Test these conjectures. Give three examples. Explain if the

conjecture is correct or incorrect.

1. If a number is divisible by 4, it is always an even number._________________________________

2. All multiples of 5 have a 5 in the ones place.__________________________________

3. If a number has a 9 in the ones place, it is always divisible by 3.________________________________

4. The least common denominator of two fractions is always greater than the
denominators of the fractions.______________________________

5. Write a conjecture about the product of two odd numbers. Then test your
conjecture.__________________________________________________________

6. How is testing a conjecture like finding a statement to be true
or false? How is it different?_______________________________________________________________________________________________________________________

1-incorrect ex.26,106, and 102

2-incorrect ex.110,100,and 20
3-incorrect ex.29,19,and 49
4-i'm not positive
5-the product of two odd numbers will not be divisible by a positive number. (i'm not sure)i think it's correct
6-it is the same because you are finding if the conjecture works in all case or no cases or in sometimes. it is different because in some case it may be sometimes but you don't have that option.

4. The LCD may be the same as the denominator of one of the fractions. It will never be less than both of them.

5. The product of two odd numbers is always odd. For some m and n, let the two numbers be (2m+1) and (2n+1). Why? Any multiple of 2 is even. Add 1 to make an odd number. Multiply the two numbers and get 2mn + 2m + 2n + 1 = 2(mn+m+n)+1. This is odd because it is one more than an even number.

6. Testing a conjecture is often easy. Just try some values. Proving it is true or false is usually more involved, as in the statement #5 above.

Inncorect-because twenty eight divided by four is seven and seven is not an even number.

some of the answers don't even make sense.

I love you thank you. You really helped my kid get better at math

1. To test the conjecture "If a number is divisible by 4, it is always an even number," we can take three examples:

Example 1: 12. This number is divisible by 4 since 12 divided by 4 is equal to 3. It is also an even number since it can be divided by 2 without leaving a remainder.

Example 2: 21. This number is not divisible by 4 since 21 divided by 4 results in a remainder of 1. Therefore, the conjecture is incorrect in this case.

Example 3: 8. This number is divisible by 4 since 8 divided by 4 is equal to 2. It is also an even number since it can be divided by 2 without leaving a remainder.

Based on these examples, we can see that the conjecture is incorrect, as not all numbers divisible by 4 are even.

2. To test the conjecture "All multiples of 5 have a 5 in the ones place," we can take three examples:

Example 1: 10. This number is a multiple of 5 since 10 divided by 5 is equal to 2. However, it does not have a 5 in the ones place as the ones digit is 0.

Example 2: 25. This number is a multiple of 5 since 25 divided by 5 is equal to 5. It does have a 5 in the ones place.

Example 3: 45. This number is a multiple of 5 since 45 divided by 5 is equal to 9. It does have a 5 in the ones place.

Based on these examples, we can see that the conjecture is correct, as all multiples of 5 do indeed have a 5 in the ones place.

3. To test the conjecture "If a number has a 9 in the ones place, it is always divisible by 3," we can take three examples:

Example 1: 29. This number has a 9 in the ones place, but it is not divisible by 3 since 29 divided by 3 results in a remainder of 2. Therefore, the conjecture is incorrect in this case.

Example 2: 39. This number has a 9 in the ones place and is divisible by 3 since 39 divided by 3 is equal to 13.

Example 3: 49. This number has a 9 in the ones place, but it is not divisible by 3 since 49 divided by 3 results in a remainder of 1.

Based on these examples, we can see that the conjecture is incorrect, as not all numbers with a 9 in the ones place are divisible by 3.

4. To test the conjecture "The least common denominator of two fractions is always greater than the denominators of the fractions," we need to work with specific fractions.

Example 1: Fractions with denominators 4 and 6. The least common denominator is 12, which is greater than both 4 and 6. Therefore, the conjecture is correct in this case.

Example 2: Fractions with denominators 3 and 9. The least common denominator is 9, which is equal to one of the denominators. Therefore, the conjecture is incorrect in this case.

Example 3: Fractions with denominators 2 and 8. The least common denominator is 8, which is equal to one of the denominators. Therefore, the conjecture is incorrect in this case.

Based on these examples, we can see that the conjecture is incorrect, as the least common denominator may or may not be greater than the denominators of the fractions.

5. Conjecture: The product of two odd numbers is always odd.

To test this conjecture, we can take three examples:

Example 1: 3 * 3 = 9. The product of two odd numbers is odd.

Example 2: 5 * 7 = 35. The product of two odd numbers is odd.

Example 3: 9 * 11 = 99. The product of two odd numbers is odd.

Based on these examples, we can conclude that the conjecture is correct, as the product of any two odd numbers is indeed odd.

6. Testing a conjecture is similar to finding a statement to be true or false because it involves gathering evidence or examples that support or contradict the conjecture. Both processes require examining specific cases to determine the validity of the statement or conjecture.

However, testing a conjecture is different in that it involves making an educated guess or hypothesis about a general relationship or pattern, whereas finding a statement to be true or false typically involves assessing the truth value of a specific statement or statement form. Additionally, testing a conjecture often requires examining multiple cases or examples to make a conclusion, whereas finding a statement to be true or false may involve logical reasoning or proof techniques.