Convert mixed fractions into improper fractions and vice versa.
a. 37/18
b. 4 7/6
c. 12 1/9
The correct answer and explanation is:
Answers:
a. 3718\frac{37}{18} → Mixed fraction: 2 118\frac{1}{18}
b. 4 76\frac{7}{6} → Improper fraction: 316\frac{31}{6}
c. 12 19\frac{1}{9} → Improper fraction: 1099\frac{109}{9}
Explanation:
Mixed and improper fractions are two ways of expressing the same value. A mixed fraction shows a whole number and a fraction combined, such as 3123 \frac{1}{2}, while an improper fraction has a numerator larger than the denominator, such as 72\frac{7}{2}.
a. Convert 3718\frac{37}{18} to a mixed fraction:
To convert an improper fraction to a mixed number, divide the numerator by the denominator.
- 37÷18=237 \div 18 = 2 remainder 11
- So, 3718=2118\frac{37}{18} = 2 \frac{1}{18}
b. Convert 4 76\frac{7}{6} to an improper fraction:
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator.
- 4×6=244 \times 6 = 24
- 24+7=3124 + 7 = 31
- So, 476=3164 \frac{7}{6} = \frac{31}{6}
Note that although the fractional part has a numerator larger than the denominator (7/6), it is still treated as a regular fraction in the conversion. The result, 316\frac{31}{6}, is improper.
c. Convert 12 19\frac{1}{9} to an improper fraction:
- 12×9=10812 \times 9 = 108
- 108+1=109108 + 1 = 109
- So, 1219=109912 \frac{1}{9} = \frac{109}{9}
These conversions are useful in arithmetic operations like addition, subtraction, multiplication, and division, where improper fractions are easier to handle. Being able to move between the two forms strengthens number sense and helps in solving fraction problems accurately.