Add and subtract fractions with like denominators: word problems

Learning Objectives Translate real-world scenarios into mathematical expressions involving fractions with like denominators. Set up and solve addition and subtraction equations derived from word problems. Solve multi-step word problems that require a sequence of additions and subtractions. Interpret and state the final fractional answer in the context of the original problem. Simplify fractional results to their lowest terms and express them appropriately. Solve problems where the 'whole' must be represented as a fraction (e.g., 1 = n/n) to find a remaining part. Verify the reasonableness of a solution within the problem's context. A satellite's data storage is 7/12 full. After transmitting a batch of data equivalent to 4/12 of its total capacity, what...

TermDefinitionExample Like DenominatorsThis occurs when two or more fractions have the exact same denominator. This common denominator indicates that the 'whole' has been divided into the same number of equal parts for each fraction.The fractions 5/11 and 2/11 have like denominators because both are divided into 11 equal parts. NumeratorThe top number in a fraction. It represents how many of the equal parts of the whole are being considered.In the fraction 7/10, the numerator is 7. DenominatorThe bottom number in a fraction. It represents the total number of equal parts the whole has been divided into.In the fraction 7/10, the denominator is 10. The WholeIn the context of fractions, the 'whole' represents the entire quantity or 1. It can be expressed as a fraction wher...

Addition of Fractions with Like Denominators \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} To add fractions that share the same denominator, simply add their numerators together and place the sum over the common denominator. Always check if the resulting fraction can be simplified. Subtraction of Fractions with Like Denominators \frac{a}{c} - \frac{b}{c} = \frac{a-b}{c} To subtract fractions that share the same denominator, subtract the second numerator from the first and place the difference over the common denominator. Ensure the final answer is simplified.