Problem 28 Write the improper fraction as a... [FREE SOLUTION]

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Chapter 5: Problem 28

Write the improper fraction as a mixed number. $$\frac{19}{2}$$

Short Answer

Expert verified

Answer: The mixed number representation of the improper fraction $$\frac{19}{2}$$ is $$9\frac{1}{2}$$.

Step by step solution

Find quotient and remainder

To find the quotient and remainder, divide 19 by 2: $$19 \div 2 = 9 \text{ with a remainder of } 1$$

Write the mixed number

Now we can convert the improper fraction to a mixed number by writing the quotient as the whole number, and the remainder over the original denominator as the fractional part: $$\frac{19}{2} = 9\frac{1}{2}$$ So, the mixed number representation of the improper fraction $$\frac{19}{2}$$ is $$9\frac{1}{2}$$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Improper Fractions

Improper fractions are a type of fraction where the numerator is greater than or equal to the denominator. This simply means that the top number, which represents how many parts we have, is bigger than the bottom number, which represents how many parts make up a whole.
For example, in the fraction $\frac{19}{2}$, the number 19 (numerator) is larger than the number 2 (denominator). This is what makes it an improper fraction.
Improper fractions are useful in many situations, like when dividing objects into larger groups. But sometimes, it鈥檚 more intuitive to convert them into mixed numbers, especially for practical applications like cooking or measuring.

Mixed Numbers

Mixed numbers make it easier to understand improper fractions by showing both the whole units and the leftover parts.
A mixed number is composed of a whole number and a proper fraction. The whole number represents how many complete sets you have, while the fraction shows any remaining parts beyond the whole.
For example, with $\frac{19}{2}$, when you convert it to a mixed number, you get $9\frac{1}{2}$. Here, 9 is the whole number, representing 9 complete groups of 2, and $\frac{1}{2}$ is the proper fraction representing the leftover 1 out of 2 parts.

Division with Remainders

Division with remainders is an essential skill for converting improper fractions to mixed numbers.
When you divide a number and it doesn't go evenly, you end up with a remainder. This leftover part is what becomes the fractional part of a mixed number.
Let's see this in action with $19 \div 2$:

The quotient, 9, tells us that there are 9 full groups of the parts.
The remainder, 1, is the fraction part left over after forming these full groups.

So, when converting $\frac{19}{2}$, the division gives us 9 whole groups (the quotient) plus a remainder of 1 (the leftover part), which forms $9\frac{1}{2}$ as the mixed number.

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91影视

Write the improper fraction as a mixed number. $$\frac{19}{2}$$

Short Answer

Step by step solution

Find quotient and remainder

Write the mixed number

Key Concepts

Improper Fractions

Mixed Numbers

Division with Remainders

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