In simplest form the problem is 7/6 divided by 4 can be what in what simplest form
The Correct Answer and Explanation is:
To solve ( \frac{7}{6} \div 4 ) in its simplest form, we first rewrite the division as multiplication by the reciprocal of 4.
Step-by-Step Solution:
- Rewrite the Division:
[
\frac{7}{6} \div 4 = \frac{7}{6} \times \frac{1}{4}
]
Dividing by a number is equivalent to multiplying by its reciprocal. Since the reciprocal of 4 is ( \frac{1}{4} ), we multiply ( \frac{7}{6} ) by ( \frac{1}{4} ). - Multiply the Fractions:
To multiply two fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
[
\frac{7 \times 1}{6 \times 4} = \frac{7}{24}
] - Simplify the Fraction:
Now, we check if ( \frac{7}{24} ) can be simplified further by finding any common factors between the numerator and the denominator. In this case, 7 and 24 do not have any common factors other than 1, so the fraction is already in its simplest form. Therefore:
[
\frac{7}{6} \div 4 = \frac{7}{24}
]
Explanation:
Dividing fractions involves multiplying by the reciprocal of the divisor. Here, ( \frac{7}{6} \div 4 ) became ( \frac{7}{6} \times \frac{1}{4} ), which simplifies to ( \frac{7}{24} ).
It’s essential to understand that when dividing fractions or mixed numbers by whole numbers, you convert the division to multiplication using the reciprocal of the whole number. The resulting fraction, ( \frac{7}{24} ), is in simplest form because it has no common factors between the numerator and denominator, other than 1. This fraction represents a portion of the whole (24 parts), and it shows that ( \frac{7}{6} ) divided by 4 yields about one-fourth of the original fraction’s value.
This method of division using reciprocals is widely applicable, ensuring accuracy without needing complex calculations. Understanding this rule makes fraction division more intuitive and easier to apply across different types of mathematical problems.