Divide fractions and mixed numbers: word problems

Learning Objectives Identify keywords and phrases in word problems that indicate division of fractions or mixed numbers. Accurately convert mixed numbers to improper fractions and vice versa. Apply the 'Keep, Change, Flip' method to divide fractions and mixed numbers. Solve multi-step word problems involving the division of fractions and mixed numbers. Interpret the quotient in the context of the word problem, including simplifying and expressing answers appropriately. Check the reasonableness of their answers in real-world contexts. Ever wondered how many smaller portions you can get from a larger quantity, like how many 1/2 cup servings are in a 3 3/4 cup recipe? 🥣 Let's find out! This lesson will equip you with the strategies to confidently solve word pro...

TermDefinitionExample FractionA number representing part of a whole, expressed as a numerator over a denominator (e.g., 3/4).If a pizza is cut into 8 slices and you eat 3, you've eaten 3/8 of the pizza. Mixed NumberA number consisting of a whole number and a proper fraction (e.g., 2 1/2).If you have 2 whole apples and half of another apple, you have 2 1/2 apples. Improper FractionA fraction where the numerator is greater than or equal to the denominator (e.g., 5/2).The mixed number 2 1/2 can be written as the improper fraction 5/2. ReciprocalThe multiplicative inverse of a number; for a fraction, it's found by flipping the numerator and denominator (e.g., the reciprocal of 2/3 is 3/2).To find the reciprocal of 4/5, you flip it to get 5/4. QuotientThe result obtained when one num...

Converting Mixed Numbers to Improper Fractions $$a\frac{b}{c} = \frac{(a \times c) + b}{c}$$ Before dividing mixed numbers, convert them into improper fractions. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Dividing Fractions (Keep, Change, Flip) $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ To divide by a fraction, 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 denominators. Converting Improper Fractions to Mixed Numbers $$\frac{\text{numerator}}{\text{denominator}} = \text{whole number} \frac{\text{remainder}}{\text{denominator}}$$ (where whole number = numera...