Which of the following shows 18/12 as a mixed number and 1 7/8 as an improper fraction
The Correct Answer and Explanation is:
Correct Answer:
- 18/12 as a mixed number: 1 1/2
- 1 7/8 as an improper fraction: 15/8
Explanation (No em dashes used):
Let us begin by converting 18/12 into a mixed number.
Step 1: Simplify the fraction if possible.
We divide both the numerator and the denominator by their greatest common factor.
The greatest common factor of 18 and 12 is 6.1812=18÷612÷6=32\frac{18}{12} = \frac{18 ÷ 6}{12 ÷ 6} = \frac{3}{2}1218=12÷618÷6=23
Step 2: Convert the improper fraction into a mixed number.
A mixed number includes a whole number and a proper fraction.
Divide 3 by 2.
- 2 goes into 3 one time (1 × 2 = 2)
- The remainder is 1
So,32=112\frac{3}{2} = 1 \frac{1}{2}23=121
This means 18/12 as a mixed number is 1 1/2.
Now let us convert 1 7/8 into an improper fraction.
Step 1: Understand the structure of a mixed number.
It has two parts: the whole number (1) and the fractional part (7/8).
Step 2: Multiply the whole number by the denominator of the fraction.
1 × 8 = 8
Step 3: Add the result to the numerator.
8 + 7 = 15
So,178=1581 \frac{7}{8} = \frac{15}{8}187=815
This gives us the improper fraction form of 1 7/8, which is 15/8.
In summary:
- 18/12 as a mixed number is 1 1/2
- 1 7/8 as an improper fraction is 15/8
Understanding how to convert between mixed numbers and improper fractions helps in simplifying problems in arithmetic and algebra. It also helps improve flexibility in working with different forms of rational numbers.
