The Distributive Property for 7th Grade: Worded problems

We use a formula to calculate the volume: height times width times length.

We rewrite the exercise using the existing data:

$21\times(14+30x)\times15=$

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

$(21\times14+21\times30x)\times15=$

We solve the multiplication exercise in parentheses:

$(294+630x)\times15=$

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

$294\times15+630x\times15=$

We solve each of the exercises in parentheses to find the volume:

$4,410+9,450x$

We calculate the area using the distributive property:

$23x\times20x+23x\times7+12\times20x+12\times7=$

We solve each of the multiplication exercises:

$460x^2+161x+240x+84=$

We join the x coefficients:

$460x^2+401x+84=$

We begin by simplifying the two exercises using the distributive property:

We start with the first expression.

$30x\times(4x+8)=$

$30x\times4x+30x\times8=$

$120x^2+240x$

We now address the second expression:

$(7+27x)\times5=$

$5\times7+5\times27x=$

$35+135x$

In order to calculate the expressions, let's assume that in each expression x is equal to 1.

We can now substitute the X value into the equation:

$120x^2+240x=120\times1^2+240\times1=120+240=360$

$35+135\times1=35+135=170$

Hence it seems that the first expression is larger and requires more fabric.

Let's now calculate the expressions assuming that x is less than 1. We substitute this value into each of the expressions as follows:$x=\frac{1}{10}$

$\frac{120}{100}+\frac{240}{10}=1\frac{1}{5}+24=25\frac{1}{5}$

$35+\frac{135}{10}=48.5$

This time the second expression seems to be larger and requires more fabric.

Therefore, it is impossible to determine.

In order to solve the exercise, we first need to know the total area of the fence.

Let's remember that the area of a rectangle equals length times width.

Let's write the exercise according to the given data:

$7x\times(30x+4)$$$

We'll use the distributive property to solve the exercise. That means we'll multiply 7x by each term in the parentheses:

$(7x\times30x)+(7x\times4)=$

Let's solve each term in the parentheses and we'll get:

$210x^2+28x$

Now to calculate the painting time, we'll use the formula:

$\frac{7m^2}{\frac{1}{2}hr}=14\frac{m^2}{hr}$

The time will be equal to the area divided by the work rate, meaning:

$\frac{210x^2+28x}{14}$

Let's separate the exercise into addition between fractions:

$\frac{210x^2}{14}+\frac{28x}{14}=$

We'll reduce by 14 and get:

$15x^2+2x$

And this is Isaac's work time.