The Distributive Property for 7th Grade: Using fractions

According to the distribution law rules, we will multiply both thirds by each term in parentheses:

$\frac{2}{3}\times12+\frac{2}{3}\times0-\frac{2}{3}\times5=$

Remember that any whole number can be written as a fraction with a denominator of 1, except for the digit 0.

Let's write the exercise in the following form:

$\frac{2}{3}\times\frac{12}{1}+\frac{2}{3}\times0-\frac{2}{3}\times\frac{5}{1}=$

We multiply numerator by numerator and denominator by denominator in each multiplication exercise.

Remember that when we multiply any number by 0, the result will be 0.

Therefore we get:

$\frac{24}{3}+0-\frac{10}{3}=$

Let's solve the first fraction exercise, and simplify the remaining fraction to get the exercise:

$8-3\frac{1}{3}=4\frac{2}{3}$

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 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:

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

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:

$8+10=18$

First, let's solve what's in the parentheses vertically.

Let's remember that:

$1.2=1.20$

We'll make sure to write the exercise correctly.

Note that the decimal point is in place and ones are under ones, tens under tens, etc.

$1.20\\+0.75\\$

And we'll get the result:

$1.95$

Now we have the exercise:

$10\times1.95=$

This exercise doesn't require calculation, but rather moving the decimal point "one step" to the right, since we are multiplying by ten.

In other words, if we move the decimal point to the right we'll get:

$19.5$

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:

$\frac{5}{6}x$

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

The common denominator between the fractions is 4, so we will multiply each numerator by the number needed for its denominator to reach 4.

We will multiply the first fraction's numerator by 2 and the second fraction's numerator by 1:

$(\frac{9}{2}-\frac{3}{4})=\frac{2\times9-1\times3}{4}=\frac{18-3}{4}=\frac{15}{4}$

Now we have the expression:

$\frac{1}{3}\times\frac{15}{4}=$

Note that we can reduce 15 and 3:

$\frac{1}{1}\times\frac{5}{4}=$

Now we multiply numerator by numerator and denominator by denominator:

$\frac{1\times5}{1\times4}=\frac{5}{4}=1\frac{1}{4}$