Solve: 3 × 2¼ Mixed Number Multiplication Problem

$3\times2\frac{1}{4}=$

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 allows us to break down 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

$3\times(2+\frac{1}{4})=$

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

$(3\times2)-(3\times\frac{1}{4})=$

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

$3\times2=6$

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

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

$\frac{3}{1}\times\frac{1}{4}=\frac{3\times1}{1\times4}=\frac{3}{4}$

And we get the exercise:

$6+\frac{3}{4}=6\frac{3}{4}$

And now let's see the solution centered:

$3\times2\frac{1}{4}=3\times(2+\frac{1}{4})=(3\times2)+(3\times\frac{1}{4})=6+\frac{3}{4}=6\frac{3}{4}$