To determine which number sentence is true, we need to evaluate each given statement step-by-step.
Statement A: [tex]\(4 \times (5 \times 2) = (4 \times 5) \times 2\)[/tex]
Evaluate both sides of the equation separately:
1. Left hand side: [tex]\(4 \times (5 \times 2)\)[/tex]
- [tex]\(5 \times 2 = 10\)[/tex]
- [tex]\(4 \times 10 = 40\)[/tex]
2. Right hand side: [tex]\((4 \times 5) \times 2\)[/tex]
- [tex]\(4 \times 5 = 20\)[/tex]
- [tex]\(20 \times 2 = 40\)[/tex]
Both sides are equal: [tex]\(40 = 40\)[/tex]
So, statement A is true.
Statement B: [tex]\(4 \times (5 \times 2) = 4 \times 5 + 2\)[/tex]
Evaluate both sides of the equation separately:
1. Left hand side: [tex]\(4 \times (5 \times 2)\)[/tex]
- [tex]\(5 \times 2 = 10\)[/tex]
- [tex]\(4 \times 10 = 40\)[/tex]
2. Right hand side: [tex]\(4 \times 5 + 2\)[/tex]
- [tex]\(4 \times 5 = 20\)[/tex]
- [tex]\(20 + 2 = 22\)[/tex]
Both sides are not equal: [tex]\(40 \neq 22\)[/tex]
So, statement B is false.
Statement C: [tex]\(4 \times (5 \times 2) = (4 + 5) \times 2\)[/tex]
Evaluate both sides of the equation separately:
1. Left hand side: [tex]\(4 \times (5 \times 2)\)[/tex]
- [tex]\(5 \times 2 = 10\)[/tex]
- [tex]\(4 \times 10 = 40\)[/tex]
2. Right hand side: [tex]\((4 + 5) \times 2\)[/tex]
- [tex]\(4 + 5 = 9\)[/tex]
- [tex]\(9 \times 2 = 18\)[/tex]
Both sides are not equal: [tex]\(40 \neq 18\)[/tex]
So, statement C is false.
Statement D: [tex]\(4 \times 5 = 4 \times 2\)[/tex]
Evaluate both sides of the equation separately:
1. Left hand side: [tex]\(4 \times 5 = 20\)[/tex]
2. Right hand side: [tex]\(4 \times 2 = 8\)[/tex]
Both sides are not equal: [tex]\(20 \neq 8\)[/tex]
So, statement D is false.
After evaluating all the statements, the only true statement is:
Statement A: [tex]\(4 \times (5 \times 2) = (4 \times 5) \times 2\)[/tex]
