Use the distributive property to calculate each value mentally. 12358⋅112−2358⋅112123 \frac{5}{8} \cdot 1 \frac{1}{2} - 23 \frac{5}{8} \cdot 1 \frac{1}{2} 12385⋅121−2385⋅121

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 139

1장, 문제 139

Use the distributive property to calculate each value mentally. $123 $\frac{5}{8}$ $\cdot$ 1 $\frac{1}{2}$ - 23 $\frac{5}{8}$ $\cdot$ 1 $\frac{1}{2}$$

검증된 단계별 안내

First, convert the mixed numbers into improper fractions for easier multiplication. For example, convert $123 \frac{5}{8}$ and $1 \frac{1}{2}$ into improper fractions.

Express the problem as $\left(123 \frac{5}{8}\right) \times \left(1 \frac{1}{2}\right) - \left(23 \frac{5}{8}\right) \times \left(1 \frac{1}{2}\right)$ using the improper fractions.

Notice that both terms share a common factor of $1 \frac{1}{2}$, so apply the distributive property: factor out $1 \frac{1}{2}$ from both terms.

Rewrite the expression as $\left(123 \frac{5}{8} - 23 \frac{5}{8}\right) \times 1 \frac{1}{2}$, simplifying inside the parentheses first.

Finally, subtract the two mixed numbers inside the parentheses and then multiply the result by $1 \frac{1}{2}$ to find the answer.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. It is expressed as a(b + c) = ab + ac. This property helps simplify expressions and perform mental calculations efficiently.

Mixed Numbers and Improper Fractions

Mixed numbers combine whole numbers and fractions, such as 1 1/2. Converting mixed numbers to improper fractions (e.g., 1 1/2 = 3/2) simplifies multiplication and subtraction. Understanding this conversion is essential for accurate calculations.

Mental Math Strategies

Mental math involves performing calculations in your head without paper. Using properties like distributive property and converting mixed numbers helps break down complex problems into simpler parts, enabling quicker and more accurate mental computation.

Use the distributive property to calculate each value mentally. 12358⋅112−2358⋅112123 \(\frac{5}{8}\) \(\cdot\) 1 \(\frac{1}{2}\) - 23 \(\frac{5}{8}\) \(\cdot\) 1 \(\frac{1}{2}\) 12385⋅121−2385⋅121

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Distributive Property

Mixed Numbers and Improper Fractions

Mental Math Strategies

Use the distributive property to calculate each value mentally. $123 \(\frac{5}{8}\) \(\cdot\) 1 \(\frac{1}{2}\) - 23 \(\frac{5}{8}\) \(\cdot\) 1 \(\frac{1}{2}\)$