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Answer :
To find which expression has the same value as [tex]\(84 \times 25\)[/tex], let's first determine what [tex]\(84 \times 25\)[/tex] equals:
1. Calculate [tex]\(84 \times 25\)[/tex]:
[tex]\[
84 \times 25 = 2100
\][/tex]
Next, we'll evaluate each option to see which one equals 2100.
2. Option 1: [tex]\(80 \times 25 + 5\)[/tex]
[tex]\[
80 \times 25 = 2000, \quad \text{then add 5:} \quad 2000 + 5 = 2005
\][/tex]
This does not equal 2100.
3. Option 2: [tex]\(80 \times 25 + 4 \times 25\)[/tex]
[tex]\[
80 \times 25 = 2000, \quad \text{and} \quad 4 \times 25 = 100
\][/tex]
[tex]\[
\text{So, add them together:} \quad 2000 + 100 = 2100
\][/tex]
This equals 2100.
4. Option 3: [tex]\(85 \times 25 - 1\)[/tex]
[tex]\[
85 \times 25 = 2125, \quad \text{then subtract 1:} \quad 2125 - 1 = 2124
\][/tex]
This does not equal 2100.
5. Option 4: [tex]\(80 \times 25 + 40 \times 25\)[/tex]
[tex]\[
80 \times 25 = 2000, \quad \text{and} \quad 40 \times 25 = 1000
\][/tex]
[tex]\[
\text{So, add them together:} \quad 2000 + 1000 = 3000
\][/tex]
This does not equal 2100.
After evaluating each option, Option 2: [tex]\(80 \times 25 + 4 \times 25\)[/tex] has the same value as [tex]\(84 \times 25\)[/tex], which is 2100.
1. Calculate [tex]\(84 \times 25\)[/tex]:
[tex]\[
84 \times 25 = 2100
\][/tex]
Next, we'll evaluate each option to see which one equals 2100.
2. Option 1: [tex]\(80 \times 25 + 5\)[/tex]
[tex]\[
80 \times 25 = 2000, \quad \text{then add 5:} \quad 2000 + 5 = 2005
\][/tex]
This does not equal 2100.
3. Option 2: [tex]\(80 \times 25 + 4 \times 25\)[/tex]
[tex]\[
80 \times 25 = 2000, \quad \text{and} \quad 4 \times 25 = 100
\][/tex]
[tex]\[
\text{So, add them together:} \quad 2000 + 100 = 2100
\][/tex]
This equals 2100.
4. Option 3: [tex]\(85 \times 25 - 1\)[/tex]
[tex]\[
85 \times 25 = 2125, \quad \text{then subtract 1:} \quad 2125 - 1 = 2124
\][/tex]
This does not equal 2100.
5. Option 4: [tex]\(80 \times 25 + 40 \times 25\)[/tex]
[tex]\[
80 \times 25 = 2000, \quad \text{and} \quad 40 \times 25 = 1000
\][/tex]
[tex]\[
\text{So, add them together:} \quad 2000 + 1000 = 3000
\][/tex]
This does not equal 2100.
After evaluating each option, Option 2: [tex]\(80 \times 25 + 4 \times 25\)[/tex] has the same value as [tex]\(84 \times 25\)[/tex], which is 2100.
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