Multiplication of Integers by a Fraction and a Mixed number: Applying the formula

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:

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

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:

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