Addition of Fractions: Using fractions

We'll use the distributive property and multiply 9 by each term in the parentheses:

$(9\times\frac{1}{3})+(9\times\frac{1}{4})=$

Let's solve the left parentheses. Remember that:

$9=\frac{9}{1}$

$\frac{9}{1}\times\frac{1}{3}=\frac{9\times1}{1\times3}=\frac{9}{3}$

Let's solve the right parentheses.

$\frac{9}{1}\times\frac{1}{4}=\frac{9\times1}{1\times4}=\frac{9}{4}$

Now we have the expression:

$\frac{9}{3}+\frac{9}{4}=$

Let's solve the left fraction:

$\frac{9}{3}=3$

For the right fraction, we'll separate the numerator into an addition problem:

$\frac{9}{4}=\frac{8+1}{4}$

We'll separate the fraction we got into an addition of fractions and get the expression:

$3+\frac{8}{4}+\frac{1}{4}=$

Let's solve the fraction:

$\frac{8}{4}=2$

And now we get:

$3+2+\frac{1}{4}=5\frac{1}{4}$

We'll use the distributive property and multiply 24 by each term in parentheses:

$(\frac{1}{3}\times24)+(\frac{5}{12}\times24)=$

Let's solve the left parentheses. Remember that:

$24=\frac{24}{1}$

$\frac{1}{3}\times\frac{24}{1}=\frac{1\times24}{3\times1}=\frac{24}{3}$

Now let's look at the right parentheses, where we'll split 24 into a smaller multiplication exercise that will help us later with reduction:

$(\frac{5}{12}\times24)=(\frac{5}{12}\times12\times2)$

Now we'll reduce the 12 in the numerator and the 12 in the multiplication exercise and get:

$\frac{24}{3}+5\times2=$

Let's solve the fraction:

$\frac{24}{3}=8$

Now we'll get the exercise:

$8+(5\times2)=$

According to the order of operations, we'll solve what's in the parentheses and get:

$8+10=18$

We'll use the distributive property and multiply 33 by each term in the parentheses:

$(\frac{1}{3}\times33)+(\frac{9}{1}\times33)=$

Let's solve the left parentheses. Remember that:

$33=\frac{33}{1}$

$\frac{1}{3}\times\frac{33}{1}=\frac{1\times33}{3\times1}=\frac{33}{3}$

Now let's address the right parentheses, where we'll break down 33 into a smaller multiplication exercise that will help us later with reduction:

$(\frac{9}{11}\times33)=(\frac{9}{11}\times11\times3)$

Now we'll reduce the 11 in the numerator and the 11 in the multiplication exercise and get:

$\frac{33}{3}+9\times3=$

Let's solve the fraction:

$\frac{33}{3}=11$

Now we'll get the exercise:

$11+(9\times3)=$

According to the order of operations, we'll solve what's in the parentheses and get:

$11+27=38$

According to the order of operations rules, we will first address the expression in parentheses.

The common denominator between the fractions is 6, so we will multiply each numerator by the number needed to make its denominator reach 6.

We will multiply the first fraction's numerator by 2 and the second fraction's numerator by 3:

$(\frac{1}{3}+\frac{1}{2})=\frac{1\times2+1\times3}{6}=\frac{2+3}{6}=\frac{5}{6}$

Now we have the expression:

$x\times\frac{5}{6}=$

We will use the distributive property and get the result:

$\frac{5}{6}x$

First, let's find a common denominator for 4, 8, and 6: it's 24.

Now, we'll multiply each fraction by the appropriate number to get:

$\frac{5\times4}{6\times4}x+\frac{7\times3}{8\times3}x+\frac{2\times6}{4\times6}x=$

Let's solve the multiplication exercises in the numerator and denominator:

$\frac{20}{24}x+\frac{21}{24}x+\frac{12}{24}x=$

We'll connect all the numerators:

$\frac{20+21+12}{24}x=\frac{41+12}{24}x=\frac{53}{24}x$

Let's break down the numerator into a smaller addition exercise:

$\frac{48+5}{24}=\frac{48}{24}+\frac{5}{24}=2+\frac{5}{24}=2\frac{5}{24}x$