Evaluate:
$1 \frac{1}{3} \div 4$
The expression is \(1 \frac{1}{3} \div 4\). The first step is to convert the mixed number \(1 \frac{1}{3}\) into an improper fraction. This is done by multiplying the whole number part (1) by the denominator (3) and adding the numerator (1), then placing the result over the original denominator. Thus, \(1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}\). Now the expression is \(\frac{4}{3} \div 4\).
Division by a number is equivalent to multiplication by its reciprocal. The reciprocal of 4 is \(\frac{1}{4}\). Therefore, we can rewrite the division problem as: \[\frac{4}{3} \div 4 = \frac{4}{3} \times \frac{1}{4}\]
To multiply fractions, multiply the numerators together and the denominators together: \[\frac{4}{3} \times \frac{1}{4} = \frac{4 \times 1}{3 \times 4} = \frac{4}{12}\]
Finally, simplify the fraction \(\frac{4}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4: \[\frac{4 \div 4}{12 \div 4} = \frac{1}{3}\] So, \(1 \frac{1}{3} \div 4 = \frac{1}{3}\).
Imagine you have a cake that is 1 and 1/3 in size, and you need to share it equally among 4 people. To determine how much each person gets, you perform the division 1 1/3 ÷ 4. By converting the cake size to an improper fraction (4/3) and dividing by 4, you find that each person receives 1/3 of the cake. This is a practical way to ensure everyone receives an equal share when splitting amounts that aren't whole numbers.