I'm not sure how to answer this.
Select two fractions whose sum is 3/4 and whose denominators are both the same but not equal to 4
To find two fractions whose sum is 3/4 and whose denominators are the same but not equal to 4, we can follow these steps:
1. Let's assume the denominator of both fractions as 'x'. Since the denominators should be the same, this will help us find the numerator of each fraction.
2. Let's suppose the numerators of the fractions as 'a' and 'b'. Therefore, the fractions can be written as a/x and b/x.
3. According to the problem, the sum of the fractions is 3/4. So, the equation will be: a/x + b/x = 3/4.
4. To solve this equation, we need to find the values of 'a', 'b', and 'x'.
5. One way to approach this is to express 3/4 with a common denominator of 'x' so that we can equate the numerators and solve for 'a' and 'b'. Multiply 3/4 by 'x/x' to get 3x/4x.
6. Now, setting the numerators equal, we have:
a + b = 3x/4x.
7. Since 'x' is common to both fractions, we can set 'a' and 'b' equal to a factor of 'x'. Let's select 'a' as 'x' and 'b' as '2x' for convenience.
8. Now, we have: x + 2x = 3x/4x.
9. Simplifying further, we get: 3x = 3x/4.
10. To solve this equation, we can multiply both sides by 4x (the common denominator) to eliminate fractions: 4x * 3x = 3x * 3x/4.
11. Simplifying, we have: 12x^2 = 9x^2.
12. Dividing both sides by 3x^2, we get: 12/9 = x^2/x^2.
13. This simplifies to: 4/3 = 1.
14. However, since 4/3 does not equal 1, this means that there is no solution that satisfies the conditions given in the problem.
Therefore, there are no two fractions with the same denominator, not equal to 4, whose sum is equal to 3/4.
How about 3/8 and 3/8 or
1/8 and 5/8 ? or
13/40 and 17/40 ?
method, pick a multiple of 4, e.g. 36
then 3/4 = ?/36 or 27/36 = 3/4
now split the 27 into 2 parts so they have a sum of 27
how about 5/36 and 22/36
check: 5/36 and 22/36 have the same denominator, not 4
and their sum is 5/36 + 22/36 = 27/36 = 3/4
Thanks! Also, how are equivalent fractions used in writing a sum of two like fractions in simplest form?
Ans: Equivalent fractions can be reduced into simplest form.
1/8 + 5/8 = 6/8 = 3/4
7/12 + 2/12 = 9/12 = 3/4
and so on