3 1/2 divided by 2 1/4 in simplest form
The Correct Answer and Explanation is:
To solve 3 1/2 divided by 2 1/4 and express the answer in the simplest form, we first need to convert the mixed numbers to improper fractions.
Step 1: Convert the mixed numbers to improper fractions.
- 3 1/2: Multiply the whole number (3) by the denominator of the fraction (2), then add the numerator (1). This gives us: 31/2=(3×2)+12=723 1/2 = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}31/2=2(3×2)+1=27
- 2 1/4: Similarly, for 2 1/4, we multiply the whole number (2) by the denominator (4), then add the numerator (1). This gives us: 21/4=(2×4)+14=942 1/4 = \frac{(2 \times 4) + 1}{4} = \frac{9}{4}21/4=4(2×4)+1=49
Step 2: Set up the division problem.
Now we need to divide 7/2 by 9/4. Dividing by a fraction is the same as multiplying by its reciprocal. So:72÷94=72×49\frac{7}{2} \div \frac{9}{4} = \frac{7}{2} \times \frac{4}{9}27÷49=27×94
Step 3: Multiply the fractions.
To multiply two fractions, multiply the numerators together and the denominators together: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. The greatest common divisor (GCD) of 28 and 18 is 2. Divide both the numerator and denominator by 2:2818=28÷218÷2=149\frac{28}{18} = \frac{28 \div 2}{18 \div 2} = \frac{14}{9}1828=18÷228÷2=914
Final Answer:
The result of 3 1/2 divided by 2 1/4 is 14/9. Since this fraction is already in its simplest form, this is the final answer. Alternatively, it can be written as a mixed number:14/9=15914/9 = 1 \frac{5}{9}14/9=195
Explanation:
To divide two fractions, you multiply the first fraction by the reciprocal of the second. By converting the mixed numbers into improper fractions, performing the multiplication, and then simplifying the result, we arrive at the simplest form.
