Math in Business: Background You’ll Need 1

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Math in Business: Background You’ll Need 1

Write percents and perform calculations

Percents to Fractions

Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per [latex]100[/latex], so the denominator of the fraction is [latex]100[/latex].

How To: Convert a Percent to a Fraction

Write the percent as a ratio with the denominator [latex]100[/latex].
Simplify the fraction if possible.

Convert each percent to a fraction:

[latex]\text{36%}[/latex]
[latex]\text{125%}[/latex]

The previous example shows that a percent can be greater than [latex]1[/latex]. We saw that [latex]\text{125%}[/latex] means [latex]{\Large\frac{125}{100}}[/latex], or [latex]{\Large\frac{5}{4}}[/latex]. These are improper fractions, and their values are greater than one.

Convert each percent to a fraction:

[latex]\text{24.5%}[/latex]
[latex]33\Large\frac{1}{3}\normalsize\%[/latex]

Percents to Decimals

To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.

How To: Convert a Percent to a Decimal

Write the percent as a ratio with the denominator [latex]100[/latex].
Convert the fraction to a decimal by dividing the numerator by the denominator.

Convert each percent to a decimal:

[latex]\text{6%}[/latex]
[latex]\text{78%}[/latex]

Convert each percent to a decimal:

[latex]\text{135%}[/latex]
[latex]\text{12.5%}[/latex]

[latex]36\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{36}{100}}[/latex]
Simplify.	[latex]{\Large\frac{9}{25}}[/latex]

[latex]125\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{125}{100}}[/latex]
Simplify.	[latex]{\Large\frac{5}{4}}[/latex]

[latex]24.5\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{24.5}{100}}[/latex]
Clear the decimal by multiplying numerator and denominator by [latex]10[/latex].	[latex]{\Large\frac{24.5\left(10\right)}{100\left(10\right)}}[/latex]
Multiply.	[latex]{\Large\frac{245}{1000}}[/latex]
Rewrite showing common factors.	[latex]{\Large\frac{5\cdot {49}}{5\cdot {200}}}[/latex]
Simplify.	[latex]{\Large\frac{49}{200}}[/latex]

[latex]33\Large\frac{1}{3}\normalsize\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{33\Large\frac{1}{3}}{100}}[/latex]
Write the numerator as an improper fraction.	[latex]{\Large\frac{\frac{100}{3}}{100}}[/latex]
Rewrite as fraction division, replacing [latex]100[/latex] with [latex]\frac{100}{1}[/latex].	[latex]{\Large\frac{100}{3}}\div {\Large\frac{100}{1}}[/latex]
Multiply by the reciprocal.	[latex]{\Large\frac{100}{3}} \cdot {\Large\frac{1}{100}}[/latex]
Simplify.	[latex]{\Large\frac{1}{3}}[/latex]

[latex]6\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{6}{100}}[/latex]
Change the fraction to a decimal by dividing the numerator by the denominator.	[latex]0.06[/latex]

[latex]78\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{78}{100}}[/latex]
Change the fraction to a decimal by dividing the numerator by the denominator.	[latex]0.78[/latex]

[latex]135\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{135}{100}}[/latex]
Change the fraction to a decimal by dividing the numerator by the denominator.	[latex]1.35[/latex]

[latex]12.5\%[/latex]
Write as a ratio with denominator [latex]100[/latex].	[latex]{\Large\frac{12.5}{100}}[/latex]
Change the fraction to a decimal by dividing the numerator by the denominator.	[latex]0.125[/latex]