Divide fractions and mixed numbers: word problems

Learning Objectives Identify the dividend and divisor in word problems involving division of fractions and mixed numbers. Accurately convert mixed numbers to improper fractions and vice versa within word problem contexts. Apply the 'Keep, Change, Flip' method to divide fractions and improper fractions derived from mixed numbers. Solve multi-step word problems requiring division of fractions and mixed numbers. Simplify fractional answers and express them appropriately as fractions or mixed numbers in context. Interpret the meaning of the quotient in the context of the original word problem. Ever wonder how many smaller pieces you can get from a larger one, or how many servings are in a big recipe? 🍰 Division with fractions helps us figure that out! In this lesson,...

TermDefinitionExample FractionA number representing a part of a whole, expressed as a numerator (top number) over a denominator (bottom number).If you eat 1 out of 4 slices of pizza, you've eaten $\frac{1}{4}$ of the pizza. Mixed NumberA number consisting of a whole number and a proper fraction.If you have 2 whole pizzas and $\frac{1}{2}$ of another, you have $2\frac{1}{2}$ pizzas. Improper FractionA fraction where the numerator is greater than or equal to the denominator, representing a value of one or more whole units.The mixed number $2\frac{1}{2}$ can be written as the improper fraction $\frac{5}{2}$. ReciprocalThe reciprocal of a fraction is found by flipping the numerator and the denominator. It's what you multiply a number by to get 1.The reciprocal of $\frac{2}{3}$ is $\...

Dividing Fractions (Keep, Change, Flip) $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ To divide one fraction by another, keep the first fraction as it is, change the division sign to multiplication, and flip (find the reciprocal of) the second fraction. Then, multiply the numerators and multiply the denominators. Converting Mixed Numbers to Improper Fractions $A\frac{b}{c} = \frac{(A \times c) + b}{c}$ Before dividing with mixed numbers, always convert them into improper fractions. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Converting Improper Fractions to Mixed Numbers $\frac{N}{D} = Q\frac{R}{D}$ (where N is numerator, D is denominator, Q is quotient, R is remainder) After d...