Question

Which uses the greatest common factor (GCF) to generate an expression equivalent to 0.8a + 1.6?

1) Multiplying both terms by 10
2) Multiplying both terms by 5
3) Dividing both terms by 0.8
4) Dividing both terms by 1.6

Answer 1

To generate an expression equivalent to 0.8a + 1.6 using the GCF, option 3 is correct. Dividing both terms by 0.8 gives us the factored expression a + 2, indicating that 0.8 is the GCF of the two terms.

Step-by-step explanation:

To find an expression equivalent to 0.8a + 1.6 using the greatest common factor (GCF), we look for a factor that can be divided from both terms. We need to find a single value to factor out.

When comparing the options given, we observe that:

1. Multiplying both terms by 10 gives us 8a + 16, which is not factoring out the GCF but changing the scale of the expression.
2. Multiplying both terms by 5 gives us 4a + 8, which also scales the expression without finding the GCF.
3. Dividing both terms by 0.8 transforms the expression into a + 2, which means 0.8 is the GCF since it divides neatly into both terms.
4. Dividing both terms by 1.6 gives us 0.5a + 1, which also does not factor out the GCF.

Therefore, the option that uses the GCF is the third option: Dividing both terms by 0.8.