Multiply and divide rational numbers:word problems

Learning Objectives Identify keywords in word problems that indicate multiplication or division of rational numbers. Translate real-world scenarios involving rational numbers into mathematical expressions. Accurately multiply rational numbers (fractions, decimals, mixed numbers) to solve word problems. Accurately divide rational numbers (fractions, decimals, mixed numbers) to solve word problems. Interpret the results of calculations in the context of the original word problem. Solve multi-step word problems involving both multiplication and division of rational numbers. Ever wonder how much pizza each person gets if you share 3.5 pizzas among 7 friends? 🍕 Or how much total fabric you need if each project uses 1/4 yard and you have 12 projects? In this lesson, you'll...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. This includes fractions, decimals that terminate or repeat, and integers.$0.75$ (can be written as $\frac{3}{4}$), $-2$ (can be written as $\frac{-2}{1}$), $1\frac{1}{2}$ (can be written as $\frac{3}{2}$). ProductThe result obtained when two or more numbers are multiplied together.The product of $\frac{1}{2}$ and $4$ is $2$. QuotientThe result obtained when one number is divided by another number.The quotient of $10$ divided by $2.5$ is $4$. ReciprocalTwo numbers are reciprocals if their product is 1. To find the reciprocal of a fraction, you 'flip' the numerator and denominator.The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. The reci...

Multiplying Rational Numbers To multiply two fractions, multiply the numerators and multiply the denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$. For decimals, multiply as usual and count the total decimal places in the factors to place the decimal in the product. Use this rule when a word problem asks for a 'fraction of a quantity,' 'total amount given a rate and quantity,' or 'product.' Always convert mixed numbers to improper fractions before multiplying. Dividing Rational Numbers To divide by a fraction, multiply by its reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. For decimals, convert the divisor to a whole number by moving the decimal point, and move the dividend's decimal p...