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Answer :
To determine which expression is equal to [tex]\(137 \times 13\)[/tex], let's evaluate each option step-by-step:
1. Option A: [tex]\(13 \times 137\)[/tex]
- This expression simply reverses the order of the multiplication in [tex]\(137 \times 13\)[/tex].
- According to the commutative property of multiplication, which states that changing the order of numbers in a multiplication does not affect the product, [tex]\(13 \times 137\)[/tex] is indeed equal to [tex]\(137 \times 13\)[/tex].
2. Option B: [tex]\(137 \div 13\)[/tex]
- This option involves division, not multiplication.
- Therefore, [tex]\(137 \div 13\)[/tex] is not mathematically equivalent to multiplying [tex]\(137 \times 13\)[/tex].
3. Option C: [tex]\(13 + 137\)[/tex]
- This option involves addition.
- Adding the numbers [tex]\(13\)[/tex] and [tex]\(137\)[/tex] does not yield the same result as multiplying them, so [tex]\(13 + 137\)[/tex] is not equal to [tex]\(137 \times 13\)[/tex].
4. Option D: [tex]\(13 \div 137\)[/tex]
- This option also involves division.
- Dividing [tex]\(13\)[/tex] by [tex]\(137\)[/tex] is not equivalent to multiplying the numbers together. Hence, this option is not equal to [tex]\(137 \times 13\)[/tex].
After evaluating all the options, the expression that equals [tex]\(137 \times 13\)[/tex] is Option A: [tex]\(13 \times 137\)[/tex].
1. Option A: [tex]\(13 \times 137\)[/tex]
- This expression simply reverses the order of the multiplication in [tex]\(137 \times 13\)[/tex].
- According to the commutative property of multiplication, which states that changing the order of numbers in a multiplication does not affect the product, [tex]\(13 \times 137\)[/tex] is indeed equal to [tex]\(137 \times 13\)[/tex].
2. Option B: [tex]\(137 \div 13\)[/tex]
- This option involves division, not multiplication.
- Therefore, [tex]\(137 \div 13\)[/tex] is not mathematically equivalent to multiplying [tex]\(137 \times 13\)[/tex].
3. Option C: [tex]\(13 + 137\)[/tex]
- This option involves addition.
- Adding the numbers [tex]\(13\)[/tex] and [tex]\(137\)[/tex] does not yield the same result as multiplying them, so [tex]\(13 + 137\)[/tex] is not equal to [tex]\(137 \times 13\)[/tex].
4. Option D: [tex]\(13 \div 137\)[/tex]
- This option also involves division.
- Dividing [tex]\(13\)[/tex] by [tex]\(137\)[/tex] is not equivalent to multiplying the numbers together. Hence, this option is not equal to [tex]\(137 \times 13\)[/tex].
After evaluating all the options, the expression that equals [tex]\(137 \times 13\)[/tex] is Option A: [tex]\(13 \times 137\)[/tex].
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