3 1/2 divided by 2 1/4 in simplest form? 3 1/2 divided by 1/4
The Correct Answer and Explanation is:
To solve the division of 3 1/2 by 2 1/4, let’s break it down step by step:
Step 1: Convert Mixed Numbers to Improper Fractions
First, convert the mixed numbers into improper fractions.
3 1/2 can be converted as follows:
- Multiply the whole number (3) by the denominator (2), which gives 6.
- Add the numerator (1) to 6, resulting in 7.
- So, 3 1/2 becomes 7/2.
2 1/4 can be converted similarly:
- Multiply the whole number (2) by the denominator (4), which gives 8.
- Add the numerator (1) to 8, resulting in 9.
- So, 2 1/4 becomes 9/4.
Now, we have 7/2 divided by 9/4.
Step 2: Division of Fractions
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 9/4 is 4/9.
So, we now have:72×49\frac{7}{2} \times \frac{4}{9}27×94
Step 3: Multiply the Fractions
To multiply the fractions, simply multiply the numerators and the denominators:7×42×9=2818\frac{7 \times 4}{2 \times 9} = \frac{28}{18}2×97×4=1828
Step 4: Simplify the Fraction
Now, simplify the fraction 28/18 by finding the greatest common divisor (GCD) of 28 and 18, which is 2.
Divide both the numerator and denominator by 2:28÷218÷2=149\frac{28 \div 2}{18 \div 2} = \frac{14}{9}18÷228÷2=914
So, 3 1/2 ÷ 2 1/4 = 14/9.
Step 5: Convert to Mixed Number (Optional)
If you’d like to convert 14/9 back to a mixed number:
- Divide 14 by 9, which gives 1 with a remainder of 5.
- So, 14/9 is 1 5/9.
Now, for the second part of your question:
3 1/2 divided by 1/4 is the same as multiplying 3 1/2 by the reciprocal of 1/4, which is 4/1.
Step 1: Convert 3 1/2 to an improper fraction:
- 3 1/2 = 7/2.
Step 2: Multiply by the reciprocal of 1/4, which is 4/1:72×41=282\frac{7}{2} \times \frac{4}{1} = \frac{28}{2}27×14=228
Step 3: Simplify:282=14\frac{28}{2} = 14228=14
So, 3 1/2 ÷ 1/4 = 14.
In summary:
- 3 1/2 ÷ 2 1/4 = 14/9, or 1 5/9 as a mixed number.
- 3 1/2 ÷ 1/4 = 14.
