A second ant walks all the way 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. EXPLAIN TO ME ONLY USING NUMBER AND SIGN
To work with the fractions 5 1/10 and 7 1/5, you need to convert the mixed numbers into improper fractions.
First, let's convert 5 1/10 into an improper fraction.
To do this, multiply the whole number (5) by the denominator (10), then add the numerator (1). This gives us (5*10 + 1) = 51.
Now the fraction 1/10 becomes 51/10.
Next, let's convert 7 1/5 into an improper fraction.
To do this, multiply the whole number (7) by the denominator (5), then add the numerator (1). This gives us (7*5 + 1) = 36.
Now the fraction 1/5 becomes 36/5.
So, the two dimensions of the triangle can be written as 51/10 and 36/5 centimeters.
Let's call the length of the unknown side of the triangle "x" centimeters. The total distance traveled by the ant is the sum of the three sides of the triangle:
5 1/10 + 7 1/5 + x = 20
To add the fractions, we need to have a common denominator. The common denominator of 10 and 5 is 10. So, we convert 7 1/5 into an improper fraction: 7 1/5 = (5*7 + 1)/5 = 36/5.
Now, the equation becomes:
51/10 + 36/5 + x = 20
To simplify, we can convert 51/10 into an improper fraction: 51/10 = 5*10 + 1/10 = 51/10 = 51/10.
Now, the equation becomes:
(51/10) + (36/5) + x = 20
We can simplify the left side of the equation:
(51/10) + (36/5) = (51*5 + 36*10)/(10*5) = (255 + 360)/50 = 615/50
The equation is now: 615/50 + x = 20
To solve for "x", we need to isolate it on one side of the equation. We can do this by subtracting 615/50 from both sides of the equation:
615/50 - 615/50 + x = 20 - 615/50
x = (20*50 - 615)/50 = (1000 - 615)/50 = 385/50
The length of the third side of the triangle is 385/50 centimeters.
So whats my first step to do the problem of 5 1/10 and 7 1/5?
so the the answer?
Apologies for any misunderstanding. The two dimensions of the triangle are 51/10 centimeters and 36/5 centimeters. To find the length of the third side of the triangle, we can subtract the sum of these two dimensions from the total distance traveled by the ant, which is 20 centimeters.
Length of the third side = Total distance traveled - (51/10 + 36/5)
To add the fractions, we need a common denominator, which is 10. So, the equation becomes:
Length of the third side = 20 - ( (51/10) + (36/5) )
Simplifying the equation, we can convert 51/10 into an improper fraction:
Length of the third side = 20 - ( (51/10) + (72/10) )
Length of the third side = 20 - (123/10)
To subtract fractions, we need to have a common denominator. So, we rewrite 20 as a fraction with a denominator of 10:
Length of the third side = (200/10) - (123/10)
Now, we can subtract the fractions:
Length of the third side = (200 - 123)/10
Length of the third side = 77/10
Therefore, the length of the third side of the triangle is 77/10 centimeters.