Examples with solutions for Comparing Fractions: Fractions with common denominators

Exercise #1

Fill in the missing sign:

6737 \frac{6}{7}☐\frac{3}{7}

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Identify the two fractions: 67 \frac{6}{7} and 37 \frac{3}{7} .

  • Since both fractions have a common denominator, compare the numerators directly: 6 and 3.

  • Determine that the numerator 6 is greater than 3.

  • Based on this comparison, the fraction 67 \frac{6}{7} is greater than 37 \frac{3}{7} .

  • Thus, the correct sign to fill in the blank is >>.

The correct answer to the problem is > > .

Answer

>

Exercise #2

Fill in the missing sign:

2878 \frac{2}{8}☐\frac{7}{8}

Video Solution

Step-by-Step Solution

To solve the problem, we will compare two fractions: 28\frac{2}{8} and 78\frac{7}{8}.

Both fractions have the same denominator (8), which allows us to directly compare the numerators. Therefore, we need only consider the values of the numerators to understand the relationship between the two fractions.

  • Step 1: Identify the numerators. For 28\frac{2}{8}, the numerator is 2. For 78\frac{7}{8}, the numerator is 7.
  • Step 2: Compare the numerators. We observe that 2<72 < 7.

Since 2 is less than 7, it follows that 28\frac{2}{8} is less than 78\frac{7}{8}.

Therefore, the correct sign to place between 28\frac{2}{8} and 78\frac{7}{8} is <<.

The solution to the problem is < < .

Answer

<

Exercise #3

Fill in the missing sign:

310110 \frac{3}{10}☐\frac{1}{10}

Video Solution

Step-by-Step Solution

To solve this problem, we need to determine which of the two fractions, 310\frac{3}{10} and 110\frac{1}{10}, is greater. Since both fractions have the same denominator, the larger fraction will be the one with the larger numerator.

We'll follow these steps:

  • Step 1: Identify the numerators of the two fractions. For 310\frac{3}{10}, the numerator is 3. For 110\frac{1}{10}, the numerator is 1.
  • Step 2: Compare the numerators. Since 3 is greater than 1, this means that 310\frac{3}{10} is greater than 110\frac{1}{10}.

Therefore, the correct mathematical sign to fill in the blank is >>.

Thus, the complete inequality is: 310>110\frac{3}{10} > \frac{1}{10}.

The correct answer is choice 2: 310>110\frac{3}{10} > \frac{1}{10}.

Answer

>

Exercise #4

Fill in the missing sign:

5939 \frac{5}{9}☐\frac{3}{9}

Video Solution

Step-by-Step Solution

To compare fractions with the same denominator, focus on the numerators:

  • Given fractions: 59\frac{5}{9} and 39\frac{3}{9}
  • Since both fractions have the same denominator (9), we only need to compare the numerators.
  • Numerator of the first fraction is 5, and the numerator of the second fraction is 3.
  • Since 5 is greater than 3, 59\frac{5}{9} is greater than 39\frac{3}{9}.

Therefore, the missing sign that correctly compares the two fractions is >>, so the correct statement is:

59>39\frac{5}{9} > \frac{3}{9}.

Answer

>

Exercise #5

Fill in the missing symbol:


4717 \frac{4}{7}☐\frac{1}{7}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given fractions, 47 \frac{4}{7} and 17 \frac{1}{7} .
  • Step 2: Note that both fractions share the same denominator of 7.
  • Step 3: Compare the numerators of the fractions, 4 and 1.

Now, let's work through each step:
Step 1: The problem provides us with the fractions 47 \frac{4}{7} and 17 \frac{1}{7} .
Step 2: We can compare the numerators directly since the denominators are the same. The numerators are 4 and 1, respectively.
Step 3: Since 4 is greater than 1, 47 \frac{4}{7} is greater than 17 \frac{1}{7} .

Therefore, the correct comparison symbol to fill in the blank is > > .

