What is three-fourths times nine?
Your answer should be in whole or mixed number form.
The Correct Answer and Explanation is :
To calculate three-fourths times nine, you can follow these steps:
Step 1: Express the problem as a multiplication of fractions
Three-fourths times nine can be written as:
[
\frac{3}{4} \times 9
]
Step 2: Convert the whole number to a fraction
To multiply by a whole number, you can express it as a fraction with 1 as the denominator. So, nine becomes (\frac{9}{1}).
Now, the problem looks like this:
[
\frac{3}{4} \times \frac{9}{1}
]
Step 3: Multiply the numerators and denominators
Now, multiply the numerators (the numbers on top of the fractions) and the denominators (the numbers on the bottom of the fractions):
[
\frac{3 \times 9}{4 \times 1} = \frac{27}{4}
]
Step 4: Simplify the result
Now, we have (\frac{27}{4}), which is an improper fraction (the numerator is larger than the denominator). To express it as a mixed number, divide the numerator (27) by the denominator (4):
[
27 \div 4 = 6 \text{ with a remainder of } 3
]
So, (\frac{27}{4} = 6 \frac{3}{4}).
Final Answer:
The result of three-fourths times nine is 6 and 3/4.
Explanation:
When multiplying fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together. If you’re multiplying a fraction by a whole number, convert the whole number to a fraction with 1 as the denominator. After you multiply, you can simplify the result if necessary. In this case, the improper fraction (\frac{27}{4}) was converted into a mixed number, 6 and 3/4, for a more understandable result.