Follow the steps to write 0.75 as a fraction. Write 0.75 as a fraction. 75 Rewrite the fraction in simplest terms. \frac{\text{ } }{4}
The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
Correct Answer:
The first missing number is 100.
The second missing number is 3.
The completed problem is:
Write 0.75 as a fraction.
75/100
Rewrite the fraction in simplest terms.
3/4
Explanation
The problem asks us to convert the decimal 0.75 into a fraction and then simplify it. This is a two-step process.
Step 1: Write 0.75 as a Fraction
First, we need to convert the decimal number into a fraction. The key is to look at the place value of the last digit in the decimal. In 0.75, the number 7 is in the tenths place, and the number 5 is in the hundredths place. Since the hundredths place is the final position, we use 100 as the denominator. The digits to the right of the decimal point, 75, become the numerator. Therefore, the decimal 0.75 is written as the fraction 75/100. This answers the first part of the problem, where the missing denominator is 100.
The visual aid in the image supports this. It shows a large square divided into 100 smaller squares (a 10×10 grid). Of these 100 squares, 75 are shaded, visually representing the fraction 75/100.
Step 2: Rewrite the Fraction in Simplest Terms
Next, we must simplify the fraction 75/100. To simplify a fraction, we need to find the greatest common divisor (GCD), which is the largest number that can divide both the numerator (75) and the denominator (100) without leaving a remainder.
We can find the GCD by listing the factors of each number or by recognizing a common factor. Many people know that 75 and 100 are both divisible by 25 (thinking in terms of money, 75 cents is three quarters, and 100 cents is four quarters). The number 25 is the greatest common divisor.
Now, we divide both parts of the fraction by the GCD:
- Numerator: 75 ÷ 25 = 3
- Denominator: 100 ÷ 25 = 4
This gives us the simplified fraction 3/4. This answers the second part of the problem, where the missing numerator is 3. The visual aid also shows the large square divided into four equal quadrants, with three of them shaded, perfectly illustrating the simplified fraction 3/4.
