Add and subtract rational numbers

Learning Objectives Identify the Least Common Denominator (LCD) for any set of rational numbers. Convert mixed numbers to improper fractions and vice versa to facilitate calculations. Add and subtract rational numbers with both like and unlike denominators, including positive and negative values. Simplify the results of addition and subtraction of rational numbers to their lowest terms. Apply the rules for adding and subtracting integers to operations with negative rational numbers. Solve multi-step word problems involving the addition and subtraction of rational numbers. Ever tried to bake a cake and had to use a 1/3 cup measure three times instead of a full cup? 🍰 That's rational number arithmetic in action! This tutorial will refresh and deepen your understanding o...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction a/b, where 'a' and 'b' are integers and 'b' is not zero. This includes integers, fractions, and terminating or repeating decimals.-7, 3/5, 1.25 (which is 5/4), -0.333... (which is -1/3) Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators of two or more fractions. It's the key to adding or subtracting fractions with different denominators.For 1/6 and 3/8, the denominators are 6 and 8. The multiples of 6 are 6, 12, 18, 24... The multiples of 8 are 8, 16, 24... The LCD is 24. Equivalent FractionsFractions that have different numerators and denominators but represent the same value.1/2 is equivalent to 2/4, 3/6, and 50/100. Impro...

Adding/Subtracting with Like Denominators \frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c} When the denominators are the same, simply add or subtract the numerators and keep the denominator the same. Adding/Subtracting with Unlike Denominators \frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd} To add or subtract fractions with different denominators, you must first find a common denominator, preferably the LCD. This formula is a shortcut, but finding the LCD first often keeps the numbers smaller and easier to work with. Converting a Mixed Number to an Improper Fraction A \frac{b}{c} = \frac{(A \times c) + b}{c} To convert a mixed number, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. This is a cruci...