Which number makes this comparison statement true? 6/5 < ----- < 1.33
Understand the Problem
The question is asking which number, when placed in the blank, makes the inequality true. The given inequality is comparing fractions and decimals with a specific range. We will need to evaluate each option to determine the correct answer.
Answer
The answer is \( \frac{5}{4} \).
Answer for screen readers
The correct answer is ( \frac{5}{4} ).
Steps to Solve
- Convert the left fraction to decimal
First, convert ( \frac{6}{5} ) to decimal form.
$$ \frac{6}{5} = 1.2 $$
- Identify the required inequality
Now we can set up the inequality using the value ( 1.2 ) and the upper limit ( 1.33 ):
$$ 1.2 < x < 1.33 $$
- Evaluate each option
Next, we will examine each option:
-
Option A: ( 0.295 )
( 1.2 < 0.295 < 1.33 ) (False) -
Option B: ( \frac{5}{4} )
Convert to decimal: $$ \frac{5}{4} = 1.25 $$
Check: $$ 1.2 < 1.25 < 1.33 \quad \text{(True)} $$ -
Option C: ( 0.675 )
( 1.2 < 0.675 < 1.33 ) (False) -
Option D: ( \frac{7}{8} )
Convert to decimal: $$ \frac{7}{8} = 0.875 $$
Check: $$ 1.2 < 0.875 < 1.33 \quad \text{(False)} $$
- Choose the correct option
The only number that makes the comparison true is ( \frac{5}{4} ).
The correct answer is ( \frac{5}{4} ).
More Information
This answer fits within the constraints of the inequality ( 1.2 < x < 1.33 ).
Tips
- Failing to convert fractions to decimals before comparison can lead to incorrect answers.
- Misinterpreting the inequality symbols can also cause mistakes.
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