. Express 3.75 into Fraction
The Correct Answer and Explanation is:
Fraction Form of 3.75:
The decimal 3.75 can be expressed as a fraction in simplest form as:
3.75 = 15/4
Step-by-Step Conversion:
- Understand the Decimal:
- The number 3.75 consists of a whole number part (3) and a decimal part (.75).
- This means: 3.75=3+0.753.75 = 3 + 0.75
- Convert the Decimal (.75) into a Fraction:
- 0.75 means 75 hundredths, or: 0.75=751000.75 = \frac{75}{100}
- Simplify the Fraction:
- Find the greatest common divisor (GCD) of 75 and 100, which is 25: 75÷25100÷25=34\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
- Add the Whole Number Part:
- We now add the whole number 3 to the fraction 3/4: 3+34=124+34=1543 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4}
Why This Works – Detailed Explanation
Converting a decimal like 3.75 into a fraction involves understanding both place value and how fractions represent parts of a whole. Decimals and fractions are two different ways to show numbers that are not whole.
The decimal 3.75 means “three wholes and seventy-five hundredths.” The decimal part, 0.75, tells us that we are looking at 75 parts out of 100. That’s how we get the initial fraction 75/100. However, most fractions can be simplified by dividing both the numerator (top number) and the denominator (bottom number) by the same value — the greatest common divisor (GCD). Since both 75 and 100 are divisible by 25, we simplify 75/100 to 3/4.
Next, we add this to the whole number part of 3. In fractional form, 3 is equivalent to 12/4 (since 3 × 4 = 12). Adding 12/4 and 3/4 gives 15/4.
This result, 15/4, is called an improper fraction because the numerator is larger than the denominator. It accurately represents the same value as the decimal 3.75. If needed, you can also write this as a mixed number, which is 3 3/4.
Understanding how to convert between decimals and fractions helps in math problems involving measurement, money, and percentages, and builds stronger number sense overall.
