Question

a mason is a person who builds structures with bricks, stone, cement block, or tile. a mason usually uses mortar to hold the bricks together. a general rule of thumb in masonry is that 2\\(\frac{1}{2}\\) bags of mortar are needed for every 100 cement blocks. use a double number line to determine each answer.\
bags of mortar: 0, 2\\(\frac{1}{2}\\),?, 7\\(\frac{1}{2}\\)\
cement bricks: 0, 100, 200, 300\
\\(\boldsymbol{\circled{a}}\\) how many bags of mortar will a mason need for 350 blocks?

Explanation:

Step1: Find the rate per 100 blocks

We know that for 100 blocks, we need \(2\frac{1}{2}\) bags of mortar. First, convert \(2\frac{1}{2}\) to an improper fraction, which is \(\frac{5}{2}\).

Step2: Determine the number of 100 - block units in 350 blocks

To find how many groups of 100 blocks are in 350 blocks, we divide 350 by 100: \(\frac{350}{100}=\frac{7}{2}\) or \(3.5\).

Step3: Calculate the total bags of mortar

Since each 100 - block unit requires \(\frac{5}{2}\) bags of mortar, for \(\frac{7}{2}\) units, we multiply the rate per 100 blocks by the number of units: \(\frac{5}{2}\times\frac{7}{2}=\frac{35}{4} = 8\frac{3}{4}\) (or we can think in decimal: \(2.5\times3.5 = 8.75\), and \(8.75 = 8\frac{3}{4}\)).

Alternatively, using the double - number line:

• From the double - number line, we see that for 100 blocks, it's \(2\frac{1}{2}\) bags. For 200 blocks (which is 2 times 100 blocks), we need \(2\times2\frac{1}{2}=5\) bags. For 300 blocks (3 times 100 blocks), we need \(3\times2\frac{1}{2}=7\frac{1}{2}\) bags. Now, 350 blocks is 300 + 50 blocks. 50 blocks is half of 100 blocks, so we need half of \(2\frac{1}{2}\) bags for 50 blocks. Half of \(2\frac{1}{2}\) is \(\frac{1}{2}\times\frac{5}{2}=\frac{5}{4}=1\frac{1}{4}\) bags. Then, for 350 blocks, we add the mortar for 300 blocks and 50 blocks: \(7\frac{1}{2}+1\frac{1}{4}=7\frac{2}{4}+1\frac{1}{4}=8\frac{3}{4}\) bags.

Answer:

\(8\frac{3}{4}\) (or \(8.75\))