Final answer:
The question involves identifying non-equivalent mathematical expressions to a given expression. Expressions (15 - 1) × 29 and (10 × 29) - (6 × 29) are not equivalent to 16 × 29. Additionally, 74 × (60 - 1) is not equivalent to 74 × 59.
Step-by-step explanation:
The student's question is asking to identify which expressions are not equivalent to a given bolded expression in each scenario. Let's go through each part separately:
- 16 × 2929 sixteens: This is 16 times 29 which is the same.
- 16 × (30 – 1): Again, this is equivalent because (30 - 1) equals 29, yielding 16 times 29.
- (15 – 1) × 29: This is not equivalent because it results in (14 times 29) which is not the same as 16 times 29.
- (10 × 29) – (6 × 29): This simplifies to 16 times 29 minus 6 times 29, which is also not equivalent.
- 38 × 45
- (38 × 40) + (38 × 5): This is equivalent due to the distributive property, also known as multiplication over addition.
- 45 × (40 + 2): This is equivalent as (40 + 2) equals 42, so it simplifies to 45 times 38.
- 45 thirty-eights: This just refers to 45 times 38, which is equivalent.
- 74 × 59
- 74 × (50 + 9): This is equivalent because it simplifies to 74 times 59.
- 74 × (60 – 1): This is not equivalent, it would simplify to 74 times 59 minus 74, which is different.
- (74 × 5) + (74 × 9): This is equivalent based on the distributive property.
- 59 seventy-fours: This is equivalent as it represents 59 times 74.