Question

Докажите что произведение 1) 24*25 делится на 15 2)35*12 делится на 20 3)9*15*40 делится на 25 4)6*12*40 делится на 45

Answer 1

1) 24*25:15=600:15=40 2) 35*12:20=420:20=21 3) 9*15*40:25=135*40=5400:25=216 4) 6*12*40:45=72*40=2880:45=64

Answer 2

Claim 1: The product of 24 and 25 is divisible by 15.

To prove this claim, we need to check if the product of 24 and 25 is divisible by 15.

The product of 24 and 25 is 600. To determine if it is divisible by 15, we can check if 600 divided by 15 leaves no remainder.

600 divided by 15 equals 40, which means that the product of 24 and 25 is divisible by 15.

Therefore, the claim that the product of 24 and 25 is divisible by 15 is true.

Claim 2: The product of 35 and 12 is divisible by 20.

To prove this claim, we need to check if the product of 35 and 12 is divisible by 20.

The product of 35 and 12 is 420. To determine if it is divisible by 20, we can check if 420 divided by 20 leaves no remainder.

420 divided by 20 equals 21, which means that the product of 35 and 12 is divisible by 20.

Therefore, the claim that the product of 35 and 12 is divisible by 20 is true.

Claim 3: The product of 9, 15, and 40 is divisible by 25.

To prove this claim, we need to check if the product of 9, 15, and 40 is divisible by 25.

The product of 9, 15, and 40 is 5,400. To determine if it is divisible by 25, we can check if 5,400 divided by 25 leaves no remainder.

5,400 divided by 25 equals 216, which means that the product of 9, 15, and 40 is divisible by 25.

Therefore, the claim that the product of 9, 15, and 40 is divisible by 25 is true.

Claim 4: The product of 6, 12, and 40 is divisible by 45.

To prove this claim, we need to check if the product of 6, 12, and 40 is divisible by 45.

The product of 6, 12, and 40 is 28,800. To determine if it is divisible by 45, we can check if 28,800 divided by 45 leaves no remainder.

28,800 divided by 45 equals 640, which means that the product of 6, 12, and 40 is divisible by 45.

Therefore, the claim that the product of 6, 12, and 40 is divisible by 45 is true. In conclusion, all four claims have been proven to be true.