Number Comparison Problem: Determining Which Value is Larger

Video Solution

Solution Steps

00:00 Find the largest fraction

00:11 Multiply this fraction by the denominator of the other to find a common denominator

00:22 Multiply the second fraction by the denominator of the first

00:31 When the denominator is equal, the larger numerator indicates the larger fraction

00:49 Reduce this fraction by 2 to get a common denominator

00:56 We can see that these fractions are equal

01:01 Multiply this fraction by the denominator of the other to find a common denominator

01:08 Multiply the second fraction by the denominator of the first

01:16 When the denominator is equal, the larger numerator indicates the larger fraction

01:21 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will compare the given fractions to determine which is largest:

Compare $\frac{2}{3}$ and $\frac{7}{11}$ :
- Cross multiply: $2 \times 11 = 22$ and $3 \times 7 = 21$ .
  Since $22 > 21$ , $\frac{2}{3}$ is larger than $\frac{7}{11}$ .
Compare $\frac{2}{3}$ and $\frac{6}{10}$ :
- Simplify $\frac{6}{10} = \frac{3}{5}$ .
  Cross multiply: $2 \times 5 = 10$ and $3 \times 3 = 9$ .
  Since $10 > 9$ , $\frac{2}{3}$ is larger than $\frac{3}{5}$ (same as $\frac{6}{10}$ ).
To confirm, compare $\frac{2}{3}$ and $\frac{3}{5}$ again directly:
- Cross multiply: $2 \times 5 = 10$ and $3 \times 3 = 9$ .
  Since $10 > 9$ , $\frac{2}{3}$ is also larger than $\frac{3}{5}$ .

Therefore, the largest fraction of all given choices is indeed $\frac{2}{3}$ .