3/10 divided by 4/5 … Divided then put into simplest form
The Correct Answer and Explanation is:
To solve ( \frac{3}{10} \div \frac{4}{5} ), follow these steps:
Step 1: Rewrite the division as a multiplication
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of ( \frac{4}{5} ) is ( \frac{5}{4} ). Thus:
[
\frac{3}{10} \div \frac{4}{5} = \frac{3}{10} \times \frac{5}{4}.
]
Step 2: Multiply the fractions
To multiply fractions, multiply the numerators (top numbers) and the denominators (bottom numbers):
[
\frac{3}{10} \times \frac{5}{4} = \frac{3 \times 5}{10 \times 4} = \frac{15}{40}.
]
Step 3: Simplify the fraction
To simplify ( \frac{15}{40} ), find the greatest common factor (GCF) of 15 and 40. The factors of 15 are ( 1, 3, 5, 15 ), and the factors of 40 are ( 1, 2, 4, 5, 8, 10, 20, 40 ). The GCF is 5.
Divide the numerator and denominator by their GCF:
[
\frac{15}{40} = \frac{15 \div 5}{40 \div 5} = \frac{3}{8}.
]
Final Answer:
[
\frac{3}{10} \div \frac{4}{5} = \frac{3}{8}.
]
Explanation:
When dividing fractions, the operation is simplified by converting division into multiplication using the reciprocal of the divisor. The reciprocal flips the numerator and denominator of the second fraction, making the calculation more straightforward.
In this problem, ( \frac{4}{5} ) is replaced with ( \frac{5}{4} ), and then the multiplication process begins. The numerator of the first fraction ((3)) multiplies with the numerator of the reciprocal ((5)), while the denominators ((10) and (4)) multiply together. This produces ( \frac{15}{40} ), which is not in its simplest form.
Simplification ensures the result is as reduced as possible. Dividing both 15 and 40 by their greatest common factor, 5, reduces ( \frac{15}{40} ) to ( \frac{3}{8} ). The final fraction cannot be reduced further, as 3 and 8 have no common factors besides 1.
Understanding these steps is crucial for solving any fraction division problem accurately.