mrs. lemeke has 10 2/3 ounces of fertilizer . she plans to use 3/4 ounce of fertilizer on each plant. After she puts fertilizer on as many plants as she can, how much fertilizer will be left over?
(10 2/3) / (3/4)
= 32/3 * 4/3
= 128/9
= 14 2/9
So, there will be 14 plants fertilized, with some left over.
To find out how much fertilizer will be left over after Mrs. Lemeke puts fertilizer on as many plants as she can, we can follow these steps:
Step 1: Convert the mixed number (10 2/3) to an improper fraction:
To do this, multiply the whole number (10) by the denominator (3), and then add the numerator (2) to get the new numerator. The denominator remains the same.
10 * 3 + 2 = 32
So, the mixed number 10 2/3 can be represented as an improper fraction: 32/3.
Step 2: Divide the total amount of fertilizer by the amount used per plant to find the maximum number of plants:
To do this, divide the numerator (32) by the denominator (3).
32 ÷ 3 = 10 remainder 2
So, Mrs. Lemeke can put fertilizer on a maximum of 10 plants with 2/3 ounce remaining.
Step 3: Calculate the amount of leftover fertilizer:
To find out exactly how much fertilizer is left, we subtract the amount used on the maximum number of plants from the total amount of fertilizer:
Total amount of fertilizer - (Amount used per plant × Maximum number of plants)
10 2/3 - (3/4 × 10)
To subtract mixed numbers/fractions, we need to find a common denominator. The least common denominator (LCD) of 3 and 4 is 12.
Converting 10 2/3 to an improper fraction: 32/3
Converting 3/4 to twelfths: 9/12
32/3 - (9/12 × 10)
Now we can subtract the fractions by multiplying the denominators to get a common denominator:
32/3 - (90/12)
To subtract fractions, we need to have a common denominator. In this case, it is 12. Convert 32/3 to twelfths:
32/3 = 128/12
128/12 - 90/12
Subtract the numerators:
(128 - 90)/12 = 38/12
Step 4: Simplify the fraction:
In this case, the fraction 38/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
38 ÷ 2 / 12 ÷ 2 = 19/6
So, Mrs. Lemeke will have 19/6 ounces of fertilizer left over after putting fertilizer on as many plants as she can.
Therefore, Mrs. Lemeke will have 19/6 ounces of fertilizer remaining.