8 divided by 1 4/5 in either fraction form or just number
The Correct Answer and Explanation is:
To solve the problem of dividing 8 by ( \frac{1}{4} ) (or 1 4/5), follow these steps:
Step 1: Convert Mixed Number to Improper Fraction
The divisor is a mixed number (1 \frac{4}{5}), which needs to be converted into an improper fraction. A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, multiply the whole number by the denominator and then add the numerator. The denominator stays the same.
For ( 1 \frac{4}{5} ):
- Multiply the whole number 1 by the denominator 5: (1 \times 5 = 5).
- Add the numerator 4 to this product: ( 5 + 4 = 9).
So, (1 \frac{4}{5}) becomes ( \frac{9}{5} ).
Step 2: Division of Fractions
Now that we have the divisor as ( \frac{9}{5} ), we need to divide 8 by ( \frac{9}{5} ). Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of ( \frac{9}{5} ) is ( \frac{5}{9} ).
The problem becomes:
[
8 \div \frac{9}{5} = 8 \times \frac{5}{9}
]
Step 3: Multiplying Fractions
Now, multiply the whole number 8 by the fraction ( \frac{5}{9} ). To do this, express 8 as a fraction with a denominator of 1:
[
8 = \frac{8}{1}
]
Now multiply the two fractions:
[
\frac{8}{1} \times \frac{5}{9} = \frac{8 \times 5}{1 \times 9} = \frac{40}{9}
]
Step 4: Simplifying the Result (if needed)
The fraction ( \frac{40}{9} ) is in its simplest form, and it is an improper fraction. To convert it to a mixed number, divide 40 by 9:
- 9 goes into 40 four times (since ( 9 \times 4 = 36 )).
- The remainder is 4.
Thus, the mixed number form of ( \frac{40}{9} ) is ( 4 \frac{4}{9} ).
Final Answer:
- In improper fraction form: ( \frac{40}{9} )
- As a mixed number: ( 4 \frac{4}{9} )
Thus, the answer to ( 8 \div 1 \frac{4}{5} ) is ( \frac{40}{9} ) or ( 4 \frac{4}{9} ).