Multiply and divide rational numbers

Learning Objectives Identify rational numbers expressed as terminating or repeating decimals. Accurately multiply positive and negative decimals. Accurately divide positive and negative decimals. Correctly apply the rules for signs when multiplying and dividing decimals. Solve multi-step real-world problems involving multiplication and division of decimals. Estimate products and quotients of decimals to check the reasonableness of their answers. Ever wonder how stores calculate discounts or how chefs adjust recipes? 💰🍳 It all comes down to multiplying and dividing decimals! In this lesson, you'll master the essential skills of multiplying and dividing rational numbers expressed as decimals. Understanding these operations is crucial for everyday math and for more adva...

TermDefinitionExample Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. Decimals that terminate or repeat are rational numbers.$0.5 = \frac{1}{2}$, $-3.25 = -\frac{13}{4}$, $0.333... = \frac{1}{3}$ DecimalA number that uses a decimal point to represent parts of a whole, where each digit after the decimal point represents a power of ten.$2.75$, $-0.12$, $10.0$ ProductThe result obtained when two or more numbers are multiplied together.In $3 \times 0.5 = 1.5$, $1.5$ is the product. QuotientThe result obtained when one number is divided by another number.In $6 \div 0.2 = 30$, $30$ is the quotient. Absolute ValueThe distance of a number from zero on the number line, always represented as a positive value.$|-5.2| = 5.2$, $|...

Multiplication of Decimals 1. Multiply the numbers as if they were whole numbers, ignoring the decimal points. 2. Count the total number of decimal places in all the factors. 3. Place the decimal point in the product so it has the same total number of decimal places. 4. Apply the sign rules for multiplication. This rule helps you find the product of any two decimal numbers. The sign of the product follows the rules for multiplying integers: same signs give a positive product, different signs give a negative product. Division of Decimals 1. If the divisor is a decimal, move its decimal point to the right until it is a whole number. 2. Move the decimal point in the dividend the same number of places to the right. Add zeros if necessary. 3. Divide as with whole numbers. 4. Place...