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How can you tell whether the sum of two fractions with a common denominator is less than 1?
if you are adding two fractions that are both greater than 1/2, what must be true about the sum?
What is the sum of all the positive proper fractions with denominators less than or equal to 100?
Consider a denominator of r; It has proper fractions: 1/r, 2/r, ...., (r-1)/r Their sum is: (1 + 2 + ... + (r-1))/r The numerator of this sum is 1 + 2 + ... + (r-1) Which is an Arithmetic Progression (AP) with r-1 terms, and sum: sum = number_of_term(first + last)/2 = (r-1)(1 + r-1)/2 = (r-1)r/2 So the sum of the proper fractions with a denominator or r is: sum{r} = ((r-1)r/2)/r = ((r-1)r/2r = (r-1)/2 Now consider the sum of the proper fractions with a denominator r+1: sum{r+1} = (((r+1)-1)/2 = ((r-1)+1)/2 = (r-1)/2 + 1/2 = sum{r) + 1/2 So the sums of the proper fractions of the denominators forms an AP with a common difference of 1/2 The first denominator possible is r = 2 with sum (2-1)/2 = ½; The last denominator required is r = 100 with sum (100-1)/2 = 99/2 = 49½; And there are 100 - 2 + 1 = 99 terms to sum So the required sum is: sum = ½ + 1 + 1½ + ... + 49½ = 99(½ + 49½)/2 = 99 × 50/2 = 2475
fractions less than 1/2?
0.5
What are 2 fractions whose sum is 2 thirds?
How about: 1/3+1/3 = 2/3 as one example
How do you find the sum using fractions bars?
3 1/2+6 5/8
How can you tell whether the sum of two fractions with a common denominator is less than 1?
if you are adding two fractions that are both greater than 1/2, what must be true about the sum?
What is the sum of all the positive proper fractions with denominators less than or equal to 100?
Consider a denominator of r; It has proper fractions: 1/r, 2/r, ...., (r-1)/r Their sum is: (1 + 2 + ... + (r-1))/r The numerator of this sum is 1 + 2 + ... + (r-1) Which is an Arithmetic Progression (AP) with r-1 terms, and sum: sum = number_of_term(first + last)/2 = (r-1)(1 + r-1)/2 = (r-1)r/2 So the sum of the proper fractions with a denominator or r is: sum{r} = ((r-1)r/2)/r = ((r-1)r/2r = (r-1)/2 Now consider the sum of the proper fractions with a denominator r+1: sum{r+1} = (((r+1)-1)/2 = ((r-1)+1)/2 = (r-1)/2 + 1/2 = sum{r) + 1/2 So the sums of the proper fractions of the denominators forms an AP with a common difference of 1/2 The first denominator possible is r = 2 with sum (2-1)/2 = ½; The last denominator required is r = 100 with sum (100-1)/2 = 99/2 = 49½; And there are 100 - 2 + 1 = 99 terms to sum So the required sum is: sum = ½ + 1 + 1½ + ... + 49½ = 99(½ + 49½)/2 = 99 × 50/2 = 2475
When does the sum of two fractions equal 1?
1/2 + 1/2 = 1
What are two fractions that make a sum of two?
1/2 + 1 1/2=2
When you add 2 fractions the sum is always less than 1?
This is a false statement. An example would be 1/3 plus 3/4; the sum of wich is 13/12 or 1 1/12.
Why is the quotient of two fractions less than 1 greater than both?
It need not be. The numbers 1/2 and (-1/2) are both fractions less than 1 but their quotient is -1, which is less than both the fractions.
When does the sum of two fractions equal one?
The sum of two fractions will be equal to one when the numerator and the denominator of their sum are the same. Example: 1/3 + 2/3 = 3/3 or 1
What two fractions equal the sum 5 6ths?
1/3 + 1/2
What fractions is less then 1 over 2?
1/3
What is the sum of 2 over 5 and 1 over 2?
The sum of those fractions is 9 over 10 or 9/10.
When the sum of 2 fraction is 1 if one of the fraction is 38 greater than the other what are the 2 fractions?
The two fractions are -181/2 and 191/2.
fractions less than 1/2?
0.5
