A box contains red, blue, and yellow beads. 1/4 of the beads are red. 2/9 of the remaining beads are blue. What fraction of the beads in the box are yellow?
x = number of beads
1 / 4 of the beads are red.
x / 4 of the beads are red.
The remainder is:
x - x / 4 = 4 x / 4 - x / 4 = 3 x / 4
2 / 9 of the remaining beads are blue means:
( 2 / 9 ) • ( 3 x / 4 ) = 2 • 3 x / 9 • 4 =
6 x / 36 = 6 • x / 6 • 6 = x / 6
are blue beads.
x / 6 of the beads are blue.
red beads + blue beads =
3 x / 4 + x / 6 =
3 • 3 x / 3 • 4 + 2 • x / 2 • 6 =
9 x / 12 + 2 x / 12 = 11 x / 12
Yellow beads:
x - 11 x / 12 =
12 x / 12 - 11 x / 12 = x / 12
1 / 12 of the beads in the box are yellow.
Let's start by calculating the fraction of beads that are red. Since 1/4 of the beads are red, that means 3/4 of the beads are not red.
Next, let's calculate the fraction of beads that are blue. Since 2/9 of the remaining beads are blue, that means 7/9 of the beads that are not red are blue.
Now, let's calculate the fraction of beads that are yellow. Since we already know that 3/4 of the beads are not red, and 7/9 of those non-red beads are blue, we can subtract the fractions of red and blue beads from 1 to find the fraction of yellow beads.
Fraction of yellow beads = 1 - (fraction of red beads + fraction of blue beads)
= 1 - (3/4 + 7/9)
To add these fractions together, we need a common denominator. The least common multiple of 4 and 9 is 36.
= 1 - (27/36 + 28/36)
Now, we can subtract the fractions together.
= 1 - (55/36)
To subtract these fractions, we need a common denominator.
= 1 - (55/36)
= 1 - 55/36
To subtract these fractions, we need a common denominator.
= (36/36) - (55/36)
= (36 - 55) / 36
= -19/36
Therefore, the fraction of beads in the box that are yellow is -19/36.