How many sixths are there in 5/3?
The correct answer and explanation is:
To find how many sixths are in 53\frac{5}{3}, the problem is asking how many parts of size 16\frac{1}{6} fit into 53\frac{5}{3}.
Step 1: Understand the problem
The fraction 53\frac{5}{3} represents a quantity, and 16\frac{1}{6} is the size of one “sixth.” The question is: how many 16\frac{1}{6} parts make up 53\frac{5}{3}?
Step 2: Set up the division
To find this, divide 53\frac{5}{3} by 16\frac{1}{6}: 53÷16\frac{5}{3} \div \frac{1}{6}
Dividing by a fraction is the same as multiplying by its reciprocal. So, 53×61=5×63×1=303=10\frac{5}{3} \times \frac{6}{1} = \frac{5 \times 6}{3 \times 1} = \frac{30}{3} = 10
Answer:
There are 10 sixths in 53\frac{5}{3}.
Explanation:
Fractions can be thought of as parts of a whole. The denominator tells how many equal parts the whole is divided into. In 53\frac{5}{3}, the denominator is 3, meaning the whole is divided into three parts, and you have five of those parts (which is more than one whole because 5 is greater than 3).
When the question asks how many sixths are in 53\frac{5}{3}, it wants to express 53\frac{5}{3} in terms of smaller parts that are each one-sixth of a whole. Sixth parts are smaller than thirds because the whole is divided into six parts instead of three.
To find how many smaller parts fit into a bigger fraction, dividing the larger fraction by the smaller fraction is the right approach. Dividing fractions involves multiplying by the reciprocal, which means flipping the numerator and denominator of the divisor.
By multiplying 53\frac{5}{3} by 61\frac{6}{1}, you find the total count of sixths in 53\frac{5}{3}. The calculation simplifies to 10, meaning the fraction 53\frac{5}{3} can be divided into 10 parts, each of size 16\frac{1}{6}.
This method can be used for any similar problem where the goal is to find how many smaller fractional parts fit into a larger fraction.