Question

1.
a engineer puts two boards together and they overlap. whose problem is a regular is longer?
2.
46 : 71 = ?
3.
write the long - division number for
48 × 10(1) + (6 × 10)y + (3 × 1)y + (8 × \frac{1}{10})y + (2 × \frac{1}{100})y + (6 × \frac{1}{1000})?
4.
state the rule. then write the next three terms 18, 24, 30, ...
5.
in major league baseball, there are 30 yards between the bases. how many feet is that?
6.
8\frac{1}{4} - 2\frac{2}{4} = ?
7.
in the number 77,777 the underlined digit is ____ times as much as the place to its left.
8.
the kennel boarded many dogs for the holiday weekend. there were 42 dogs that needed boarding. each area holds 7 dogs. how many areas did the kennel need to board all the dogs?
9.
choose the numerical expression that represents dividing the product of 6 and 9 by 3.
10.
paul’s parents drove home from vacation. on saturday paul’s mom drove \frac{2}{13} of the trip. paul’s dad drove \frac{7}{13} of the trip. how much of the drive did paul’s parents complete on saturday?
11.
estimate first. then given the exact sum. 3.97 + 4.12 = ?
12.
(7 + 6) = ? = ?
13.
which length is the greatest? explain. 6.5 mi 1,000 yd 2,000 ft

Explanation:

Since the problem contains multiple sub - questions, we will solve them one by one. Let's start with question 10:

Question 10

Step 1: Identify the operation

We know that the total number of dogs is 42 and each cage holds 5 dogs. We need to find the number of cages, which requires division. But if there is a remainder, we need to add one more cage because we can't leave any dogs uncaged.
First, calculate \(42\div5\).
\(42\div5 = 8\) with a remainder of \(2\) (because \(5\times8 = 40\) and \(42-40 = 2\)).

Step 2: Determine the number of cages

Since there are 2 dogs left after filling 8 cages, we need one more cage. So the total number of cages is \(8 + 1=9\).

Step 1: Recall the operation for adding fractions

To find the total fraction of the trip Paul's parents completed, we need to add the fractions of the trip his mom and dad drove. The mom drove \(\frac{5}{13}\) and the dad drove \(\frac{7}{13}\) of the trip.
When adding fractions with the same denominator, we add the numerators and keep the denominator the same. So the formula is \(\frac{a}{b}+\frac{c}{b}=\frac{a + c}{b}\) (where \(b
eq0\)).
Here, \(a = 5\), \(c = 7\), and \(b = 13\).

Step 2: Perform the addition

\(\frac{5}{13}+\frac{7}{13}=\frac{5 + 7}{13}=\frac{12}{13}\)

Step 1: Estimate the sum

To estimate \(3.97+4.12\), we can round each number to the nearest whole number. \(3.97\) is close to \(4\) and \(4.12\) is close to \(4\). So the estimated sum is \(4 + 4=8\).

Step 2: Calculate the exact sum

Now, calculate the exact sum: \(3.97+4.12 = 8.09\)

Answer:

9

Question 12