I'm helping my son he is in 4th grade . His hw it's hard and this is the problem : find two mixed numbers. So that the sum is 7 2/8 and the difference 2 4/8.
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I don't know if this answer is too advanced for 4th grade.
Let one number = x and the other = y.
x + y = 7 2/8
x - y = 2 4/8
Add the two equations to find value of x.
2x = 9 6/8
Divide both sides by 2.
x = 4 7/8
Substitute the x value in either equation to find y.
To find two mixed numbers that satisfy the given conditions, we can set up a system of equations.
Let's assume the two mixed numbers as:
First mixed number: A = x + y/8
Second mixed number: B = z + w/8
where x, y, z, and w are integer values.
According to the problem, the sum of the two mixed numbers is equal to 7 2/8, which can be represented as:
A + B = 7 + 2/8
Substituting the values of A and B, we get:
(x + y/8) + (z + w/8) = 7 + 2/8
Simplifying the expression, we have:
(x + z) + (y/8 + w/8) = 7 + 2/8
Now let's consider the difference of the two mixed numbers, which is equal to 2 4/8:
A - B = 2 + 4/8
Substituting the values of A and B, we get:
(x + y/8) - (z + w/8) = 2 + 4/8
Simplifying the expression, we have:
(x - z) + (y/8 - w/8) = 2 + 4/8
From this system of equations, we need to solve for x, y, z, and w.
Let's focus on the first equation:
(x + z) + (y/8 + w/8) = 7 + 2/8
Now, let's look at the second equation:
(x - z) + (y/8 - w/8) = 2 + 4/8
We can use these two equations to solve for x, y, z, and w by eliminating one of the variables.
To eliminate the x term, subtract the second equation from the first equation:
[(x + z) + (y/8 + w/8)] - [(x - z) + (y/8 - w/8)] = (7 + 2/8) - (2 + 4/8)
Simplifying the equation further, we have:
x + z + y/8 + w/8 - x + z - y/8 + w/8 = 7 + 2/8 - 2 - 4/8
Canceling out the x terms and regrouping similar terms, we get:
2z + 2w/8 = 5
Multiplying both sides of the equation by 8 to eliminate the fractions, we have:
16z + 2w = 40
Now solve the first equation for x:
x + z + y/8 + w/8 = 7 + 2/8
x + z + y/8 + w/8 = 58/8 + 2/8
Combining similar terms, we get:
x + z + y/8 + w/8 = 60/8
Multiplying both sides of the equation by 8 to eliminate the fractions, we have:
8x + 8z + y + w = 60
Now we have two equations:
16z + 2w = 40
8x + 8z + y + w = 60
To solve these equations, we need to use a method like substitution or elimination.
Please note that solving these equations requires linear algebra techniques which are usually taught in higher grades. If your son is in 4th grade, it might be better to consider a simpler problem or seek assistance from his teacher.
To find two mixed numbers that satisfy the given conditions (sum and difference), you can follow these steps:
Step 1: Write down the given sum and difference to get a system of equations:
- Sum: 7 2/8 = a + b (equation 1, where a and b are the two mixed numbers)
- Difference: 2 4/8 = a - b (equation 2)
Step 2: Simplify the fractions in both equations:
- Sum: 7 1/4 = a + b (equation 1)
- Difference: 2 1/2 = a - b (equation 2)
Step 3: Convert the mixed numbers to improper fractions:
- Sum: 29/4 = a + b (equation 1)
- Difference: 5/2 = a - b (equation 2)
Step 4: Solve the system of equations by using either substitution or elimination method. Let's use the elimination method here:
Multiply equation 2 by 2 to make the denominators the same:
- 2*(5/2) = 2*(a - b)
- 10/2 = 2a - 2b
- 5 = 2a - 2b (equation 3)
Now subtract equation 3 from equation 1 to eliminate the 'b' terms:
- (29/4) - (5) = (a + b) - (2a - 2b)
- 29/4 - 20/4 = a + b - 2a + 2b
- 9/4 = -a + 3b
Rearrange this equation:
- 3b - a = 9/4 (equation 4)
Step 5: Solve the system of equations 3 and 4:
Now, you have two linear equations with two variables:
- Equation 3: 5 = 2a - 2b
- Equation 4: 3b - a = 9/4
You can solve this system of equations using any method of your preference, such as substitution, elimination, or graphing.
Once you find the values of 'a' and 'b', you can convert them back to mixed numbers.
Note: To find the specific values of 'a' and 'b', I will need more information or additional equations.