Math  /  Numbers & Operations

QuestionKareem wrote the expressions shown below. 3.272.72.94.8\lceil 3.27\lfloor 2.7\rfloor\lceil 2.9\rceil\lfloor 4.8\rfloor Which pair is equivalent? 2.7\lfloor 2.7\rfloor and 〔3.2〕 〔2.97 and 【2.7〕 3.2\lceil 3.2\rceil and 2.9\lceil 2.9\rceil 4.8\lfloor 4.8\rfloor and 3.2\lceil 3.2\rceil

Studdy Solution

STEP 1

What is this asking? We need to find which pair of Kareem's expressions are equivalent, remembering that x\lfloor x \rfloor means round *down* to the nearest integer, and x\lceil x \rceil means round *up* to the nearest integer. Watch out! Don't mix up the rounding up and rounding down symbols!
Also, don't forget that even though some numbers might round to the same integer, the original numbers aren't necessarily equivalent!

STEP 2

1. Evaluate each expression.
2. Compare the results.

STEP 3

We're rounding *down*, so 2.7=2\lfloor 2.7 \rfloor = 2.
We round down to the nearest integer!

STEP 4

This time we're rounding *up*, so 3.2=4\lceil 3.2 \rceil = 4.
Up, up, and away!

STEP 5

Rounding up, we get 2.9=3\lceil 2.9 \rceil = 3.
Almost at 3 already!

STEP 6

Rounding down, we have 4.8=4\lfloor 4.8 \rfloor = 4.
So close to 5, but not quite!

STEP 7

Rounding up gives us 3.27=4\lceil 3.27 \rceil = 4.
Remember, we always round up with those ceiling brackets!

STEP 8

The first pair is 2.7\lfloor 2.7 \rfloor and 3.2\lceil 3.2 \rceil, which we found to be 22 and 44, respectively.
Not equivalent!

STEP 9

The second pair is 2.9\lceil 2.9 \rceil and 2.7\lfloor 2.7 \rfloor, which we found to be 33 and 22, respectively.
Still not equivalent!

STEP 10

The third pair is 3.2\lceil 3.2 \rceil and 2.9\lceil 2.9 \rceil, which we found to be 44 and 33, respectively.
Nope, not the same!

STEP 11

The fourth pair is 4.8\lfloor 4.8 \rfloor and 3.2\lceil 3.2 \rceil, which we found to be 44 and 44, respectively.
Bingo! These are equivalent!

STEP 12

The equivalent pair is 4.8\lfloor 4.8 \rfloor and 3.2\lceil 3.2 \rceil.

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