Solving Simple Mixed Fraction problem?

Question

How do you wrap your head around mixed fraction, does anyone knows how to figure out, can someone give me an example how it can be solved?

Answer 1

$$a +\frac bc = \frac {a\times c}c + \frac bc = \frac{(a\times c) + b}{c} $$

What we do first is like when finding a common denominator between two fractions, only in $a$ above, we have $a = \dfrac a1$:

We multiply $a = \dfrac a1$ by $\dfrac cc = 1$, to get $\dfrac a1 \times \dfrac cc = \;\dfrac{a\times c}{c}\;$ and then add that to the fraction $\dfrac bc$.

For example

$$3 \frac 58\; = \;3 + \frac 58\; = \;\frac{3 \times 8}{8} + \frac 58\; = \;\frac{(3\times 8)+ 5}{8}\; = \;\frac{24 + 5}{8} \;= \;\frac{29}{8}$$

Answer 2

Here is an example.

$$2 \frac{3}{11}=\frac{2 \cdot 11}{11}+\frac3{11}=\frac{22}{11}+\frac3{11}=\frac{25}{11}$$

Or conversely,

$$\frac{11}3=\frac{11-3 \cdot 3}{3}+\frac{3 \cdot 3}{3}=\frac{11-9}{3}+\frac{9}{3}=\frac{2}{3}+3=3 \frac{2}3$$.

In general,

$$x+\frac{y}{z}=\frac{x \cdot z}{z}+\frac{y}{z}=\frac{x \cdot z +y}z$$ and vice versa.

In most cases you'll encounter $y<z$.