Question

Niko made a generalization.
She said that a 6s fact can break into a 4s fact and a 2s fact.
Choose the correct explanation to tell whether Niko's generalization is true or false.

(1 point)
Responses

true; 6×9=(4×9)+(2×9)=54
true; 6 × 9 = ( 4 × 9 ) + ( 2 × 9 ) = 54

true; 6×9=(5×9)+(1×9)=54
true; 6 × 9 = ( 5 × 9 ) + ( 1 × 9 ) = 54

false; 6×9=(6×2)+(6×4)=36
false; 6 × 9 = ( 6 × 2 ) + ( 6 × 4 ) = 36

false; 6×9=(4×5)+(2×4)=28

Answer 1

Niko's generalization states that a 6s fact can break into a 4s fact and a 2s fact. This means that if you can express \(6 \times 9\) as the sum of two other multiplication expressions, \(4 \times 9\) and \(2 \times 9\), it would support her generalization.

Let's evaluate the first option:

**true; 6×9=(4×9)+(2×9)=54**

Calculating both sides:
- \(6 \times 9 = 54\)
- \(4 \times 9 = 36\) and \(2 \times 9 = 18\)
- So, \(4 \times 9 + 2 \times 9 = 36 + 18 = 54\)

This statement is true.

Now let's analyze the other options:

**true; 6 × 9 = (5 × 9) + (1 × 9) = 54**
- \(6 \times 9 = 54\)
- \(5 \times 9 = 45\) and \(1 \times 9 = 9\)
- So, \(5 \times 9 + 1 \times 9 = 45 + 9 = 54\)

This statement is true, but it doesn't support Niko's generalization of breaking a 6s fact into a 4s and a 2s fact.

**false; 6×9=(6×2)+(6×4)=36**
- \(6 \times 9 = 54\)
- \(6 \times 2 = 12\) and \(6 \times 4 = 24\)
- So, \(6 \times 2 + 6 \times 4 = 12 + 24 = 36\)

This statement is false since it results in 36 instead of 54.

**false; 6×9=(4×5)+(2×4)=28**
- \(6 \times 9 = 54\)
- \(4 \times 5 = 20\) and \(2 \times 4 = 8\)
- So, \(4 \times 5 + 2 \times 4 = 20 + 8 = 28\)

This statement is false since it also results in 28 instead of 54.

The best response that supports Niko's generalization is:

**true; 6×9=(4×9)+(2×9)=54**