Question

Why does
$3 * \frac{(4 * 2) + 2 }{4}$
is equivalent to
$3*2+3*\frac{2}{4}$
?

Answer 1

Step-by-step explanation:

You must apply BODMAS to these types of equations

Brackets

Of

Division

Multiplication

Addition and

Subtraction

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

First, solve what's in the brackets

$3 \times \frac{(8) + 2}{ 4}$

Now we can simplify the numerator

$3 \times \frac{10}{4}$

Since everything is simplified we can just multiply as usual and put the whole number over 1 to convert to a fraction

$\frac{3}{1} \times \frac{10}{4}$

3*10=30

1*4=4

Therefore the answer is 30/4

And once it's simplified its 15/2

$3 \times 2 + 3 \times \frac{2}{4}$

Since there are no brackets in the original equation, we can add our own brackets which follows BODMAS

Our brackets will contain all the multiplication taking place

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

Now we can simplify our brackets like we did before

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

Here we have simplified 2*3 to 6 and made 3 into a fraction. We can once again just multiply our fractions like usual.

$6 + ( \frac{6}{4} )$

$6 + ( \frac{3}{2} )$

To make it easier we simplify the fraction

To add it together we need to change 6 into a fraction with the denominator of 2. When we do this we get 12/2

Now we can add

$\frac{12}{2} + \frac{3}{2}$

Once it is added we get 15/2