Oh my gosh this is driving me nuts, I just started 6th grade last week, please help...A piece of paper is 280 millimeters long and 200 millimeters wide. you want to draw a grid on the paper so that there is a whole number of squares on the paper. What are the possible sizes of the squares? What is the largest possible square?
Arghh!! I miss summer!
First, calculate the area.
280 * 200 = 56,000mm^2
Any number that will divide into that area without leaving a remainder will give you the number of whole squares.
I hope this helps. Thanks for asking.
40 for the first one
48 is the last one
I know starting a new grade can be overwhelming, but don't worry, I'm here to help you with this math problem!
To find the possible sizes of the squares that can fit on the paper, we need to find the greatest common divisor (GCD) of the length and width of the paper. The GCD will give us the maximum size of the squares that can be drawn.
First, let's find the GCD of 280 and 200:
GCD(280, 200) = 40
So, the largest possible square that can be drawn is a square with sides measuring 40 millimeters.
Now, let's consider the other possible sizes of the squares. We can find these sizes by dividing the length and width of the paper by the GCD:
Length ÷ GCD = 280 ÷ 40 = 7
Width ÷ GCD = 200 ÷ 40 = 5
So, the possible sizes of the squares are 7 millimeters by 5 millimeters.
Remember, these are the possible sizes for the squares, but you can also have smaller squares by dividing each side further. I hope this helps!
Don't worry, I'm here to help you with your math problem. Let's break it down step by step.
To find the possible sizes of the squares that can fit on the piece of paper, we need to find the greatest common divisor (GCD) of the length and width of the paper. The GCD is the largest number that divides both values evenly.
So, for the given dimensions:
Length = 280 millimeters
Width = 200 millimeters
To find the GCD, you can use a method called prime factorization. Start by finding the prime factors of both 280 and 200:
280 = 2 * 2 * 2 * 5 * 7
200 = 2 * 2 * 2 * 5 * 5
Next, identify the common prime factors between the two numbers:
Common prime factors: 2 * 2 * 2 * 5 = 40
So, the GCD of 280 and 200 is 40 millimeters.
To determine the possible sizes of the squares on the paper, we need to find all the factors of the GCD. The factors are the numbers that can divide the GCD evenly:
Factors of 40: 1, 2, 4, 5, 8, 10, 20, and 40
These are the possible sizes of the squares that can fit on the paper.
To find the largest possible square, we take the largest factor of the GCD, which is 40. Therefore, the largest possible square size is 40 millimeters by 40 millimeters.