Solve: (3/5 ÷ 5/6) + 1/5 - Mixed Fraction Operations

Question

Solve the following exercise:

35:56+15=? \frac{3}{5}:\frac{5}{6}+\frac{1}{5}=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 Instead of division, we'll use multiplication by reciprocal
00:09 Flip between the numerator and denominator of the fraction
00:15 Make sure to multiply numerator with numerator and denominator with denominator
00:24 Calculate the multiplications
00:30 Now multiply this fraction by 5 to find the common denominator
00:41 Make sure to multiply both numerator and denominator
00:48 Calculate the multiplications
00:56 Divide by the common denominator
01:02 Calculate the numerator
01:05 And this is the solution to the question

Step-by-Step Solution

To solve the problem, we'll follow the outlined steps:

  • Step 1: Calculate the division 35:56 \frac{3}{5} : \frac{5}{6} .
  • Step 2: Add 15 \frac{1}{5} to the result from Step 1.
  • Step 3: Simplify the resulting fraction.

Now, let's work through each step:

Step 1: To divide 35 \frac{3}{5} by 56 \frac{5}{6} , we multiply by the reciprocal of 56 \frac{5}{6} . This gives us:

35×65=3×65×5=1825 \frac{3}{5} \times \frac{6}{5} = \frac{3 \times 6}{5 \times 5} = \frac{18}{25}

Step 2: Now, add 15 \frac{1}{5} to 1825 \frac{18}{25} . First, we convert 15 \frac{1}{5} to the same denominator as 1825 \frac{18}{25} :

15=525 \frac{1}{5} = \frac{5}{25}

Step 3: Add 1825 \frac{18}{25} and 525 \frac{5}{25} :

1825+525=18+525=2325 \frac{18}{25} + \frac{5}{25} = \frac{18 + 5}{25} = \frac{23}{25}

Thus, the solution to the problem is 2325\frac{23}{25}.

Answer

2325 \frac{23}{25}