Question

Dr.Cubbin collects rocks. She has 100 rocks, one fourth blue, two fifth red, one tenth green, and the rest are multicolored. What Fraction of the rocks are multicolored rocks?

Answer 1

`(1)/(4)`

Explanation:

To find the fraction of the rocks that are multicolored, we need to subtract the fractions of the rocks that are blue, red, and green from 1. We can do this by finding a common denominator and then subtracting the numerators.

One way to find a common denominator is to multiply the denominators of the fractions: 4 x 5 x 10 = 200. Then, we can rewrite each fraction with the new denominator by multiplying the numerator and denominator by the same factor. For example, to rewrite one-fourth as a fraction with 200 as the denominator, we multiply the numerator and denominator by 50: (1 x 50) / (4 x 50) = 50 / 200.

Using this method, we can rewrite the fractions as follows:

• One-fourth = 50 / 200
• Two fifth = 80 / 200
• One-tenth = 20 / 200

Now, we can subtract these fractions from 1, which is equivalent to 200 / 200:

• 1 - (50 / 200 + 80 / 200 + 20 / 200)
• = (200 / 200) - (150 / 200)
• = (200 - 150) / 200
• = 50 / 200

Therefore, the fraction of the rocks that are multicolored is 50 / 200. However, this fraction can be simplified by dividing both the numerator and denominator by the greatest common factor, which is 50:

• (50 / 50) / (200 / 50)
• = 1 / 4

Hence, the simplified fraction of the rocks that are multicolored is one-fourth. This means that out of the 100 rocks, Dr.Cubbin has 25 multicolored rocks.

Answer 2

Answer: 1/4 (25 Rocks)

Explanation:

Start with 100 rocks.

Subtract 25(1/4 of 100) rocks

Subtract 40(2/5 of 100) rocks

Subtract 10(1/10 of 100) rocks

and that leaves you with 25

100 - 25 - 40 - 10 = 25

25/100 = 1/4

1/4th of the rocks are multicolored