When you divide a proper fraction by an improper fraction, is the quotient less than 1,greater than 1,or equal to 1?
I think it is less than one but I'm not sure
The answer is less than one
(3/4) /(5/4) = (3/4) * (4/5) = 12/20 = 3/5
You're right. It's less than 1 because we invert the divisor and multiply.
Commutative property
In addition =a+b=b+a
Example =2+3=3+2
Well, when you divide a proper fraction by an improper fraction, the quotient can be greater than 1, equal to 1, or it could be less than 1. It all depends on the specific fractions involved.
But hey, let me tell you a joke to make things more lighthearted. Why did the fraction go to therapy? Because it had a lot of unresolved issues!
When you divide a proper fraction (a fraction where the numerator is smaller than the denominator) by an improper fraction (a fraction where the numerator is equal to or larger than the denominator), the quotient will always be less than 1.
To determine this, you can follow these steps:
Step 1: Convert the improper fraction to a mixed number (a whole number and a fraction).
Step 2: Perform the division by multiplying the numerator of the proper fraction with the reciprocal of the mixed number obtained in Step 1.
Step 3: Simplify the resulting fraction, if possible.
Let's use an example to illustrate this:
Suppose we want to divide the proper fraction 2/3 by the improper fraction 4/3.
Step 1: Convert the improper fraction 4/3 to a mixed number.
- Divide the numerator (4) by the denominator (3), which yields a quotient of 1 and a remainder of 1.
- The mixed number representation is 1 1/3.
Step 2: Multiply the proper fraction 2/3 by the reciprocal of 1 1/3.
- The reciprocal of 1 1/3 is 3/4.
2/3 * (3/4) = (2/3) * (3/4) = 2/4 = 1/2
Step 3: Simplify the resulting fraction.
- The fraction 1/2 is already in its simplest form.
Therefore, when you divide the proper fraction 2/3 by the improper fraction 4/3, the quotient is 1/2, which is less than 1.