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.

neighborhood number of
lake forest 54
meadow breeze 12
cherry farms 42

1. 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.
2. 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.
3. 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 teachers 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?
think about the lowest multiple of 4 that is the same or greater than the number of letters of the alphabet.

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
48÷8
12÷2
33÷11
6÷6

Explanation:

25.

Step1: Set up division formula

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

Step2: Calculate for Lake Forest

For Lake Forest with 54 lots, $n_{1}=\frac{54}{6}=9$.

Step3: Calculate for Meadow Breeze

For Meadow Breeze with 12 lots, $n_{2}=\frac{12}{6}=2$.

Step4: Calculate for Cherry Farms

For Cherry Farms with 42 lots, $n_{3}=\frac{42}{6}=7$.

The Commutative Property of Multiplication is $a\times b = b\times a$. But when finding $45\div9$, we use the related multiplication fact $9\times5 = 45$ (or $5\times9 = 45$). Division is the inverse of multiplication. We recall the multiplication fact $9\times5=45$ to get $45\div9 = 5$. The Commutative Property is not directly used in the process of finding the quotient of a division problem by recalling multiplication facts.

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 draw a rectangle and divide it into 60 equal - sized parts to represent the 60 miles. Then, group the parts into sets of 12 to represent the number of miles per hour. We will find that there are 5 such groups.

Answer:

Lake Forest: 9 fire - hydrants; Meadow Breeze: 2 fire - hydrants; Cherry Farms: 7 fire - hydrants

26.