Fill in the missing sign:
Fill in the missing sign:
\( \frac{3}{4}☐\frac{1}{9} \)
Fill in the missing sign:
\( \frac{1}{3}☐\frac{3}{10} \)
Fill in the missing sign:
\( \frac{3}{4}☐\frac{2}{6} \)
Fill in the missing sign:
\( \frac{1}{5}☐\frac{3}{4} \)
Fill in the missing sign:
\( \frac{2}{3}☐\frac{6}{4} \)
Fill in the missing sign:
To determine the correct inequality sign to compare and , we'll use the technique of cross-multiplication. This method involves multiplying the numerator of each fraction by the denominator of the other fraction. By calculating and comparing these products, we can determine the relative size of the fractions.
Let's perform the cross-multiplication:
Now we compare these two results. Since is greater than , we conclude that:
Therefore, the correct inequality sign to fill in the blank is .
>
Fill in the missing sign:
To solve this problem, we'll compare the fractions and by finding a common denominator.
Let's follow these steps:
Therefore, the correct comparison sign is .
>
Fill in the missing sign:
To solve this problem, we will follow these steps:
Now, let's work through each step:
Step 1: The fractions we have are and .
Step 2: Simplify . The greatest common factor of 2 and 6 is 2, so .
Step 3: Find a common denominator for and . The least common multiple of 4 and 3 is 12.
Step 4: Convert each fraction to have the common denominator:
Step 5: Compare the numerators of the converted fractions:
Now, compare and .
Since , it follows that .
Therefore, , and hence .
The correct comparison sign is .
>
Fill in the missing sign:
To compare the fractions and , we'll use the following steps:
Step 1: The denominators of the two fractions are 5 and 4. To find a common denominator, we multiply these together, getting . So, our common denominator is 20.
Step 2: Convert each fraction to have the denominator of 20.
Step 3: Now compare the numerators of the equivalent fractions:
compared to (both having the denominator of 20):
implies .
Therefore, .
Thus, the correct mathematical sign to fill in is .
Therefore, the missing sign in the expression is .
<
Fill in the missing sign:
To solve this problem, we will use cross-multiplication to compare the two fractions and .
Now, let's work through the steps:
Step 1: Cross-multiply the two fractions:
Step 2: Compare the resulting products:
Since , it follows that .
Therefore, the solution to the problem is .
<
Fill in the missing sign:
\( \frac{2}{15}☐\frac{1}{3} \)
Fill in the missing sign:
\( \frac{3}{7}☐\frac{1}{6} \)
Fill in the missing sign:
\( \frac{2}{9}☐\frac{3}{14} \)
Fill in the missing sign:
\( \frac{3}{8}☐\frac{1}{9} \)
Fill in the missing sign:
\( \frac{3}{7}☐\frac{1}{8} \)
Fill in the missing sign:
To solve this problem, we'll convert both fractions to have a common denominator and compare:
Therefore, the correct sign to fill in the missing slot is .
Consequently, the completed expression is .
Therefore, the solution to the problem is .
<
Fill in the missing sign:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Determine a common denominator for and . The common denominator is the product of the denominators .
Step 2: Convert each fraction to have this common denominator:
- Convert : Multiply the numerator and denominator by 6: .
- Convert : Multiply the numerator and denominator by 7: .
Step 3: Compare the numerators: and .
Since , we have . Thus, .
Therefore, the correct inequality sign is .
>
Fill in the missing sign:
To solve this problem, we'll compare the fractions and by finding a common denominator:
Therefore, the fraction is greater than , and the correct inequality sign is .
Hence, the answer is .
>
Fill in the missing sign:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: The denominators of the given fractions are 8 and 9. The least common multiple (LCM) of these numbers is 72. Therefore, the least common denominator (LCD) is 72.
Step 2: Convert each fraction to an equivalent fraction with a denominator of 72.
Step 3: Now compare the numerators of and .
Since is greater than , it follows that is greater than .
Step 4: Therefore, the correct inequality sign to fill the blank is .
Thus, we conclude that .
The correct answer is .
>
Fill in the missing sign:
To solve this problem, we will compare the fractions and by converting them to have a common denominator.
Step 1: Find the least common multiple (LCM) of the denominators 7 and 8. Since 7 and 8 are coprime (have no common factors other than 1), the LCM is simply the product of the two numbers:
Step 2: Convert each fraction to an equivalent fraction with the common denominator of 56.
Convert :
Convert :
Step 3: Compare the new numerators:
Since 24 > 7, we conclude that \frac{24}{56} > \frac{7}{56}.
Therefore, the original inequality we are solving is:
\frac{3}{7} > \frac{1}{8}
Thus, the correct sign to fill in the blank is \bm{>}.
>