Which expression is equivalent to 3/5
The Correct Answer and Explanation is :
To find expressions equivalent to ( \frac{3}{5} ), we can explore a few methods, including multiplication by a fraction or a whole number, and representation as a decimal or percentage.
Equivalent Fractions
One of the simplest ways to generate equivalent fractions is by multiplying both the numerator (top number) and the denominator (bottom number) by the same non-zero integer. For example:
- Multiply by 2:
[
\frac{3 \times 2}{5 \times 2} = \frac{6}{10}
] - Multiply by 3:
[
\frac{3 \times 3}{5 \times 3} = \frac{9}{15}
] - Multiply by 4:
[
\frac{3 \times 4}{5 \times 4} = \frac{12}{20}
]
Each of these fractions—( \frac{6}{10} ), ( \frac{9}{15} ), and ( \frac{12}{20} )—is equivalent to ( \frac{3}{5} ) because they simplify back to ( \frac{3}{5} ) when you divide the numerator and denominator by their greatest common divisor.
Decimal and Percentage Forms
Another way to express ( \frac{3}{5} ) is by converting it into a decimal or a percentage. To convert a fraction to a decimal, divide the numerator by the denominator:
[
\frac{3}{5} = 3 \div 5 = 0.6
]
To express it as a percentage, multiply the decimal form by 100:
[
0.6 \times 100 = 60\%
]
Thus, ( \frac{3}{5} ) can also be represented as ( 0.6 ) or ( 60\% ).
Summary
In summary, ( \frac{3}{5} ) can be represented in multiple ways: as equivalent fractions like ( \frac{6}{10} ), ( \frac{9}{15} ), or ( \frac{12}{20} ); as a decimal ( 0.6 ); and as a percentage ( 60\% ). Understanding these various forms helps in different mathematical contexts, such as comparing proportions or performing calculations that require different representations.