Multi-Step Rational Number Problems Worksheets for Grade 7

📚 Topic Summary

Multi-step rational number problems involve solving equations or expressions that require multiple mathematical operations (addition, subtraction, multiplication, division) using fractions, decimals, and integers. These problems build upon basic arithmetic skills, challenging you to apply the order of operations (PEMDAS/BODMAS) accurately. Mastering these concepts is crucial for advanced algebra and problem-solving.

🧠 Part A: Vocabulary

Match the term with its definition:

1. Term: Rational Number
2. Term: Integer
3. Term: Operation
4. Term: Expression
5. Term: Order of Operations

1. Definition: A rule that defines the sequence of steps for evaluating mathematical expressions.
2. Definition: A number that can be expressed as a fraction \(\frac{p}{q}\), where p and q are integers and q ≠ 0.
3. Definition: A whole number (not a fraction) that can be positive, negative, or zero.
4. Definition: A mathematical process such as addition, subtraction, multiplication, or division.
5. Definition: A combination of numbers, variables, and operations representing a mathematical quantity.

(Match each term 1-5 with its correct definition 1-5.)

✍️ Part B: Fill in the Blanks

When solving multi-step rational number problems, it's important to follow the ______ of operations. This is often remembered by the acronym ______. A ______ number can be written as a simple fraction. When adding or subtracting fractions, they must have a common ______. Simplifying your answer to its ______ form is always a good practice.

(Word Bank: simplest, order, denominator, rational, PEMDAS/BODMAS)

🤔 Part C: Critical Thinking

Imagine you are baking a cake and need to triple a recipe that uses fractional measurements. How would you ensure you accurately calculate all the ingredients using your knowledge of rational number operations?