Answer

>

Exercise #6

Fill in the missing sign:

1323 \frac{1}{3}☐\frac{2}{3}

Video Solution

Step-by-Step Solution

To find the correct comparison sign for the fractions 13\frac{1}{3} and 23\frac{2}{3}, follow these logical steps:

  • Step 1: Look at the fractions 13\frac{1}{3} and 23\frac{2}{3}. Both fractions have the same denominator, which is 3.
  • Step 2: Identify the numerators of the fractions. The numerator of 13\frac{1}{3} is 1, and the numerator of 23\frac{2}{3} is 2.
  • Step 3: Compare these numerators. Since 1 is less than 2, we deduce that 13<23\frac{1}{3} \lt \frac{2}{3}.

Therefore, the missing sign to correctly complete the expression 1323\frac{1}{3} ☒ \frac{2}{3} is <\lt. Thus, the solution to the problem is 13<23 \frac{1}{3} \lt \frac{2}{3} .

Answer

<

Exercise #7

Fill in the missing answer:

7424 \frac{7}{4}☐\frac{2}{4}

Video Solution

Step-by-Step Solution

Let's solve the problem step-by-step:

Both fractions in the problem, 74 \frac{7}{4} and 24 \frac{2}{4} , have the same denominator. This allows us to directly compare their numerators.

The numerators are 7 and 2, respectively. Therefore, we need to determine whether 7 is less than, greater than, or equal to 2.

Comparing 7 and 2:

  • 7>2 7 > 2

Since 7 is greater than 2, it follows that:

  • 74>24 \frac{7}{4} > \frac{2}{4}

The correct inequality symbol to fill in the blank is > > .

Thus, the solution to the problem is 74>24 \frac{7}{4} > \frac{2}{4} .

Therefore, the correct choice from the available options is choice 2: > > .

Answer

>

Exercise #8

Fill in the missing sign:

2565 \frac{2}{5}☐\frac{6}{5}

Video Solution

Step-by-Step Solution

To solve this problem, we need to compare two fractions with the same denominator and determine the appropriate comparison sign:

  • Step 1: Notice that both fractions, 25 \frac{2}{5} and 65 \frac{6}{5} , have the same denominator, 5 5 .
  • Step 2: Focus on comparing the numerators of both fractions: 2 2 and 6 6 .
  • Step 3: Since 2 2 is less than 6 6 , it follows that the fraction 25 \frac{2}{5} is less than 65 \frac{6}{5} .

Therefore, the correct comparison sign to fill in the blank is < < .

The missing sign is < < .

Answer

<

Exercise #9

Fill in the missing sign:

19327 \frac{1}{9}☐\frac{3}{27}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Simplify each fraction.
  • Step 2: Compare the simplified fractions.

Now, let's work through each step:
Step 1: Simplify the fractions.
- The fraction 19\frac{1}{9} is already in its simplest form.
- The fraction 327\frac{3}{27} can be simplified by dividing both the numerator and the denominator by 3, resulting in 19\frac{1}{9}.

Step 2: Compare the simplified fractions.
Both simplified fractions are 19\frac{1}{9} and 19\frac{1}{9}, which are equal.

Therefore, the correct sign to fill in is = = .

Answer

= =

Exercise #10

Fill in the missing sign:

28416 \frac{2}{8}☐\frac{4}{16}

Video Solution

Step-by-Step Solution

We need to compare the fractions 28 \frac{2}{8} and 416 \frac{4}{16} . To do this, we'll simplify each fraction to see if they are equal or if one is greater than the other.

Step 1: Simplify 28 \frac{2}{8}
To simplify, find the greatest common divisor (GCD) of 2 and 8, which is 2. Divide the numerator and denominator by this GCD:
28=2÷28÷2=14 \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}

Step 2: Simplify 416 \frac{4}{16}
Similarly, find the GCD of 4 and 16, which is 4. Divide both the numerator and denominator by this GCD:
416=4÷416÷4=14 \frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4}

Both fractions simplify to 14 \frac{1}{4} . Thus, they are equal.

Conclusion:
Since the simplified forms of both fractions are equal, the correct sign to fill in is = = .

Therefore, the solution to the problem is = = .

Answer

= =