Solve: Division of Mixed Numbers 5 4/5 ÷ 2 1/10

Video Solution

Solution Steps

00:04 Let's start by solving the problem.

00:07 First, we need to convert any mixed fractions into improper fractions.

00:31 Next, express the division as a fraction, like a numerator over a denominator.

00:42 Now, multiply by the reciprocal of the divisor. Just flip it upside down.

00:50 Great! Let's calculate the numerator by multiplying the top numbers.

00:57 Now, let's convert the result back to a mixed fraction.

01:01 Break down 290 into 210 plus 80, just to make it simpler.

01:08 Separate the fraction into a whole number part and a remainder.

01:14 Finally, reduce or simplify any parts that can be simplified.

01:23 Convert everything into a whole number, and combine it with the mixed number.

01:28 And there we have it, that's the solution to our question!

Step-by-Step Solution

To solve the problem $5\frac{4}{5} \div 2\frac{1}{10}$ , we follow these steps:

Step 1: Convert mixed numbers to improper fractions.
$5\frac{4}{5} = \frac{5 \times 5 + 4}{5} = \frac{25 + 4}{5} = \frac{29}{5}$
$2\frac{1}{10} = \frac{2 \times 10 + 1}{10} = \frac{20 + 1}{10} = \frac{21}{10}$
Step 2: Divide $\frac{29}{5}$ by $\frac{21}{10}$ by multiplying by the reciprocal.
$\frac{29}{5} \div \frac{21}{10} = \frac{29}{5} \times \frac{10}{21}$
Step 3: Multiply the fractions and simplify.
$\frac{29}{5} \times \frac{10}{21} = \frac{29 \times 10}{5 \times 21} = \frac{290}{105}$
Step 4: Simplify $\frac{290}{105}$ .
Find the greatest common divisor (GCD) of 290 and 105. The GCD is 5.
$\frac{290 \div 5}{105 \div 5} = \frac{58}{21}$
Step 5: Convert the improper fraction $\frac{58}{21}$ into a mixed number.
$58 \div 21 = 2$ remainder $16$ , so $\frac{58}{21} = 2\frac{16}{21}$

Therefore, the solution is $2\frac{16}{21}$ .