A rectangle has been divided into two strips, A and B.
The strips have the same width.
2/5 of strip A is shaded.
5/8 of strip B is shaded.
The length of the rectangle is 40cm.
What fraction of the rectangle is not shaded?
Thank you.
Joseph.
2/5 x 8 = 16/40
5/8 x 5 = 25/40
16/40 + 25/40 = 41/80 (shaded)
80/80 - 41/80 = 39/80 (not shaded)
41/40 of the rectangle is shaded so none
3/4 is not shaded
8/5
To find the fraction of the rectangle that is not shaded, we need to find the total fraction that is shaded and subtract it from 1 (since 1 represents the whole rectangle).
Let's first find the fraction of strip A that is shaded:
Since 2/5 of strip A is shaded, the shaded portion can be represented as 2/5 * 1 (where 1 represents the whole strip). Therefore, the shaded portion of strip A is 2/5.
Next, let's find the fraction of strip B that is shaded:
Since 5/8 of strip B is shaded, the shaded portion can be represented as 5/8 * 1 (where 1 represents the whole strip). Therefore, the shaded portion of strip B is 5/8.
Now, we can find the total fraction that is shaded by adding the shaded portions of strip A and strip B together:
Total shaded fraction = shaded portion of A + shaded portion of B = 2/5 + 5/8.
To add these fractions, we need to find a common denominator. In this case, since 5 and 8 have a common multiple of 40, we can express the fractions with the same denominator:
Total shaded fraction = (2/5 * 8/8) + (5/8 * 5/5) = 16/40 + 25/40 = 41/40.
Now that we have the total shaded fraction, we can find the fraction that is not shaded by subtracting it from 1:
Fraction not shaded = 1 - total shaded fraction = 1 - 41/40.
To subtract fractions, we also need to find a common denominator:
Fraction not shaded = (40/40) - (41/40) = -1/40.
However, a fraction cannot be negative, so we can consider the negative sign as an indication that the shaded area is larger than the actual size of the rectangle due to overlapping strips. Therefore, the fraction not shaded is 0.
So, the fraction of the rectangle that is not shaded is 0.