is...

Fraction Division Algorithm \frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c} = \frac{a}{b \times c} To divide a fraction by a whole number, you multiply the fraction by the reciprocal of the whole number. In practice, this means keeping the first fraction (the dividend), changing the division sign to multiplication, and using the reciprocal of the whole number (the divisor). Whole Number as a Fraction c = \frac{c}{1} Any whole number 'c' can be expressed as a fraction by placing it over a denominator of 1. This step is crucial for identifying the correct reciprocal to use in the division algorithm. Mixed Number Conversion A \frac{b}{c} = \frac{(A \times c) + b}{c} To convert a mixed number to an improper fraction, multiply the whole number part (A) by th...