Which of the following equations is true?(1 point)

Responses

6 2/5÷3 1/6=32/5⋅6/19
6 Start Fraction 2 over 5 End Fraction divided by 3 Start Fraction 1 over 6 End Fraction equals Start Fraction 32 over 5 End Fraction times Start Fraction 6 over 19 End Fraction

10 1/3÷3 2/5=3/31 ⋅2/17
10 Start Fraction 1 over 3 End Fraction divided by 3 Start Fraction 2 over 5 End Fraction equals Start Fraction 3 over 31 End Fraction times Start Fraction 2 over 17 End Fraction

9 3/7÷4 3/4=66/7⋅19/4
9 Start Fraction 3 over 7 End Fraction divided by 4 Start Fraction 3 over 4 End Fraction equals Start Fraction 66 over 7 End Fraction times Start Fraction 19 over 4 End Fraction

8 2/9÷3 4/5=9/74⋅5/19

1 answer

To determine which of the equations is true, we need to calculate each side of the equations separately and compare them.

1. \(6 \frac{2}{5} \div 3 \frac{1}{6}\)

Convert to improper fractions:

  • \(6 \frac{2}{5} = \frac{32}{5}\)
  • \(3 \frac{1}{6} = \frac{19}{6}\)

Now perform the division: \[ \frac{32}{5} \div \frac{19}{6} = \frac{32}{5} \times \frac{6}{19} = \frac{32 \cdot 6}{5 \cdot 19} = \frac{192}{95} \]

Now let's check the right side: \[ \frac{32}{5} \cdot \frac{6}{19} = \frac{192}{95} \]

Both sides are equal, so this equation is true.

2. \(10 \frac{1}{3} \div 3 \frac{2}{5}\)

Convert to improper fractions:

  • \(10 \frac{1}{3} = \frac{31}{3}\)
  • \(3 \frac{2}{5} = \frac{17}{5}\)

Perform the division: \[ \frac{31}{3} \div \frac{17}{5} = \frac{31}{3} \times \frac{5}{17} = \frac{31 \cdot 5}{3 \cdot 17} = \frac{155}{51} \]

Now check the right side: \[ \frac{3}{31} \cdot \frac{2}{17} = \frac{6}{527} \]

The two sides are not equal.

3. \(9 \frac{3}{7} \div 4 \frac{3}{4}\)

Convert to improper fractions:

  • \(9 \frac{3}{7} = \frac{66}{7}\)
  • \(4 \frac{3}{4} = \frac{19}{4}\)

Perform the division: \[ \frac{66}{7} \div \frac{19}{4} = \frac{66}{7} \times \frac{4}{19} = \frac{66 \cdot 4}{7 \cdot 19} = \frac{264}{133} \]

Now check the right side: \[ \frac{66}{7} \cdot \frac{19}{4} = \frac{1254}{28} \quad \text{(not equal)} \]

4. \(8 \frac{2}{9} \div 3 \frac{4}{5}\)

Convert to improper fractions:

  • \(8 \frac{2}{9} = \frac{74}{9}\)
  • \(3 \frac{4}{5} = \frac{19}{5}\)

Perform the division: \[ \frac{74}{9} \div \frac{19}{5} = \frac{74}{9} \times \frac{5}{19} = \frac{370}{171} \]

Now check the right side: \[ \frac{9}{74} \cdot \frac{5}{19} = \frac{45}{1406} \]

The two sides are not equal.

Conclusion:

The only true equation among the provided options is: \[ 6 \frac{2}{5} \div 3 \frac{1}{6} = \frac{32}{5} \cdot \frac{6}{19} \]