Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.start fraction, 9, divided by, 8, end fraction, divided by, start fraction, 5, divided by, 4, end fraction89 ÷ 45
The given expression is \(\frac{9}{8} \div \frac{5}{4}\).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of \(\frac{5}{4}\) is \(\frac{4}{5}\).
Thus, \(\frac{9}{8} \div \frac{5}{4} = \frac{9}{8} \cdot \frac{4}{5}\).
Multiplying the numerators and denominators, we get \(\frac{9 \cdot 4}{8 \cdot 5} = \frac{36}{40}\).
The fraction \(\frac{36}{40}\) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4.
So, \(\frac{36}{40} = \frac{36 \div 4}{40 \div 4} = \frac{9}{10}\).
Hence, the simplified fraction after performing the operation is \(\frac{9}{10}\).
To solve the expression, "start fraction 9 divided by 8 end fraction divided by start fraction 5 divided by 4 end fraction," follow these steps:
1. Simplify the division of the fractions separately:
a. Divide 9 by 8: start fraction 9 divided by 8 end fraction = 9/8.
b. Divide 5 by 4: start fraction 5 divided by 4 end fraction = 5/4.
2. Now, divide the fractions obtained in step 1.
a. Divide 9/8 by 5/4: start fraction 9/8 divided by 5/4 end fraction.
3. To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
a. Multiply 9/8 by the reciprocal of 5/4, which is 4/5.
4. Multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together:
a. Multiply the numerators: 9 * 4 = 36.
b. Multiply the denominators: 8 * 5 = 40.
5. Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:
a. Divide the numerator, 36, by 4: 36/4 = 9.
b. Divide the denominator, 40, by 4: 40/4 = 10.
6. The final simplified fraction is 9/10.
Therefore, the result of the expression "start fraction 9 divided by 8 end fraction divided by start fraction 5 divided by 4 end fraction" is 9/10.
To perform the operation and simplify the answer as a fraction, we can follow the steps below:
Step 1: Start by dividing the numerator of the first fraction (9) by the denominator of the first fraction (8):
⇒ 9 ÷ 8 = 1.125
Step 2: Divide the numerator of the second fraction (5) by the denominator of the second fraction (4):
⇒ 5 ÷ 4 = 1.25
Step 3: Divide the result from step 1 (1.125) by the result from step 2 (1.25):
⇒ 1.125 ÷ 1.25 = 0.9
We now have the decimal result of the division operation. To express it as a simplified fraction, we need to convert the decimal to fraction form.
Step 4: To convert the decimal 0.9 to a fraction, we can write it as a fraction over 1 and remove the decimal:
⇒ 0.9 = 9/10
Therefore, the simplified fraction form of 89 ÷ 45 is 9/10.