Compare Fractions: Find the Missing Symbol Between 4/6 and 3/4

Fill in the missing sign:

4634 \frac{4}{6}☐\frac{3}{4}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:03 We want to find a common denominator
00:06 We'll multiply each fraction so the denominator will be 12, the lowest common denominator
00:09 Therefore we'll multiply this fraction by 2
00:12 Remember to multiply both numerator and denominator
00:18 Now we'll use the same method for the second fraction, but multiply by 3
00:23 Remember to multiply both numerator and denominator
00:29 Now we have a common denominator between the fractions
00:33 When denominators are equal, the larger the numerator, the larger the fraction
00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing sign:

4634 \frac{4}{6}☐\frac{3}{4}

2

Step-by-step solution

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

  • Step 1: Identify the given fractions 46 \frac{4}{6} and 34 \frac{3}{4} .
  • Step 2: Calculate the least common denominator (LCD) of 6 and 4.
  • Step 3: Convert each fraction to have the common denominator and compare numerators.

Now, let's work through these steps:

Step 1: The given fractions are 46 \frac{4}{6} and 34 \frac{3}{4} .

Step 2: Find the least common denominator of 6 and 4. The prime factorization of 6 is 2×3 2 \times 3 and of 4 is 22 2^2 . The LCD is 22×3=12 2^2 \times 3 = 12 .

Step 3: Convert each fraction to this common denominator.

  • Convert 46 \frac{4}{6} to have a denominator of 12: Multiply both numerator and denominator by 2 to get 4×26×2=812 \frac{4 \times 2}{6 \times 2} = \frac{8}{12} .
  • Convert 34 \frac{3}{4} to have a denominator of 12: Multiply both numerator and denominator by 3 to get 3×34×3=912 \frac{3 \times 3}{4 \times 3} = \frac{9}{12} .

Compare the numerators: 8 and 9. Since 8 is less than 9, we find that 46<34 \frac{4}{6} < \frac{3}{4} .

Therefore, the correct sign to fill in is < < , and the correct answer is:

46<34 \frac{4}{6} < \frac{3}{4} .

3

Final Answer

< <

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

\( \frac{1}{2}☐\frac{2}{4} \)

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