5 2/3 - 5= 2/3.
Use a division algorithm to find the quotient. State the final answer as a mixed number.
Why is the fractional part of your quotient different from your answer in the original equation 5 2/3 - 5= 2/3?
To find the quotient using a division algorithm, we need to divide the numerator (5 2/3) by the denominator (5) of the fraction.
Step 1: Convert the whole number 5 to a fraction with a denominator of 3.
5 = 5/1
Step 2: Find a common denominator for the fractions 5/1 and 2/3, which is 3.
5/1 = 15/3 (multiply numerator and denominator by 3)
Now we have (15/3) - (5/1) = 2/3
Step 3: Subtract the fractions:
15/3 - 5/1 = (15-15)/3 = 0/3 = 0
Therefore, the quotient is 0.
The fractional part of the quotient is 0/3, which is different from the original equation 5 2/3 - 5 = 2/3 because the original equation did not involve division. It was subtracting 5 from 5 2/3, which resulted in a fraction of 2/3. The division algorithm is used to find the quotient when dividing one fraction by another.
To find the quotient using a division algorithm, we can rewrite the equation as a division problem. Let's start by subtracting 5 from 5 2/3:
5 2/3 - 5 = 2/3
To find the quotient, we need to divide the numerator (2) by the denominator (3). We can represent this as follows:
2 ÷ 3
When dividing fractions, we can convert the division problem into a multiplication problem by taking the reciprocal of the divisor and multiplying it with the dividend:
2/1 × 3/3 = 6/3
Simplifying the fraction, we have:
6/3 = 2
Therefore, the quotient is 2.
Now, let's address the issue of the fractional part being different. The original equation, 5 2/3 - 5 = 2/3, does not equal 2 as a mixed number. To understand why, let's break down the original equation:
5 2/3 - 5 = 2/3
First, we rewrite the whole number (5) as a fraction with the same denominator (3) as the fractional part:
15/3 + 2/3 - 5/1 = 2/3
Next, we add the numerators together and keep the denominator the same:
17/3 - 5/1 = 2/3
Now, let's subtract the fractions:
(17/3) - (5/1) = 2/3
To simplify the equation, we need to find a common denominator for 3 and 1, which is 3:
(17/3) - (15/3) = 2/3
Finally, we subtract the numerators:
2/3 = 2/3
As we can see, the fraction on both sides of the equation is indeed the same. Therefore, the fractional part of the quotient is not different from the answer in the original equation.