Problem 14 - Elementary Algebra

Question

For exercises 13-22, rewrite the improper fraction as a mixed number. $$ \frac{9}{7} $$

Step-by-Step Solution

Answer

1 \( \frac{2}{7} \)

Step 1 - Divide the numerator by the denominator

Divide 9 by 7 to find the whole number part of the mixed number. \[ 9 \text{ divided by } 7 = 1 \text{ R } 2 \]Here, 1 is the whole number part and 2 is the remainder.

Step 2 - Express the remainder as a fraction

Take the remainder (2) and place it over the original denominator (7) to create the fractional part of the mixed number: \[ \frac{2}{7} \]

Step 3 - Combine the whole number and the fraction

Combine the whole number part and the fractional part: \[ 1 \frac{2}{7} \]So, \( \frac{9}{7} \) as a mixed number is \( 1 \frac{2}{7} \).

Key Concepts

mixed numbers

Mixed numbers are used to express improper fractions in a more intuitive way. An improper fraction is a fraction where the numerator (the top number) is larger than or equal to the denominator (the bottom number).
When you convert an improper fraction into a mixed number, you have a combination of a whole number and a proper fraction (where the numerator is smaller than the denominator).
This translation makes it easier to understand and visualize the quantity being represented.
For example, in the exercise where we converted \(\frac{9}{7}\), we found that \(9 \div 7 = 1 R 2\).
This means that there is one whole unit and a remainder of 2, which is expressed as a fraction over the original denominator 7.
Putting these together, you get the mixed number \(1 \frac{2}{7}\).

fraction conversion

Fraction conversion is a fundamental skill in mathematics that involves changing the form of a fraction without altering its value.
This includes converting improper fractions to mixed numbers and vice versa.
Sometimes, converting fractions makes calculations easier and helps in better understanding.
To convert an improper fraction like \(\frac{9}{7}\) to a mixed number, follow these simple steps:

• First, divide the numerator by the denominator. The quotient (whole number) is the first part of your mixed number.
• Second, the remainder of this division becomes the numerator of the fraction part of your mixed number.
• Lastly, the original denominator remains the same and becomes the denominator of your fraction part.

So, \(\frac{9}{7}\) converts to \(1 \frac{2}{7}\).
Similarly, any mixed number can be converted back to an improper fraction by multiplying the whole number part by the denominator and adding the numerator.

division in fractions

Understanding division in fractions is essential to mastering fraction conversion.
When dividing fractions, the numerator is divided by the denominator, which can easily be done through long division.
Let's take the fraction \(\frac{9}{7}\). Dividing 9 by 7 gives:

• The quotient, which is 1 (this becomes the whole number).
• The remainder, which is 2 (this becomes the numerator of the fractional part).

So we have \(1 \frac{2}{7}\).
This method makes it straightforward to interpret improper fractions as mixed numbers.
It not only simplifies calculations but also helps in identifying how many whole parts exist and what fraction remains.