The Distributive Property for 7th Grade: Worded problems

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

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:

$4,410+9,450x$

$4410+9450x$

In a fabric factory, the possible sizes of fabric are:

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

$(7+27x)\times5$

How much more material does the factory need?

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.

It is not possible to calculate.

A painter buys a canvas with the following dimensions:

$(23x+12)\times(20x+7)$

How much space to paint does she have?

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:

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

$460x^2+401x+84$

Gerard plans to paint a fence 7X meters high and 30X+4 meters long.

Gerardo paints at a rate of 7 m² per half an hour.

Choose the expression that represents the time it takes for Gerardo to paint one side of the fence.

$15x^2+2x$ hours