What is 4/3 in expanded form?
Understand the Problem
The question is asking for the expanded form of the fraction 4/3. This involves expressing it in a different way, potentially showing it as a mixed number or identifying its decimal equivalent.
Answer
The expanded form of $\frac{4}{3}$ is $1 \frac{1}{3}$ and $1.\overline{3}$.
Answer for screen readers
The expanded form of the fraction $\frac{4}{3}$ is $1 \frac{1}{3}$ as a mixed number and $1.\overline{3}$ as a decimal.
Steps to Solve
- Convert to Mixed Number
To convert the improper fraction $\frac{4}{3}$ into a mixed number, divide the numerator by the denominator.
$$ 4 \div 3 = 1 \quad \text{(whole number)} $$
The remainder will be:
$$ 4 - (3 \times 1) = 1 $$
So, $\frac{4}{3}$ can be written as:
$$ 1 \frac{1}{3} $$
- Convert to Decimal
To find the decimal equivalent, perform the division again:
$$ 4 \div 3 = 1.333... $$
This can also be expressed as $1.\overline{3}$ (where the 3 repeats indefinitely).
- Final Representation
Now we have both forms:
The mixed number is $1 \frac{1}{3}$, and the decimal form is $1.\overline{3}$.
The expanded form of the fraction $\frac{4}{3}$ is $1 \frac{1}{3}$ as a mixed number and $1.\overline{3}$ as a decimal.
More Information
The improper fraction $\frac{4}{3}$ represents a value greater than one, and converting it to a mixed number helps in visualizing that value more clearly. The decimal $1.\overline{3}$ represents the infinite repeating nature of the division, indicating it is a non-terminating decimal.
Tips
- Confusing mixed numbers with improper fractions. A mixed number is made up of a whole part and a fractional part, while an improper fraction has a numerator larger than the denominator. Be sure to separate these when converting.
- Failing to express the repeating decimal correctly. Remember to use a bar above the repeating digit when writing $1.333...$ as $1.\overline{3}$.