Compare Fractions: Determine the Symbol Between 2/9 and 3/14

Video Solution

Solution Steps

00:00 Choose the appropriate sign

00:03 We want to find a common denominator

00:06 So we'll multiply each fraction by the denominator of the second fraction

00:09 Remember to multiply both numerator and denominator

00:19 Now let's use the same method for the second fraction

00:24 Remember to multiply by the denominator of the second fraction

00:27 Remember to multiply both numerator and denominator

00:31 Now we have a common denominator between the fractions

00:37 When denominators are equal, the larger the numerator, the larger the fraction

00:45 And that's the solution to the question

Step-by-Step Solution

To solve this problem, we'll compare the fractions $\frac{2}{9}$ and $\frac{3}{14}$ by finding a common denominator:

Step 1: Find the common denominator. The denominators are $9$ and $14$ . The least common multiple of $9$ and $14$ is $126$ .
Step 2: Convert each fraction to an equivalent fraction with a denominator of $126$ .
For $\frac{2}{9}$ : $\frac{2}{9} = \frac{2 \times 14}{9 \times 14} = \frac{28}{126}$ .
For $\frac{3}{14}$ : $\frac{3}{14} = \frac{3 \times 9}{14 \times 9} = \frac{27}{126}$ .
Step 3: Compare the numerators of the equivalent fractions. $28 > 27$ , so $\frac{28}{126} > \frac{27}{126}$ .

Therefore, the fraction $\frac{2}{9}$ is greater than $\frac{3}{14}$ , and the correct inequality sign is $>$ .

Hence, the answer is $\frac{2}{9} > \frac{3}{14}$ .