Number Comparison Problem: Determining Which Value is Larger

Video Solution

Solution Steps

00:02 Let's start by finding the largest fraction.

00:13 First, multiply the first fraction by the second fraction's denominator to get a common base.

00:24 Now, multiply the second fraction by the first fraction's denominator.

00:33 With equal denominators, compare the numerators. The bigger one shows the larger fraction.

00:51 You can reduce the fraction by dividing by 2 to find a common base.

00:58 Both fractions are equal here.

01:03 Again, multiply the first fraction by the other’s bottom number for a common base.

01:10 Multiply the other fraction by the first one's denominator.

01:18 Remember, with equal bottoms, a larger top number is the larger fraction.

01:23 And this is how we solve the problem. Great job!

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 $\frac{2}{3}$ .