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.
double number line chart with bags of mortar (0, $2\frac{1}{2}$, 5, $7\frac{1}{2}$) and cement bricks (0, 100, 200, 300) shown
(b) how many bags of mortar will a mason need for 50 blocks?
\bigcirc 1 1/4
\bigcirc 1/2
\bigcirc 1 3/4
\bigcirc 1 1/2

Explanation:

Step1: Analyze the ratio

We know that for 100 cement blocks, we need $2\frac{1}{2}$ bags of mortar. So the ratio of mortar bags to cement blocks is $2\frac{1}{2}:100$. We need to find the number of mortar bags for 50 blocks. Since 50 is half of 100, we can find half of $2\frac{1}{2}$.

Step2: Calculate half of $2\frac{1}{2}$

First, convert $2\frac{1}{2}$ to an improper fraction: $2\frac{1}{2}=\frac{5}{2}$. Then, find half of it: $\frac{1}{2}\times\frac{5}{2}=\frac{5}{4}=1\frac{1}{4}$? Wait, no, wait. Wait, 50 is half of 100, so the amount of mortar should be half of $2\frac{1}{2}$. Wait, $2\frac{1}{2}$ divided by 2. $2\frac{1}{2}=\frac{5}{2}$, dividing by 2 is $\frac{5}{2}\div2=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4}=1\frac{1}{4}$? But wait, let's check the double number line. The first mark on the mortar line is 0, then $2\frac{1}{2}$ at 100 blocks. The space between 0 and $2\frac{1}{2}$: if we split the interval from 0 to 100 blocks into two parts (since 50 is half of 100), then the mortar for 50 blocks should be half of $2\frac{1}{2}$. Wait, $2\frac{1}{2}$ is 2.5, half of 2.5 is 1.25, which is $1\frac{1}{4}$. Wait, but let's check the options. One of the options is $1\frac{1}{4}$ (which is 1 1/4). Wait, the options are 1 1/4, 1/2, 1 3/4, 1 1/2. So let's re-examine.

Wait, the double number line: for 100 blocks, it's $2\frac{1}{2}$ bags. So the rate is $2\frac{1}{2}$ bags per 100 blocks. To find bags per block, it's $2\frac{1}{2}\div100=\frac{5}{2}\div100=\frac{5}{200}=\frac{1}{40}$ bags per block. Then for 50 blocks, it's $50\times\frac{1}{40}=\frac{50}{40}=\frac{5}{4}=1\frac{1}{4}$ bags. So the answer should be $1\frac{1}{4}$, which is option 1 1/4.

Wait, but let's check the double number line. The first interval on the mortar line: from 0 to $2\frac{1}{2}$ is over 0 to 100 blocks. So if we take half of 100 blocks (50), we take half of $2\frac{1}{2}$ bags. Half of $2\frac{1}{2}$: $2\frac{1}{2}\div2 = 1\frac{1}{4}$. So that's the calculation.

Answer:

1 1/4 (the first option)