High School

Which statements are true about adding 95 and 76 mentally? Check all that apply.

- 95 is 5 less than 100.
- 76 can be separated into [tex]5 + 71[/tex].
- [tex]95 + 5 + 76[/tex] is the same as [tex]95 + 76[/tex].
- [tex]95 + 5 + 71[/tex] is the same as [tex]95 + 76[/tex].
- [tex]95 + 76 = 181[/tex]

Answer :

Let's go through each of the statements step-by-step to determine whether they are true or false.

1. 95 is 5 less than 100.
- To verify this, we can add 5 to 95:
[tex]\(95 + 5 = 100\)[/tex].
- Therefore, the statement is true, as 95 is indeed 5 less than 100.

2. 76 can be separated into [tex]\(5 + 71\)[/tex].
- To verify this, add 5 and 71:
[tex]\(5 + 71 = 76\)[/tex].
- Therefore, the statement is true, since 76 can be broken down into the sum of 5 and 71.

3. [tex]\(95 + 5 + 76\)[/tex] is the same as [tex]\(95 + 76\)[/tex].
- Let's compute both expressions:
- [tex]\(95 + 5 + 76 = 176\)[/tex].
- [tex]\(95 + 76 = 171\)[/tex].
- These are not equal. Therefore, this statement is false.

4. [tex]\(95 + 5 + 71\)[/tex] is the same as [tex]\(95 + 76\)[/tex].
- Let's compute both expressions:
- [tex]\(95 + 5 + 71 = 171\)[/tex].
- [tex]\(95 + 76 = 171\)[/tex].
- These are equal. Therefore, this statement is true.

5. [tex]\(95 + 76 = 181\)[/tex].
- Let's compute the sum:
- [tex]\(95 + 76 = 171\)[/tex].
- Therefore, this statement is false as the sum is not 181.

So, the true statements are:
- 95 is 5 less than 100.
- 76 can be separated into [tex]\(5 + 71\)[/tex].
- [tex]\(95 + 5 + 71\)[/tex] is the same as [tex]\(95 + 76\)[/tex].

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