Question

Carl grows trees to study their height. He recorded the data as follows

Tree type	Height (meters)
Apple	$\frac{3}{10}$
Cherry	$\frac{7}{15}$

What is the difference between the heights of the cherry and apple trees (in m) ?

• A. $\frac{7}{2}$
• B. $\frac{1}{2}$
• C. $\frac{1}{6}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{1}{6}$

From the table:
The cheery tree is $\frac{7}{15}m$ tall and the apple tree is $\frac{3}{10}m$ tall.

Difference between the heights of the cherry and apple trees
$=\frac{7}{15}-\frac{3}{10}$

As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 15 and 10
Multiples of 15: 15, 30, 45, 60, ...
Multiples of 10: 10, 20, 30, 40, ...

30 is the common multiple of 15 and 10. So, LCM of 15 and 10 is 30.

Step 2: Now, we have to convert the denominators of both the fractions into 30 (LCM of 15 and 10) without changing the fraction value.

$\frac{7}{15}=\frac{7\times 2}{15\times 2}=\frac{14}{30}$
$\frac{3}{10}=\frac{3\times 3}{10\times 3}=\frac{9}{30}$

$\therefore \frac{7}{15}-\frac{3}{10}=\frac{14}{30}-\frac{9}{30}$
$=\frac{5}{30}$
$=\frac{5\times 1}{5\times 3\times 2}$
$=\frac{1}{6}$