Add and subtract rational numbers

Learning Objectives Identify rational numbers in real-world problem scenarios. Translate word problems involving rational numbers into mathematical expressions. Accurately add and subtract fractions, decimals, and mixed numbers, including negative values. Apply a systematic problem-solving strategy to multi-step problems involving rational numbers. Check the reasonableness of their answers to rational number problems. Solve practical problems involving measurements, money, and quantities using rational number operations. Ever wonder how much change you'll get back after buying items with fractional prices, or how much fabric you need for a project? 📏💰 These everyday questions require us to add and subtract rational numbers! In this lesson, we'll dive into solvin...

TermDefinitionExample Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. This includes integers, fractions, and terminating or repeating decimals.$\frac{3}{4}$, $-5$, $0.75$, $2\frac{1}{2}$ Common DenominatorA common multiple of the denominators of two or more fractions. It is necessary to find a common denominator before adding or subtracting fractions.For $\frac{1}{3}$ and $\frac{1}{4}$, a common denominator is 12. Mixed NumberA number consisting of an integer and a proper fraction.$3\frac{1}{2}$ (which is equivalent to $3 + \frac{1}{2}$) Improper FractionA fraction where the numerator is greater than or equal to the denominator.$\frac{7}{2}$ (which is equivalent to $3\frac{1}{2}$) Problem-Solving StrategyA systematic...

Adding/Subtracting Fractions $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$ (after finding a common denominator) To add or subtract fractions, they must have the same denominator. Find the least common multiple (LCM) of the denominators, convert the fractions to equivalent fractions with the LCM as the new denominator, then add or subtract the numerators. Keep the denominator the same. Adding/Subtracting Decimals Align the decimal points vertically, then add or subtract digits in each place value column, carrying over or borrowing as needed. When adding or subtracting decimals, it is crucial to align the decimal points to ensure that you are combining or separating digits of the same place value. You can add trailing zeros to make the numbers have the same number of de...