Write as either a fraction or a mixed number: 15 divided by 4
The correct answer and explanation is:
Correct Answer:
15 ÷ 4 = 3 ¾ (mixed number) or 15/4 (improper fraction)
Explanation (300 words):
To write 15 divided by 4 as a fraction or mixed number, start by understanding what division and fractions mean.
Step 1: Write the Division as a Fraction
Any division problem can be expressed as a fraction. So,
15 ÷ 4 = 15/4
This is called an improper fraction because the numerator (15) is larger than the denominator (4).
Step 2: Convert to a Mixed Number
A mixed number has two parts: a whole number and a proper fraction. To convert 15/4 to a mixed number, divide 15 by 4:
- 4 goes into 15 3 times (because 4 × 3 = 12)
- The remainder is 15 − 12 = 3
So,
15/4 = 3 whole parts and 3 left over out of 4, which is:
3 ¾
This means 15 divided by 4 equals 3 and ¾. You can verify this:
3 ¾ = 3 + ¾ = (3 × 4 + 3)/4 = (12 + 3)/4 = 15/4
Understanding the Concept:
- Fractions represent division: the numerator (top number) is divided by the denominator (bottom number).
- Improper fractions (like 15/4) are useful in math operations like multiplication and division.
- Mixed numbers (like 3 ¾) are easier to understand in real-life contexts (e.g., “3 and three quarters of a pizza”).
In conclusion, 15 divided by 4 can be written as either 15/4 (improper fraction) or 3 ¾ (mixed number). Both represent the same value, just in different forms.