Please help me understand this simple fraction

Question

I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this

Now as I'm trying to find further exercices, I keep stumbling upon fraction-based problems that are built like this one.

What does the number on the left mean? I mean the huge 5 and huge 2. is it a whole + a fraction? like 5 + (1/4)??

I would like to further my research on this topic, but I don't know what the name of these types of fractions are.

receiving a link to a tutorial would be fine too, I just don't know what search terms to use.

Also why is the solution 14?

Answer 1

As stated by @probablyme what you've encountered are mixed fractions. A mixed fraction has a whole number (such as the $5$ in $5\frac{1}{4}$) and a proper fraction (such as the $\frac{1}{4}$ in $5\frac{1}{4}$). The link given by probablyme is a very good tutorial as it introduces and explains the three types of fractions. Here's another just in case you need more material. Let's work out your problem: $$5\frac{1}{4}\times 2\frac{2}{3}$$ $$=\dfrac{21*8}{4*3}$$ $$=\dfrac{168}{12}$$ $$=\dfrac{14}{1}$$ $$=14$$

Don't understand how we went from step 1 to step 2? The denominators in step 1 when multiplied produce $4*3$, but how did we get $21$ and $8$? $(5*4)+1=21$ and $(2*3)+2=8$.

Answer 2

"is it a whole + a fraction?"

Yes. That is exactly what that means.

$5\frac 14 = 5 + \frac 14$. It is a value that is between 5 and 6 that is 1/4 of the way between 5 and 6. It is 5 and then 1/4 more. These are called "mixed fractions"

Now the way to solve this...

$5 = 5*4/4 = 20/4$ so $5\frac 14 = 5 + \frac 14 = \frac {20}{4} + \frac 14 = \frac {21}4$.

So

$5\frac 14 \times 2\frac 23 = (\frac{4*5}{4} + \frac 14)\times(\frac{2*3}{3} + \frac{2}{3}) = \frac{21}4 \times \frac 83 = \frac{21*8}{3*4} =14$