Compare Fractions: Determine the Correct Sign Between 3/7 and 21/28

Question

Fill in the missing sign:

372128 \frac{3}{7}☐\frac{21}{28}

Video Solution

Solution Steps

00:00 Choose the appropriate sign
00:03 We want to reduce fraction 4 to get a common denominator
00:09 Remember to divide both numerator and denominator
00:14 Now we have a common denominator between the fractions
00:19 When denominators are equal, the larger the numerator, the larger the fraction
00:28 And this is the solution to the question

Step-by-Step Solution

< To solve this problem, we must determine which relational operator (<, >, = ) should be placed between the fractions 37\frac{3}{7} and 2128\frac{21}{28}.

Step 1: Simplify 2128\frac{21}{28}.

To simplify 2128\frac{21}{28}, find the greatest common divisor (GCD) of 21 and 28. Factors of 21 are 1, 3, 7, 21, and factors of 28 are 1, 2, 4, 7, 14, 28. The GCD is 7.

Divide both the numerator and denominator of 2128\frac{21}{28} by 7:

2128=21÷728÷7=34\frac{21}{28} = \frac{21 \div 7}{28 \div 7} = \frac{3}{4}.

Now we compare 37\frac{3}{7} and 34\frac{3}{4}.

Step 2: Convert both fractions to a common denominator for easy comparison. Use the least common multiple (LCM) of 7 and 4, which is 28.

- Convert 37\frac{3}{7} to have a denominator of 28:

37=3×47×4=1228\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}.

- 34\frac{3}{4} is already simplified and does not need to convert again, as we have considered LCM:

34=3×74×7=2128\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}.

Step 3: Compare the fractions 1228\frac{12}{28} and 2128\frac{21}{28}.

- Since \frac{12}{28} < \frac{21}{28}, therefore, \frac{3}{7} < \frac{21}{28}.

Hence, the missing sign is < .

Answer

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