Write the fraction as an equivalent fraction with the given denominator 5/6= /18
The Correct Answer and Explanation is:
To write the fraction ( \frac{5}{6} ) as an equivalent fraction with a denominator of 18, follow these steps:
Step 1: Determine the factor to scale the denominator
The current denominator is 6, and we need to convert it to 18. To find the scaling factor, divide the new denominator by the current denominator:
[
\text{Scaling Factor} = \frac{\text{New Denominator}}{\text{Old Denominator}} = \frac{18}{6} = 3
]
Step 2: Multiply the numerator and denominator by the scaling factor
Multiply both the numerator and denominator of ( \frac{5}{6} ) by 3 to maintain the value of the fraction:
[
\frac{5}{6} \times \frac{3}{3} = \frac{15}{18}
]
Thus, ( \frac{5}{6} = \frac{15}{18} ).
Explanation (300 Words)
Fractions are equivalent when they represent the same value or proportion, even if their numerators and denominators differ. The key to finding an equivalent fraction is multiplying (or dividing) both the numerator and denominator by the same non-zero number. This process keeps the value of the fraction unchanged because multiplying by ( \frac{x}{x} ) is like multiplying by 1.
In this example, the fraction ( \frac{5}{6} ) has a denominator of 6, but the goal is to rewrite it with a denominator of 18. To achieve this, identify the scaling factor by comparing the new denominator (18) to the old denominator (6). Dividing 18 by 6 gives a factor of 3, meaning the denominator needs to be multiplied by 3 to reach 18.
However, to keep the fraction equivalent, the numerator must also be multiplied by the same factor. The numerator 5, when multiplied by 3, becomes 15. This creates the fraction ( \frac{15}{18} ), which is equivalent to ( \frac{5}{6} ).
This method ensures consistency because scaling both parts of the fraction by the same factor preserves the relationship between the numerator and denominator. In essence, the proportion of 5 parts out of 6 is the same as 15 parts out of 18, making the two fractions equal in value.