5th Grade Math Quiz: Test Your Math Knowledge

Explanation
The number thirty-four thousand two hundred and eighty-four is written numerically as 34,284. This is because "thirty-four thousand" represents 34,000, and "two hundred and eighty-four" represents 284. When combined, they form 34,284.

Explanation
To calculate 75 m x 15 cm x 5 m and keep the result in cubic meters (m3), you need to convert 15 cm to meters.
15 cm = 0.15 m
Now, perform the calculation:
75 m x 0.15 m x 5 m
= 75 x 0.15 x 5
= 75 x 0.75
= 56.25 m3
So, 75 m x 15 cm x 5 m = 56.25 cubic meters (m3).

Explanation
The number 400,256 is written in words as "Four hundred thousand, two hundred fifty-six." It is broken down into two parts: "Four hundred thousand" represents the 400,000, and "two hundred fifty-six" represents the remaining 256. The comma separates the thousands from the hundreds, making it easier to read. Writing numbers in words helps to clearly communicate large values without confusion, especially in formal or legal contexts.

Explanation
To find the missing numbers in the sequence 1, 3, 6, ___, 15, ____, 28, we need to determine the pattern.
The sequence is: 1, 3, 6, ___, 15, ____, 28
Notice that each number in the sequence is a triangular number. Triangular numbers are calculated using the formula n(n+1)/2, where n is the position in the sequence.
Let's calculate the triangular numbers to identify the pattern:
For n = 1: 1(1+1)/2 = 1
For n = 2: 2(2+1)/2 = 3
For n = 3: 3(3+1)/2 = 6
For n = 4: 4(4+1)/2 = 10
For n = 5: 5(5+1)/2 = 15
For n = 6: 6(6+1)/2 = 21
For n = 7: 7(7+1)/2 = 28
So, the complete sequence of triangular numbers up to 28 is: 1, 3, 6, 10, 15, 21, 28.
Therefore, the missing numbers in the sequence are 10 and 21. The sequence should be: 1, 3, 6, 10, 15, 21, 28.

Explanation
Both 1 and 36 are common to both square and triangular numbers.
1 is a square number (1 = 1 * 1) and a triangular number (1 = 1 * (1 + 1) / 2).
36 is a square number (36 = 6 * 6) and a triangular number (36 = 8 * (8 + 1) / 2).
The other pairs do not have both numbers fitting the criteria of being both square and triangular numbers.

Explanation
First, add the kilometers: 5 km + 12 km = 17 km
Next, add the meters: 700 m + 450 m = 1150 m
Since 1000 meters equal 1 kilometer, we convert 1150 meters: 1150 m = 1 km 150 m
Now, add this to the kilometers: 17 km + 1 km = 18 km
So, the final total is: 18 km + 150 m
Therefore: 5 km 700 m + 12 km 450 m = 18 km 150 m

Explanation
To calculate 55 km 75 m - 23 km 40 m:
Subtract the kilometers: 55 km - 23 km = 32 km
Subtract the meters: 75 m - 40 m = 35 m
So, 55 km 75 m - 23 km 40 m = 32 km 35 m
Therefore, the correct answer is: 32 km 35 m

Explanation
In a cylinder, the two bases are circular and lie on the upper and lower surfaces. These bases are parallel and congruent to each other. The side surface, called the lateral surface, connects the two bases.

Explanation
At 3:00, the minute hand is on the 12, and the hour hand is on the 3. The angle between the 12 and the 3 on a clock is 90 degrees because each number on the clock represents a 30-degree increment (360 degrees divided by 12 hours = 30 degrees per hour). Since 3 hours is three 30-degree increments, the total angle between the hands at 3:00 is 90 degrees. A 90-degree angle is known as a right angle, not an acute angle. An acute angle is any angle that is less than 90 degrees. Therefore, the hands of the clock at 3:00 do not form an acute angle.

Explanation
To calculate the total time Ash works on his computer from 10:00 AM to 3:30 PM, follow these steps:
Calculate the time from 10:00 AM to 12:00 PM:
This is 2 hours.
Calculate the time from 12:00 PM to 3:30 PM:
From 12:00 PM to 3:00 PM is 3 hours.
From 3:00 PM to 3:30 PM is 0.5 hours.
Add the hours together:
2 hours (10:00 AM to 12:00 PM)
3 hours (12:00 PM to 3:00 PM)
0.5 hours (3:00 PM to 3:30 PM)
Total time Ash works on his computer:
2 hours + 3 hours + 0.5 hours = 5.5 hours
Therefore, Ash works on his computer for 5 hours and 30 minutes.