4 3/10 divided by 2 1/4 mixed number or whole number
The Correct Answer and Explanation is:
To solve 4310÷2144 \frac{3}{10} \div 2 \frac{1}{4}4103÷241, we first need to convert the mixed numbers into improper fractions and then divide them. Here’s the step-by-step process:
Step 1: Convert the mixed numbers into improper fractions.
- For 43104 \frac{3}{10}4103:
- Multiply the whole number (4) by the denominator (10): 4×10=404 \times 10 = 404×10=40.
- Add the numerator (3): 40+3=4340 + 3 = 4340+3=43.
- So, 4310=43104 \frac{3}{10} = \frac{43}{10}4103=1043.
- For 2142 \frac{1}{4}241:
- Multiply the whole number (2) by the denominator (4): 2×4=82 \times 4 = 82×4=8.
- Add the numerator (1): 8+1=98 + 1 = 98+1=9.
- So, 214=942 \frac{1}{4} = \frac{9}{4}241=49.
Step 2: Rewrite the division problem as a multiplication problem.
To divide by a fraction, we multiply by its reciprocal (flip the numerator and denominator). So, we have: 4310÷94=4310×49\frac{43}{10} \div \frac{9}{4} = \frac{43}{10} \times \frac{4}{9}1043÷49=1043×94
Step 3: Multiply the fractions.
Now, multiply the numerators and denominators: 43×410×9=17290\frac{43 \times 4}{10 \times 9} = \frac{172}{90}10×943×4=90172
Step 4: Simplify the fraction.
To simplify, we find the greatest common divisor (GCD) of 172 and 90, which is 2. Divide both the numerator and denominator by 2: 17290=172÷290÷2=8645\frac{172}{90} = \frac{172 \div 2}{90 \div 2} = \frac{86}{45}90172=90÷2172÷2=4586
Step 5: Convert the improper fraction back into a mixed number.
To convert 8645\frac{86}{45}4586 into a mixed number, divide 86 by 45. The quotient is 1, and the remainder is 41, so: 8645=14145\frac{86}{45} = 1 \frac{41}{45}4586=14541
Final Answer:
The solution to 4310÷2144 \frac{3}{10} \div 2 \frac{1}{4}4103÷241 is 141451 \frac{41}{45}14541.
This mixed number represents the result of the division, and since the remainder is smaller than the denominator, the fraction is already in its simplest form.
