Page 45 - Mathematics of Business and Finance

Chapter 1 | Review of Basic Arithmetic 25

Converting an Improper Fraction into a Mixed Number

Follow these steps to convert an improper fraction into a mixed number:
■ Divide the numerator by the denominator.
■ The quotient becomes the whole number and the remainder becomes the numerator of the fraction.
■ The denominator of the fraction is the same as the denominator of the original improper fraction.
32 2 6 Quotient: whole number of the fraction
For example, = 6 because,
5 5 5g 32
30
2 Remainder: numerator of the fraction

Converting a Fraction to its Decimal Form

A proper or improper fraction can be converted to its decimal form by dividing the numerator by the
denominator.
2 13
For example, = 0.4, = 1.625.
5 8

A mixed number can be converted to its decimal form by first converting the fractional part by
dividing the numerator by the denominator and then adding the whole number part to the decimal
equivalent of the fraction.
For example,
2
2
■ 3 = 3 + = 3 + 0.4 = 3.4
5
5
9
9
■ 7 = 7 + 11 = 7 + 0.818181... = 7.81...
11
Or, we can first change the mixed number to an improper fraction and then convert it to its decimal
equivalent.
For example,
2
■ 3 = (3 × 5) + 2 = 17 = 3.4
5
5
5
9
■ 7 = (7 × 11) + 9 + 86 = 7.8181... = 7.81
11
11
11
Some fractions, when converted to decimals, result in “repeating decimals”, that is, a repeated pattern.
We represent the repeated pattern with a bar over the repeating digits as shown in the above examples.
Converting a Fraction into an Equivalent Fraction

When both the numerator and denominator of a fraction are either multiplied by the same number
Dividing both the
numerator and or divided by the same number, the result is a new fraction called an equivalent fraction. Equivalent
denominator of a fraction fractions imply that the old and new fractions have the same value.
by the same number
is called reducing or
simplifying a fraction.