Use the distributive property to calculate each value mentally. 123 5/8 * 1 1/2 - 23 5/8 * 1 1/2

Verified step by step guidance

1. Identify the expression: \((123 \frac{5}{8} \times 1 \frac{1}{2}) - (23 \frac{5}{8} \times 1 \frac{1}{2})\).
2. Use the distributive property: \((a \times c) - (b \times c) = (a - b) \times c\).
3. Rewrite the expression using the distributive property: \((123 \frac{5}{8} - 23 \frac{5}{8}) \times 1 \frac{1}{2}\).
4. Subtract the mixed numbers: \(123 \frac{5}{8} - 23 \frac{5}{8}\).
5. Multiply the result by \(1 \frac{1}{2}\).

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside a set of parentheses. In the context of the given question, it can be used to simplify calculations by distributing the multiplication across the addition or subtraction of mixed numbers.

Mixed Numbers

Mixed numbers are numbers that consist of a whole number and a proper fraction, such as 1 1/2 or 23 5/8. To perform operations with mixed numbers, it is often helpful to convert them into improper fractions, which can simplify multiplication and addition. Understanding how to manipulate mixed numbers is essential for solving the problem accurately.

Mental Math Techniques

Mental math techniques involve strategies that allow individuals to perform calculations in their heads without the use of paper or a calculator. Techniques such as breaking numbers into easier components, rounding, and using the distributive property can enhance efficiency and accuracy in solving arithmetic problems, especially when dealing with fractions and mixed numbers.