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 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.

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:

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

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.