I need at least 5 mixed numbers that equal up to 10 and are all different. They must use only 1/4 and 1/3.
To find 5 mixed numbers that equal up to 10 and use only 1/4 and 1/3, follow these steps:
Step 1: Start with the largest fraction, 1/3, and find the equivalent mixed numbers that equal up to 10.
1/3 = 0.33 (approx.)
So, one possible mixed number using 1/3 is 3 1/3.
Step 2: Subtract this mixed number from 10 to find the remaining amount.
10 - 3 1/3 = 6 2/3
Step 3: Next, use the remaining amount (6 2/3) and try to find mixed numbers using 1/4.
6 2/3 expressed as an improper fraction is 20/3.
Step 4: Divide 20/3 by 1/4 to find how many times 1/4 fits in 20/3.
(20/3) ÷ (1/4) = (20/3) × (4/1) = 80/3 = 26 2/3
So, another mixed number using 1/4 is 26 2/3.
Step 5: Subtract this mixed number from the remaining amount (6 2/3) to find the new remaining amount.
(6 2/3) - (26 2/3) = -20 (negative sign indicates that we have used more than what was available)
Since the result is negative, it means that we can't find any more mixed numbers using 1/4 to equal up to 10 using only 1/4 and 1/3.
Therefore, two mixed numbers using 1/3 and 1/4 that equal up to 10 are 3 1/3 and 26 2/3.
To find five mixed numbers that equal up to 10 using only 1/4 and 1/3, we can follow these steps:
Step 1: Determine the maximum number of each fraction you can use to reach 10.
To do this, divide 10 by each fraction:
10 / 1/4 = 40
10 / 1/3 = 30
So, we need to find five mixed numbers that add up to a number between 30 and 40.
Step 2: Start with the largest fraction (1/3) and use it as an iterator.
We can start with the largest fraction, 1/3, and see how many times it goes into the remaining total.
Step 3: Find the first mixed number.
To do this, divide the remaining total by the largest fraction without considering the whole number. For example:
30 / 1/3 = 90
So, we can have a mixed number of 1 and 2/3.
Step 4: Subtract the value of the first mixed number from the remaining total.
To find the remaining total, subtract the value of the first mixed number from the original total:
30 - 90 = -60
Step 5: Repeat steps 3 and 4 for the remaining mixed numbers.
Using the same process, we can find four more mixed numbers:
1. Second mixed number: 1 and 1/4
Remaining total: -60 - 15 = -75
2. Third mixed number: 1 and 1/3
Remaining total: -75 - 30 = -105
3. Fourth mixed number: 1 and 2/4
Remaining total: -105 - 30 = -135
4. Fifth mixed number: 1 and 1/3
Remaining total: -135 - 30 = -165
We cannot reach a positive value with only these two fractions while using different mixed numbers that sum up to 10.