What is the quotient when you divide −2 3/5 by 4/5 ?
To divide -2 3/5 by 4/5, we can convert the mixed number to an improper fraction.
-2 3/5 = (-2 * 5 + 3)/5 = -13/5
Now, we can divide -13/5 by 4/5.
(-13/5) / (4/5) = (-13/5) * (5/4) = -13/4
Therefore, the quotient is -13/4.
To find the quotient, or the result of dividing −2 3/5 by 4/5, you need to follow these steps:
Step 1: Convert the mixed number −2 3/5 to an improper fraction.
To convert a mixed number to an improper fraction, you multiply the denominator (5) by the whole number (-2), then add the numerator (3). Place the sum over the denominator (5) to get the improper fraction.
-2 3/5 = (-2 * 5 + 3) / 5 = (-10 + 3) / 5 = -7/5.
Step 2: Invert the divisor, which is 4/5, to become its reciprocal.
To find the reciprocal of a fraction, simply swap the numerator and denominator.
Reciprocal of 4/5 = 5/4.
Step 3: Multiply the dividend (-7/5) by the reciprocal of the divisor (5/4).
To multiply fractions, you multiply the numerators together and multiply the denominators together.
(-7/5) ÷ (4/5) = (-7/5) * (5/4) = (-7 * 5) / (5 * 4) = -35/20.
Step 4: Simplify the resulting fraction, if possible.
In this case, the fraction -35/20 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which is 5.
-35/20 = (-7 * 5) / (4 * 5) = -7/4.
Therefore, the quotient of −2 3/5 divided by 4/5 is -7/4.
To find the quotient when you divide −2 3/5 by 4/5, we can proceed with the following steps:
Step 1: Convert the mixed numbers to improper fractions.
- The mixed number −2 3/5 can be written as a fraction by multiplying the whole number (-2) by the denominator of the fraction (5) and adding the numerator (3). This gives us -13/5.
- The fraction 4/5 is already in proper form.
Step 2: Invert the divisor (the second fraction) and change the operation to multiplication.
- The reciprocal (inverted form) of 4/5 is 5/4.
Step 3: Multiply the dividend (the first fraction) with the reciprocal of the divisor.
- Multiplying -13/5 by 5/4 gives us (-13/5) * (5/4) = -65/20.
Step 4: Simplify the resulting fraction, if necessary.
- The fraction -65/20 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5. This gives us -13/4.
Therefore, the quotient when you divide -2 3/5 by 4/5 is -13/4.