Question

related questions: lesson 2: expressions

q. choose the expression that shows the result after the first operation is completed.

\\(\frac{20+40}{10}-5\\)

a. \\(\frac{60}{10}-5\\)

b. \\(\frac{60}{5}\\)

c. \\(20+4-5\\)

d. \\(20-35-5\\)

Explanation:

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<reasoning>

Identify the expression and operations

We are given the numerical expression:
\[
\frac{20+40}{10} - 5
\]
Using the Numerical Expressions knowledge point, we must determine which operation to perform first according to the order of operations.

Analyze grouping in fractions

In mathematics, a fraction bar acts as a grouping symbol (like parentheses) for both the numerator and the denominator. This means we must evaluate the entire numerator and the entire denominator before performing the division.

• Numerator: \(20 + 40\)
• Denominator: \(10\)

Therefore, the addition in the numerator must be completed first.

Perform the first operation

We calculate the sum in the numerator:
\[
20 + 40 = 60
\]
Substituting this result back into our original expression gives:
\[
\frac{60}{10} - 5
\]

Match with the given options

We compare our resulting expression, \(\frac{60}{10} - 5\), with the choices:

• Option A: \(\frac{60}{10} - 5\)
• Option B: \(\frac{60}{5}\)
• Option C: \(20 + 4 - 5\)
• Option D: \(20 - 35 - 5\)

The expression matches Option A.
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{60}{10} - 5\)</mcq-correct>
<mcq-option>(B) \(\frac{60}{5}\)</mcq-option>
<mcq-option>(C) \(20 + 4 - 5\)</mcq-option>
<mcq-option>(D) \(20 - 35 - 5\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the expression and operations

We are given the numerical expression:
\[
\frac{20+40}{10} - 5
\]
Using the Numerical Expressions knowledge point, we must determine which operation to perform first according to the order of operations.

Analyze grouping in fractions

In mathematics, a fraction bar acts as a grouping symbol (like parentheses) for both the numerator and the denominator. This means we must evaluate the entire numerator and the entire denominator before performing the division.

• Numerator: \(20 + 40\)
• Denominator: \(10\)

Therefore, the addition in the numerator must be completed first.

Perform the first operation

We calculate the sum in the numerator:
\[
20 + 40 = 60
\]
Substituting this result back into our original expression gives:
\[
\frac{60}{10} - 5
\]

Match with the given options

We compare our resulting expression, \(\frac{60}{10} - 5\), with the choices:

• Option A: \(\frac{60}{10} - 5\)
• Option B: \(\frac{60}{5}\)
• Option C: \(20 + 4 - 5\)
• Option D: \(20 - 35 - 5\)

The expression matches Option A.
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{60}{10} - 5\)</mcq-correct>
<mcq-option>(B) \(\frac{60}{5}\)</mcq-option>
<mcq-option>(C) \(20 + 4 - 5\)</mcq-option>
<mcq-option>(D) \(20 - 35 - 5\)</mcq-option>
</answer>

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