Solve Fraction Division: 2/5 ÷ 4/7 Step-by-Step

Question

Complete the following exercise:

25:47=? \frac{2}{5}:\frac{4}{7}=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 Instead of division, we'll use multiplication by the reciprocal
00:09 We'll swap the numerator and denominator of the fraction
00:16 Make sure to multiply numerator by numerator and denominator by denominator
00:21 Calculate the multiplications
00:24 Reduce the fraction as much as possible
00:27 Make sure to divide both numerator and denominator
00:32 Calculate the quotients
00:35 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll employ the division of fractions technique:

  • Step 1: Find the reciprocal of the divisor. Here, the divisor is 47\frac{4}{7}. Its reciprocal is 74\frac{7}{4}.
  • Step 2: Multiply the dividend 25\frac{2}{5} by the reciprocal of the divisor.
  • Step 3: Calculate 25×74\frac{2}{5} \times \frac{7}{4}.
  • Step 4: Simplify the result, if possible.

Now, let's work through these steps:

Step 1: The reciprocal of 47\frac{4}{7} is 74\frac{7}{4}.

Step 2: Multiply the fractions: 25×74=2×75×4=1420\frac{2}{5} \times \frac{7}{4} = \frac{2 \times 7}{5 \times 4} = \frac{14}{20}.

Step 3: Simplify 1420\frac{14}{20}. The greatest common divisor (GCD) of 14 and 20 is 2, so divide both the numerator and the denominator by 2:

1420=14÷220÷2=710\frac{14}{20} = \frac{14 \div 2}{20 \div 2} = \frac{7}{10}.

Therefore, the solution to the problem is 710\frac{7}{10}.

Answer

710 \frac{7}{10}