Compare Fractions: Finding the Missing Sign Between 3/7 and 1/8

Question

Fill in the missing sign:

3718 \frac{3}{7}☐\frac{1}{8}

Video Solution

Solution Steps

00:00 Choose the appropriate sign
00:03 We want to find a common denominator
00:06 So we'll multiply each fraction by the denominator of the second fraction
00:09 Remember to multiply both numerator and denominator
00:20 Now we'll use the same method for the second fraction
00:23 Remember to multiply by the denominator of the second fraction
00:27 Remember to multiply both numerator and denominator
00:32 Now we have a common denominator between the fractions
00:37 When denominators are equal, the larger the numerator, the larger the fraction
00:44 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will compare the fractions 37\frac{3}{7} and 18\frac{1}{8} by converting them to have a common denominator.

Step 1: Find the least common multiple (LCM) of the denominators 7 and 8. Since 7 and 8 are coprime (have no common factors other than 1), the LCM is simply the product of the two numbers:

LCM(7,8)=7×8=56 \text{LCM}(7, 8) = 7 \times 8 = 56

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 56.

  • Convert 37\frac{3}{7}:

  • 37=3×87×8=2456 \frac{3}{7} = \frac{3 \times 8}{7 \times 8} = \frac{24}{56}

  • Convert 18\frac{1}{8}:

  • 18=1×78×7=756 \frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56}

Step 3: Compare the new numerators:

2456and756 \frac{24}{56} \quad \text{and} \quad \frac{7}{56}

Since 24 > 7, we conclude that \frac{24}{56} > \frac{7}{56}.

Therefore, the original inequality we are solving is:

\frac{3}{7} > \frac{1}{8}

Thus, the correct sign to fill in the blank is \bm{>}.

Answer

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