Multiply and divide rational numbers

Learning Objectives Multiply positive and negative fractions and mixed numbers. Divide positive and negative fractions and mixed numbers by multiplying by the reciprocal. Multiply and divide positive and negative decimals accurately. Consistently apply the rules of signs for multiplication and division to all rational numbers. Convert between fractions and decimals to solve multiplication and division problems efficiently. Solve multi-step word problems involving the multiplication and division of rational numbers. Ever tried to split a pizza bill of $25.50 three ways, or calculate the materials needed for 1/2 of a construction plan? 🤔 You're already dividing and multiplying rational numbers! This tutorial will solidify your skills in multiplying and dividing all type...

TermDefinitionExample Rational NumberAny number that can be written as a fraction `p/q`, where `p` and `q` are integers and `q` is not zero. This includes integers, fractions, and terminating or repeating decimals.-5, 2/3, 7.25, -0.333... Reciprocal (Multiplicative Inverse)The number you multiply by to get a product of 1. To find the reciprocal of a fraction, you 'flip' the numerator and the denominator.The reciprocal of `4/7` is `7/4`. The reciprocal of `-3` (or `-3/1`) is `-1/3`. Improper FractionA fraction where the absolute value of the numerator is greater than or equal to the absolute value of the denominator.`11/5`, `-7/2` Mixed NumberA number composed of an integer and a proper fraction. It's crucial to convert mixed numbers to improper fractions before multiplying...

Multiplying Fractions \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Always simplify the result if possible. Dividing Fractions \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} To divide by a fraction, multiply by its reciprocal. This is often remembered as 'Keep, Change, Flip': Keep the first fraction, change division to multiplication, and flip the second fraction. Rules of Signs (for Multiplication & Division) Same Signs = Positive Answer. Different Signs = Negative Answer. If the two numbers have the same sign (both positive or both negative), the result is positive. If they...