Josiah is asked to simplify the expression 2/3+1/2(8+3 1/4).

45/4

Step-by-step explanation:

Exponential function: exp() = e = 1

Multiple: i * 2

3

= 0.66666667i

Multiple: the result of step No. 2 * 1

2

= 0.66666667i * 1

2

= 0.33333333i

Add: the result of step No. 1 + the result of step No. 3 = 1 + 0.33333333i = 1+0.33333333i

Real part of the complex number: Re(the result of step No. 4) = Re(1+0.33333333i) = 1

Add: 8 + 13

4

= 8

1

+ 13

4

= 8 · 4

1 · 4

+ 13

4

= 32

4

+ 13

4

= 32 + 13

4

= 45

4

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(1, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 4 = 4. In the next intermediate step the fraction result cannot be further simplified by cancelling.

In words - eight plus thirteen quarters = forty-five quarters.

Multiple: the result of step No. 5 * the result of step No. 6 = 1 * 11.25 = 1 · 45

1 · 4

= 45

4

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(45, 4) = 1. In the next intermediate step the fraction result cannot be further simplified by cancelling.

In words - one multiplied by forty-five quarters = forty-five quarters.

45

4

is already in the simplest form. It can be written as 11.25 in decimal form (rounded to 6 decimal places).

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