Please show work
6 1/6 ÷ 2 3/10
in what form:
decimal
fraction
6 1/6=6*6+1/6=37/6
2 3/10=2*10+3/10=23/10
now
(37/6)/(23/10)
=37/6*10/23 =37*10/6*23 =370/138
To divide fractions, we'll need to follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
Step 2: Find the reciprocal of the second fraction.
Step 3: Multiply the first fraction by the reciprocal.
Step 4: Simplify the resulting fraction, if possible.
Now let's apply these steps to the given expression:
Step 1: Converting mixed numbers to improper fractions:
6 1/6 = (6 × 6 + 1) / 6 = 37/6
2 3/10 = (2 × 10 + 3) / 10 = 23/10
Step 2: Finding the reciprocal of the second fraction:
Reciprocal of 23/10 = 10/23
Step 3: Multiplying the first fraction by the reciprocal:
37/6 × 10/23 = (37 × 10) / (6 × 23) = 370/138
Step 4: Simplifying the resulting fraction:
To simplify the fraction, we need to find their greatest common divisor (GCD). In this case, both 370 and 138 are divisible by 2, so we can simplify further.
370 ÷ 2 = 185
138 ÷ 2 = 69
Therefore, the simplified fraction is:
370/138 = 185/69
So the final result of 6 1/6 ÷ 2 3/10, when shown in work, is 185/69.