ADD & SUBTRACT RATIONAL NUMBERS APPLY SHOW WORK HOW YOU WORKED THE QUESTION BY STEPS !
1. AN ANT STANDS AT ONE VERTEX OF A RECTANGULAR SHEET OF PAPER. THE ANT THEN PROCEEDS TO WALK ALL THE WAY AROUND THE PERIMETER OF THE PAPER. THE DIMENSIONS OF THE SHEET OF PAPER ARE 3 5/8 INCHES BY 2 7/8 INCHES/ HOW MANY INCHES DOES THE ANT TRAVEL? SHOW YOUR WORK HOW YOU GOT THE ANSWER WITH ALL STEPS.
2. SUPPOSE THAT EACH DIMENSION OF THE SHEET OF PAPER DESCRIBED IN QUESTION 1 IS INCREASED BY ONE INCH. HOW MANY INCHES WILL THE ANT TRAVEL IN THIS CASE? EXPLAIN SHOW YOUR WORK HOW YOU GOT YOUR ANSWER!
3.A SECOND ANT WALKS AROUND A TRIANGLE DRAWN IN THE DIRT. TWO OF THE DIMENSIONS OF THE TRIANGLE ARE 5 1/10 CENTIMETERS AND 7 1/5 CENTIMETERS. THE TOTAL DISTANCE TRAVELED BY THE ANT IS 20 CENTIMETERS. WHAT IS THE LENGTH OF THE THIRD SIDE OF THE TRIANGLE? SHOW ALL WORK AND STEPS TO YOUR ANSWER!
1. To find the perimeter of the rectangular sheet of paper, we need to add together all four sides.
First, let's convert the mixed numbers to improper fractions:
3 5/8 = (3 * 8 + 5)/8 = 29/8
2 7/8 = (2 * 8 + 7)/8 = 23/8
Now, add the lengths of the sides:
Perimeter = 2(29/8) + 2(23/8) = 58/8 + 46/8 = 104/8 = 13
Therefore, the ant travels 13 inches.
2. If each dimension of the sheet of paper is increased by one inch, we need to add 1 to each length.
New length of one side: 29/8 + 1 = 29/8 + 8/8 = 37/8
New length of the other side: 23/8 + 1 = 23/8 + 8/8 = 31/8
Now, find the new perimeter by adding the lengths of the sides:
Perimeter = 2(37/8) + 2(31/8) = 74/8 + 62/8 = 136/8 = 17
Therefore, the ant will travel 17 inches in this case.
3. Let's first convert the mixed numbers to improper fractions:
5 1/10 = (5 * 10 + 1)/10 = 51/10
7 1/5 = (7 * 5 + 1)/5 = 36/5
To find the length of the third side of the triangle, we need to subtract the sum of the two known sides from the total distance traveled by the ant:
Length of third side = Total distance - (51/10 + 36/5) = 20 - (51/10 + 36/5)
To add these fractions, we need a common denominator:
51/10 + 36/5 = (51 * 2)/(10 * 2) + 36/5 = 102/20 + 36/5 = (102 + 72)/20 = 174/20
Now, subtract this sum from the total distance:
Length of third side = 20 - 174/20 = (20 * 20)/20 - 174/20 = 400/20 - 174/20 = 226/20
Simplify the fraction if possible:
Length of third side = 113/10
Therefore, the length of the third side of the triangle is 113/10 centimeters.
1. To find the total distance traveled by the ant around the rectangular sheet of paper, we need to calculate the perimeter.
Perimeter = 2 * (Length + Width)
Given:
Length = 3 5/8 inches
Width = 2 7/8 inches
Convert the mixed numbers to improper fractions:
Length = 3 + 5/8 = (3*8 + 5)/8 = 29/8 inches
Width = 2 + 7/8 = (2*8 + 7)/8 = 23/8 inches
Substitute the values into the formula:
Perimeter = 2 * (29/8 + 23/8)
= 2 * (52/8)
= 2 * 6.5
= 13 inches
Therefore, the ant travels 13 inches around the rectangular sheet of paper.
2. If each dimension of the sheet of paper is increased by one inch, the new length and width will be:
New Length = 29/8 + 1 = 29/8 + 8/8 = 37/8 inches
New Width = 23/8 + 1 = 23/8 + 8/8 = 31/8 inches
Calculate the new perimeter using the same formula as before:
New Perimeter = 2 * (37/8 + 31/8)
= 2 * (68/8)
= 2 * 8.5
= 17 inches
Therefore, the ant will travel 17 inches in this case.
3. To find the length of the third side of the triangle, we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given:
Side A = 5 1/10 centimeters = (5*10 + 1)/10 = 51/10 centimeters
Side B = 7 1/5 centimeters = (7*5 + 1)/5 = 36/5 centimeters
Total distance traveled = 20 centimeters
Let the length of the third side be x centimeters.
According to the triangle inequality theorem:
Side A + Side B > x
Substituting the given values:
51/10 + 36/5 > x
To simplify the equation, find a common denominator:
51/10 + (36/5 * 2/2) > x
51/10 + 72/10 > x
(51 + 72)/10 > x
123/10 > x
Therefore, the length of the third side of the triangle is less than 123/10 centimeters.
Note: Since we don't have any other information about the triangle, we cannot determine the exact length of the third side. We can only conclude that it is less than 123/10 centimeters.
1. To find the total distance traveled by the ant, we need to calculate the perimeter of the rectangular sheet of paper.
The dimensions of the sheet of paper are given as 3 5/8 inches by 2 7/8 inches.
Step 1: Convert the mixed numbers to improper fractions.
3 5/8 = (3 * 8 + 5)/8 = 29/8 inches
2 7/8 = (2 * 8 + 7)/8 = 23/8 inches
Step 2: Calculate the perimeter by adding all four sides of the rectangle.
Perimeter = 2 * (Length + Width)
= 2 * (29/8 + 23/8)
= 2 * (52/8)
= 104/8
= 13 inches
Therefore, the ant travels 13 inches.
2. In this case, each dimension of the sheet of paper is increased by one inch.
Step 1: Add one inch to each dimension.
New length = 3 5/8 + 1 = 4 5/8 inches
New width = 2 7/8 + 1 = 3 7/8 inches
Step 2: Calculate the new perimeter using the increased dimensions.
New perimeter = 2 * (New length + New width)
= 2 * (4 5/8 + 3 7/8)
= 2 * (9 13/8)
= 2 * (73/8)
= 73/4
= 18.25 inches
Therefore, the ant travels 18.25 inches in this case.
3. To find the length of the third side of the triangle, we can use the fact that the total distance traveled by the ant is equal to the sum of all three sides of the triangle.
The two given dimensions of the triangle are 5 1/10 centimeters and 7 1/5 centimeters, and the total distance traveled by the ant is 20 centimeters.
Step 1: Convert the mixed numbers to improper fractions.
5 1/10 = (5 * 10 + 1)/10 = 51/10 centimeters
7 1/5 = (7 * 5 + 1)/5 = 36/5 centimeters
Step 2: Subtract the sum of the given sides from the total distance to find the length of the third side.
Length of the third side = Total distance - (Side 1 + Side 2)
= 20 - (51/10 + 36/5)
= 20 - (51/10 + 72/10)
= 20 - 123/10
= 200/10 - 123/10
= 77/10 centimeters
Therefore, the length of the third side of the triangle is 77/10 centimeters.