Find the quotient of the given fractions below with solutions

Find the quotient of the given fractions below with solutions: 1.) 7/8 divided by 1/60 2.) 1/6 divided by 5/12 3.) 5/12 divided by 1/60 4.) 12/5 divided by 1/6

The Correct Answer and Explanation is:

Let’s work through the division of fractions step by step for each problem. The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

1) 78÷160\frac{7}{8} \div \frac{1}{60}87​÷601​

To divide 78\frac{7}{8}87​ by 160\frac{1}{60}601​, we multiply 78\frac{7}{8}87​ by the reciprocal of 160\frac{1}{60}601​, which is 601\frac{60}{1}160​.78×601=7×608×1=4208\frac{7}{8} \times \frac{60}{1} = \frac{7 \times 60}{8 \times 1} = \frac{420}{8}87​×160​=8×17×60​=8420​

Now, simplify 4208\frac{420}{8}8420​. Divide both the numerator and denominator by 4 (the greatest common divisor):4208=1052\frac{420}{8} = \frac{105}{2}8420​=2105​

So, the result is 1052\frac{105}{2}2105​.

2) 16÷512\frac{1}{6} \div \frac{5}{12}61​÷125​

To divide 16\frac{1}{6}61​ by 512\frac{5}{12}125​, multiply 16\frac{1}{6}61​ by the reciprocal of 512\frac{5}{12}125​, which is 125\frac{12}{5}512​.16×125=1×126×5=1230\frac{1}{6} \times \frac{12}{5} = \frac{1 \times 12}{6 \times 5} = \frac{12}{30}61​×512​=6×51×12​=3012​

Simplify 1230\frac{12}{30}3012​ by dividing both the numerator and denominator by 6:1230=25\frac{12}{30} = \frac{2}{5}3012​=52​

So, the result is 25\frac{2}{5}52​.

3) 512÷160\frac{5}{12} \div \frac{1}{60}125​÷601​

To divide 512\frac{5}{12}125​ by 160\frac{1}{60}601​, multiply 512\frac{5}{12}125​ by the reciprocal of 160\frac{1}{60}601​, which is 601\frac{60}{1}160​.512×601=5×6012×1=30012\frac{5}{12} \times \frac{60}{1} = \frac{5 \times 60}{12 \times 1} = \frac{300}{12}125​×160​=12×15×60​=12300​

Simplify 30012\frac{300}{12}12300​ by dividing both the numerator and denominator by 12:30012=251=25\frac{300}{12} = \frac{25}{1} = 2512300​=125​=25

So, the result is 252525.

4) 125÷16\frac{12}{5} \div \frac{1}{6}512​÷61​

To divide 125\frac{12}{5}512​ by 16\frac{1}{6}61​, multiply 125\frac{12}{5}512​ by the reciprocal of 16\frac{1}{6}61​, which is 61\frac{6}{1}16​.125×61=12×65×1=725\frac{12}{5} \times \frac{6}{1} = \frac{12 \times 6}{5 \times 1} = \frac{72}{5}512​×16​=5×112×6​=572​

So, the result is 725\frac{72}{5}572​.

Summary of Results:

1. 78÷160=1052\frac{7}{8} \div \frac{1}{60} = \frac{105}{2}87​÷601​=2105​
2. 16÷512=25\frac{1}{6} \div \frac{5}{12} = \frac{2}{5}61​÷125​=52​
3. 512÷160=25\frac{5}{12} \div \frac{1}{60} = 25125​÷601​=25
4. 125÷16=725\frac{12}{5} \div \frac{1}{6} = \frac{72}{5}512​÷61​=572​

The key to these problems is remembering that division of fractions involves multiplying by the reciprocal, which allows us to transform the division operation into a simple multiplication problem.