Question

1. a civil engineer places one fire hydrant for every 6 lots in new neighborhoods. write and solve equations to find the number of fire hydrants that will be placed in each of the neighborhoods listed in the table.
2. communicate and justify benito says, “to find the quotient of 45÷9 automatically, i can recall one related multiplication fact and then use the commutative property of multiplication to recall the other related multiplication fact.” do you agree with benito? explain.
3. envision stem ashton is planning a long bike ride. if she rides her bike at a speed of 12 miles per hour, how many hours will it take her to ride 60 miles? draw and label a model that represents the problem. then solve.
4. higher order thinking a teacher asks students to place tiles on the classroom wall to show the alphabet. the tiles will each have one letter or be blank. each letter will have only one tile. the list shows the teacher’s rules for the arrangement of tiles.

. how many columns of tiles will there be?
. how many blank tiles will be used?
. what multiplication fact helped you solve the problem?

1. they must form a rectangle.
2. the rectangle must have 4 rows.
3. the rectangle must have the least possible number of columns.
4. which number is missing in this division equation? 132÷__ = 12

a 7 c 11
b 9 d 12

1. select all of the expressions that have a quotient equal to 6.

□ 36÷9 □ 33÷11
□ 48÷8 □ 6÷6
□ 12÷2

Explanation:

25.

Step1: Set up the division formula

Let $n$ be the number of fire - hydrants. The formula is $n=\frac{\text{Number of lots}}{6}$.

Step2: Calculate for each neighborhood

For the first neighborhood with 54 lots: $n_1=\frac{54}{6}=9$.
For Lake Forest with 12 lots: $n_2=\frac{12}{6}=2$.
For Meadow Breeze with 42 lots: $n_3=\frac{42}{6}=7$.

The related multiplication facts for $45\div9$ are $5\times9 = 45$ and $9\times5=45$. The Commutative Property of Multiplication states that $a\times b=b\times a$. Benito can use the multiplication facts $5\times9 = 45$ and $9\times5 = 45$ to find that $45\div9 = 5$. So, Benito is correct.

Step1: Recall the formula for time

The formula for time $t$ is $t=\frac{d}{s}$, where $d$ is distance and $s$ is speed. Here, $d = 60$ miles and $s=12$ miles per hour.

Step2: Calculate the time

$t=\frac{60}{12}=5$ hours.
To draw a model, we can represent the 60 - mile distance as a long bar. Divide this bar into 12 - mile segments. There will be 5 such segments, representing 5 hours.

Answer:

In the first neighborhood: 9 fire - hydrants.
In Lake Forest: 2 fire - hydrants.
In Meadow Breeze: 7 fire - hydrants.

26.