Insert either , or = in the shaded area to make a true statement. 3040−34 □ 1415⋅1514\frac{30}{40} - \frac{3}{4} \ \square \ \frac{14}{15} \cdot \frac{15}{14} 4030−43 □ 1514⋅1415

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 107

1장, 문제 107

Insert either <, >, or = in the shaded area to make a true statement. $\frac{30}{40}\) - $\frac{3}{4}$ \ $\square$ \ $\frac{14}{15}$ $\cdot$ \(\frac{15}{14}$

검증된 단계별 안내

First, simplify the left side of the inequality: calculate $\frac{30}{40} - \frac{3}{4}$. Start by simplifying $\frac{30}{40}$ to its lowest terms.

Next, convert both fractions on the left side to have a common denominator so you can subtract them easily.

Then, simplify the right side of the inequality: calculate $\frac{14}{15} \cdot \frac{15}{14}$. Notice that multiplication of these fractions might simplify directly.

After simplifying both sides, compare the resulting values to determine whether the left side is less than, greater than, or equal to the right side.

Finally, insert the correct inequality symbol ($<$, $>$, or $=$) in the shaded area based on your comparison.

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.

Comparing Fractions

To compare fractions, they must be expressed with a common denominator or converted to decimal form. This allows for a direct comparison of their sizes to determine which is greater, smaller, or if they are equal.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Correct application ensures accurate evaluation of expressions.

Simplifying Fractions and Products

Simplifying fractions involves reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor. Multiplying fractions requires multiplying numerators and denominators directly, followed by simplification to compare or evaluate expressions.

Insert either <, >, or = in the shaded area to make a true statement. 3040−34 □ 1415⋅1514\(\frac{30}{40}\) - \(\frac{3}{4}\) \ \(\square\) \ \(\frac{14}{15}\) \(\cdot\) \(\frac{15}{14}\) 4030−43 □ 1514⋅1415

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Comparing Fractions

Order of Operations

Simplifying Fractions and Products

Insert either <, >, or = in the shaded area to make a true statement. $\frac{30}{40}\) - \(\frac{3}{4}\) \ \(\square\) \ \(\frac{14}{15}\) \(\cdot\) \(\frac{15}{14}$