Questions: Study Paths TX Math Bridge - Stage 1 Study Path Test Test Unit: Whole Numbers Progress: Question iD: 558100 The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used. (2 * 4) * 7 10 * 5 * 3 2+7+4 4+2+7 5 * 3 * 10 2 *(4 * 7) 3+(5+10) (4+2) * 7 5+(10 * 3) (3+5)+10 Clear Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your cursor is over the target before releasing. The target will highlight or the cursor will change. Need help? Watch this video.

Study Paths TX Math Bridge - Stage 1 Study Path Test Test Unit: Whole Numbers Progress: Question iD: 558100 The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used. (2 * 4) * 7 10 * 5 * 3 2+7+4 4+2+7 5 * 3 * 10 2 *(4 * 7) 3+(5+10) (4+2) * 7 5+(10 * 3) (3+5)+10 Clear Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your cursor is over the target before releasing. The target will highlight or the cursor will change. Need help? Watch this video.
Transcript text: Study Paths TX Math Bridge - Stage 1 Study Path Test Test Unit: Whole Numbers Progress: Question iD: 558100 The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used. \[ \begin{array}{ll} (2 \cdot 4) \cdot 7 & 10 \cdot 5 \cdot 3 \\ 2+7+4 & 4+2+7 \\ 5 \cdot 3 \cdot 10 & 2 \cdot(4 \cdot 7) \\ 3+(5+10) & (4+2) \cdot 7 \\ & 5+(10 \cdot 3) \\ & (3+5)+10 \end{array} \] Clear Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your cursor is over the target before releasing. The target will highlight or the cursor will change. Need help? Watch this video.
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Solution

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Solution Steps

To solve the problem of matching equivalent expressions, we need to apply the associative and commutative properties of addition and multiplication. These properties allow us to rearrange and regroup numbers in expressions to find equivalences. We will compare each expression on the left with those on the right to find matches.

Step 1: Evaluate Left Expressions

We evaluate the expressions on the left:

  1. \( (2 \cdot 4) \cdot 7 = 56 \)
  2. \( 2 + 7 + 4 = 13 \)
  3. \( 5 \cdot 3 \cdot 10 = 150 \)
  4. \( 3 + (5 + 10) = 18 \)

Thus, the left expressions yield the values: \( [56, 13, 150, 18] \).

Step 2: Evaluate Right Expressions

Next, we evaluate the expressions on the right:

  1. \( 10 \cdot 5 \cdot 3 = 150 \)
  2. \( 4 + 2 + 7 = 13 \)
  3. \( 2 \cdot (4 \cdot 7) = 56 \)
  4. \( (4 + 2) \cdot 7 = 42 \)
  5. \( 5 + (10 \cdot 3) = 35 \)
  6. \( (3 + 5) + 10 = 18 \)

Thus, the right expressions yield the values: \( [150, 13, 56, 42, 35, 18] \).

Step 3: Match Expressions

We find the matches between the left and right expressions based on their evaluated values:

  • \( 56 \) from the left matches with \( 56 \) from the right.
  • \( 13 \) from the left matches with \( 13 \) from the right.
  • \( 150 \) from the left matches with \( 150 \) from the right.
  • \( 18 \) from the left matches with \( 18 \) from the right.

The matches are:

  • \( (2 \cdot 4) \cdot 7 \) matches with \( 2 \cdot (4 \cdot 7) \)
  • \( 2 + 7 + 4 \) matches with \( 4 + 2 + 7 \)
  • \( 5 \cdot 3 \cdot 10 \) matches with \( 10 \cdot 5 \cdot 3 \)
  • \( 3 + (5 + 10) \) matches with \( (3 + 5) + 10 \)

Final Answer

The matches are:

  1. \( (2 \cdot 4) \cdot 7 \) matches with \( 2 \cdot (4 \cdot 7) \)
  2. \( 2 + 7 + 4 \) matches with \( 4 + 2 + 7 \)
  3. \( 5 \cdot 3 \cdot 10 \) matches with \( 10 \cdot 5 \cdot 3 \)
  4. \( 3 + (5 + 10) \) matches with \( (3 + 5) + 10 \)

Thus, the final answer is: \[ \boxed{ \begin{align_} (2 \cdot 4) \cdot 7 & \leftrightarrow 2 \cdot (4 \cdot 7) \\ 2 + 7 + 4 & \leftrightarrow 4 + 2 + 7 \\ 5 \cdot 3 \cdot 10 & \leftrightarrow 10 \cdot 5 \cdot 3 \\ 3 + (5 + 10) & \leftrightarrow (3 + 5) + 10 \end{align_} } \]

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