Solve: Multiplying 5 by 3⅓ - Step-by-Step Solution

$5\times3\frac{1}{3}=$

We will use the distributive property of multiplication and separate the fraction into an addition exercise between fractions. This allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication actually allows us to separate the larger term in the multiplication exercise into a sum or difference of smaller numbers, which makes the multiplication operation easier and gives us the ability to solve the exercise without a calculator

$5\times(3+\frac{1}{3})=$

We will use the distributive property formula $a(b+c)=ab+ac$

$(5\times3)+(5\times\frac{1}{3})=$

Let's solve what's in the left parentheses:

$5\times3=15$

Let's solve what's in the right parentheses:

$5=\frac{5}{1}$

$\frac{5}{1}\times\frac{1}{3}=\frac{5\times1}{1\times3}=\frac{5}{3}$

And we get the exercise:

$15+\frac{5}{3}=15+1\frac{2}{3}=16\frac{2}{3}$

And now let's see the solution centered:

$5\times3\frac{1}{3}=5\times(3+\frac{1}{3})=(5\times3)+(5\times\frac{1}{3})=15+\frac{5}{3}=15+1\frac{2}{3}=16\frac{2}{3}$