what is 3/16 divided by 1/4 fraction form
The Correct Answer and Explanation is:
Answer: 316÷14=34\frac{3}{16} \div \frac{1}{4} = \frac{3}{4}163÷41=43
Explanation:
To divide fractions, follow a consistent rule: multiply the first fraction by the reciprocal of the second. A reciprocal of a fraction is created by swapping the numerator and the denominator. For instance, the reciprocal of 14\frac{1}{4}41 is 41\frac{4}{1}14.
The original problem is: 316÷14\frac{3}{16} \div \frac{1}{4}163÷41
Applying the rule for dividing fractions: 316÷14=316×41\frac{3}{16} \div \frac{1}{4} = \frac{3}{16} \times \frac{4}{1}163÷41=163×14
Next, multiply the numerators together: 3×4=123 \times 4 = 123×4=12
Then multiply the denominators: 16×1=1616 \times 1 = 1616×1=16
So the product becomes: 1216\frac{12}{16}1612
This fraction is not in its simplest form. To simplify, divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 12 and 16 is 4.
Divide both: 12÷416÷4=34\frac{12 \div 4}{16 \div 4} = \frac{3}{4}16÷412÷4=43
Thus: 316÷14=34\frac{3}{16} \div \frac{1}{4} = \frac{3}{4}163÷41=43
This result can be interpreted as asking, “How many times does one-fourth fit into three-sixteenths?” Since 14\frac{1}{4}41 is larger than 316\frac{3}{16}163, it fits into 316\frac{3}{16}163 only partway—specifically, 34\frac{3}{4}43 of the way. In real-world terms, if a whole object is divided into 16 equal parts and three of them are shaded, asking how many groups of one-fourth (or four sixteenths) can be made from that amount leads to the answer: three-fourths of such a group.
