Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 29, 2023

Given a circle, $\frac{1}{8}$ is orange and $\frac{3}{16}$ is purple. Find the fraction of the circle shaded either orange or purple in simplest form.

STEP 1

Assumptions1. The fraction of the circle shaded orange is $\frac{1}{8}$ . The fraction of the circle shaded purple is $\frac{3}{16}$
3. The fractions representing the orange and purple shaded areas are mutually exclusive, i.e., there are no overlapping areas between the orange and purple shaded areas.

STEP 2

To find the total fraction of the circle that is shaded either orange or purple, we simply add the fractions representing the orange and purple shaded areas.
$Total\, shaded\, fraction = Orange\, shaded\, fraction + Purple\, shaded\, fraction$

STEP 3

Now, plug in the given values for the orange and purple shaded fractions to calculate the total shaded fraction.
$Total\, shaded\, fraction = \frac{1}{8} + \frac{3}{16}$

STEP 4

Before we can add these fractions, we must ensure they have a common denominator. The least common denominator (LCD) of8 and16 is16. So, we convert the fraction with denominator8 to an equivalent fraction with denominator16.
$\frac{1}{8} = \frac{1 \times2}{8 \times2} = \frac{2}{16}$

STEP 5

Now, we can add the fractions.
$Total\, shaded\, fraction = \frac{2}{16} + \frac{3}{16}$

STEP 6

Calculate the total shaded fraction.
$Total\, shaded\, fraction = \frac{2}{16} + \frac{3}{16} = \frac{5}{16}$ The fraction of the circle that is shaded either orange or purple is $\frac{5}{16}$ .

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