Question

practice comparing ratios with fractions
check your understanding- question 1 of 3 attempt 1 of 2
in a biology class, \\( \frac { 3 } { 4 } \\) of the students have brown hair and \\( \frac { 1 } { 8 } \\) of the students have red hair.
fill in the blanks to compare the fraction of students with brown hair with the fraction of students with red hair.
the ratio comparing the fraction of students with brown hair with the fraction of students with red hair is select...
\\( \frac { 3 } { 4 } \div \frac { 1 } { 8 } = \\) select...
the simplified ratio is select...
this means that the number of students with brown hair is select... the number of students with red hair.

Explanation:

Step1: Ratio expression

The ratio of $\frac{3}{4}$ (brown - hair fraction) to $\frac{1}{8}$ (red - hair fraction) is $\frac{3}{4}:\frac{1}{8}$.

Step2: Division operation

According to the rule of dividing fractions $\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}$, so $\frac{3}{4}\div\frac{1}{8}=\frac{3\times8}{4\times1}$.

Step3: Simplification

$\frac{3\times8}{4\times1}=\frac{24}{4}=6$.

Step4: Ratio simplification

Since $\frac{3}{4}:\frac{1}{8}=6:1$ (from the division result).

Step5: Ratio meaning

A ratio of $6:1$ implies that for every $1$ student with red hair, there are $6$ students with brown hair, so the number of brown - hair students is $6$ times the number of red - hair students.

Answer:

The ratio comparing the fraction of students with brown hair with the fraction of students with red hair is $\frac{3}{4}:\frac{1}{8}$.
$\frac{3}{4}\div\frac{1}{8}=6$.
The simplified ratio is $6:1$.
This means that the number of students with brown hair is $6$ times the number of students with red hair.