Compare Fractions: Find the Missing Symbol Between 1/3 and 3/10

Video Solution

Solution Steps

00:00 Choose the appropriate sign

00:03 We want to find a common denominator

00:06 Therefore, we'll multiply each fraction by the denominator of the other fraction

00:09 Remember to multiply both numerator and denominator

00:19 Now we'll use the same method for the second fraction

00:22 Remember to multiply by the denominator of the second fraction

00:26 Remember to multiply both numerator and denominator

00:29 Now we have a common denominator between the fractions

00:35 When denominators are equal, the larger the numerator, the larger the fraction

00:40 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll compare the fractions $\frac{1}{3}$ and $\frac{3}{10}$ by finding a common denominator.

Let's follow these steps:

Step 1: Identify the denominators of the given fractions, which are 3 and 10.
Step 2: Calculate the least common denominator (LCD) of 3 and 10. Since 3 and 10 are co-prime, their product, 30, is the LCD.
Step 3: Adjust the fractions to have a common denominator of 30:

Convert $\frac{1}{3}$ to a fraction with denominator 30 by multiplying the numerator and the denominator by 10:

\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}

Convert $\frac{3}{10}$ to a fraction with denominator 30 by multiplying the numerator and the denominator by 3:

\frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30}

Step 4: Compare the numerators of the fractions: 10 (from $\frac{10}{30}$ ) and 9 (from $\frac{9}{30}$ ).
Since 10 is greater than 9, $\frac{10}{30}$ is greater than $\frac{9}{30}$ .
Thus, $\frac{1}{3}$ is greater than $\frac{3}{10}$ .

Therefore, the correct comparison sign is $>$ .