Answer :
Sure, let's go through the problems step-by-step:
### Problem 1
We are trying to identify which expression does not equal [tex]\(84 \times 0.28\)[/tex].
1. Calculate [tex]\(84 \times 0.28\)[/tex]:
[tex]\[
84 \times 0.28 = 23.52
\][/tex]
2. Verify each given option:
- Option 1: [tex]\(84 \div \frac{1}{0.28}\)[/tex]
[tex]\[
\frac{1}{0.28} = 3.5714\ldots \quad \text{(approximately)}
\][/tex]
[tex]\[
84 \div 3.5714 \approx 23.52
\][/tex]
So, this equals [tex]\(84 \times 0.28\)[/tex].
- Option 2: [tex]\(84 \times 0.14 \times 2\)[/tex]
[tex]\[
84 \times 0.14 = 11.76
\][/tex]
[tex]\[
11.76 \times 2 = 23.52
\][/tex]
So, this equals [tex]\(84 \times 0.28\)[/tex].
- Option 3: [tex]\(84 \times \frac{7}{25}\)[/tex]
[tex]\[
\frac{7}{25} = 0.28
\][/tex]
[tex]\[
84 \times 0.28 = 23.52
\][/tex]
So, this equals [tex]\(84 \times 0.28\)[/tex].
- Option 4: [tex]\(84 \times 0 \times 0.28\)[/tex]
[tex]\[
84 \times 0 = 0
\][/tex]
Any number multiplied by 0 gives 0.
So, this does not equal [tex]\(84 \times 0.28\)[/tex].
Conclusion: The expression that is not equal to [tex]\(84 \times 0.28\)[/tex] is [tex]\(84 \times 0 \times 0.28\)[/tex].
### Problem 2
The problem states that 1251 is the product of its highest factor and a prime number.
Find the highest factor of 1251:
1. Identify prime factors of 1251:
- 1251 can be divided by the prime number 3:
[tex]\[
1251 \div 3 = 417
\][/tex]
- Then, check 417 for divisibility:
- 417 is divisible by 3:
[tex]\[
417 \div 3 = 139
\][/tex]
- 139 is itself a prime number.
2. List factor relationships:
- So, the prime factors of 1251 are 3 and 139.
- The highest factor of 1251 is 139 because it's the largest prime factor of 1251.
Conclusion: The highest factor of 1251 is 139.
### Problem 1
We are trying to identify which expression does not equal [tex]\(84 \times 0.28\)[/tex].
1. Calculate [tex]\(84 \times 0.28\)[/tex]:
[tex]\[
84 \times 0.28 = 23.52
\][/tex]
2. Verify each given option:
- Option 1: [tex]\(84 \div \frac{1}{0.28}\)[/tex]
[tex]\[
\frac{1}{0.28} = 3.5714\ldots \quad \text{(approximately)}
\][/tex]
[tex]\[
84 \div 3.5714 \approx 23.52
\][/tex]
So, this equals [tex]\(84 \times 0.28\)[/tex].
- Option 2: [tex]\(84 \times 0.14 \times 2\)[/tex]
[tex]\[
84 \times 0.14 = 11.76
\][/tex]
[tex]\[
11.76 \times 2 = 23.52
\][/tex]
So, this equals [tex]\(84 \times 0.28\)[/tex].
- Option 3: [tex]\(84 \times \frac{7}{25}\)[/tex]
[tex]\[
\frac{7}{25} = 0.28
\][/tex]
[tex]\[
84 \times 0.28 = 23.52
\][/tex]
So, this equals [tex]\(84 \times 0.28\)[/tex].
- Option 4: [tex]\(84 \times 0 \times 0.28\)[/tex]
[tex]\[
84 \times 0 = 0
\][/tex]
Any number multiplied by 0 gives 0.
So, this does not equal [tex]\(84 \times 0.28\)[/tex].
Conclusion: The expression that is not equal to [tex]\(84 \times 0.28\)[/tex] is [tex]\(84 \times 0 \times 0.28\)[/tex].
### Problem 2
The problem states that 1251 is the product of its highest factor and a prime number.
Find the highest factor of 1251:
1. Identify prime factors of 1251:
- 1251 can be divided by the prime number 3:
[tex]\[
1251 \div 3 = 417
\][/tex]
- Then, check 417 for divisibility:
- 417 is divisible by 3:
[tex]\[
417 \div 3 = 139
\][/tex]
- 139 is itself a prime number.
2. List factor relationships:
- So, the prime factors of 1251 are 3 and 139.
- The highest factor of 1251 is 139 because it's the largest prime factor of 1251.
Conclusion: The highest factor of 1251 is 139.
