Write 26 As A Fraction

1. Write 26 7 As A Mixed Fraction
2. Write 26 As A Fraction In Simplest Form
3. Convert 26% Into A Fraction

Learning Outcomes

Expressed as a proper fraction in its simplest form, by dividing the numerator and denominator by 26, 546/676 is equal to 21/26 or twenty-one twenty-sixths. Since there is a decimal in the numerator, multiply the top and bottom by 10. 26.1/3.6. 10/10. Divide the top and bottom by 9.

• Given a ratio of two integers, write it as a fraction
• Given a ratio of two decimals, write it as a fraction
• Given a ratio of two mixed numbers, write it as a fraction

When you apply for a mortgage, the loan officer will compare your total debt to your total income to decide if you qualify for the loan. This comparison is called the debt-to-income ratio. A ratio compares two quantities that are measured with the same unit. If we compare [latex]a[/latex] and [latex]b[/latex] , the ratio is written as [latex]atext{ to }b,frac{a}{b},text{or}mathit{text{a}}text{:}mathit{text{b}}text{.}[/latex]

Ratios

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of [latex]a[/latex] to [latex]b[/latex] is written [latex]atext{ to }b,frac{a}{b},text{or}mathit{text{a}}text{:}mathit{text{b}}text{.}[/latex]

In this section, we will use the fraction notation. When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as [latex]frac{4}{1}[/latex] instead of simplifying it to [latex]4[/latex] so that we can see the two parts of the ratio.

example

Write each ratio as a fraction: ⓐ [latex]15text{ to }27[/latex] ⓑ [latex]45text{ to }18[/latex].

Solution

We leave the ratio in ⓑ as an improper fraction.

In the following video you will see more examples of how to express a ratio as a fraction.

Ratios Involving Decimals

We will often work with ratios of decimals, especially when we have ratios involving money. In these cases, we can eliminate the decimals by using the Equivalent Fractions Property to convert the ratio to a fraction with whole numbers in the numerator and denominator.
For example, consider the ratio [latex]0.8text{ to }0.05[/latex]. We can write it as a fraction with decimals and then multiply the numerator and denominator by [latex]100[/latex] to eliminate the decimals.

Do you see a shortcut to find the equivalent fraction? Notice that [latex]0.8=frac{8}{10}[/latex] and [latex]0.05=frac{5}{100}[/latex]. The least common denominator of [latex]frac{8}{10}[/latex] and [latex]frac{5}{100}[/latex] is [latex]100[/latex]. By multiplying the numerator and denominator of [latex]frac{0.8}{0.05}[/latex] by [latex]100[/latex], we ‘moved’ the decimal two places to the right to get the equivalent fraction with no decimals. Now that we understand the math behind the process, we can find the fraction with no decimals like this:

You do not have to write out every step when you multiply the numerator and denominator by powers of ten. As long as you move both decimal places the same number of places, the ratio will remain the same.

example

Write each ratio as a fraction of whole numbers:
ⓐ [latex]4.8text{ to }11.2[/latex]
ⓑ [latex]2.7text{ to }0.54[/latex]

Solution

So [latex]4.8text{ to }11.2[/latex] is equivalent to [latex]frac{3}{7}[/latex].

So [latex]2.7text{ to }0.54[/latex] is equivalent to [latex]frac{5}{1}[/latex].

The following video shows more examples of how to express a ratio given as a decimal as a fraction.

Some ratios compare two mixed numbers. Remember that to divide mixed numbers, you first rewrite them as improper fractions.

example

Write the ratio of [latex]1frac{1}{4}text{ to }2frac{3}{8}[/latex] as a fraction.

Write 26 7 As A Mixed Fraction

Solution

Converting decimal numbers, fractions, proportions and ratios to percentages

Write 26 As A Fraction In Simplest Form

It's very simple to write a fraction (a proportion or a ratio) or a decimal number as a percentage. To convert a fraction just start by dividing the numerator by the denominator and then multiply the result by 100%. By multiplying the result by 100% the value we've got at the previous step is not modified, since 100% = 100/100 = 1. By multiplying by 100% only the form is being changed - it's written as a percentage.

It's even simpler to write a decimal number as a percentage. Simply multiply the number by 100%.

Examples

Convert 26% Into A Fraction

• ¹/₄ = 0.25 = 0.25 × 100% = (0.25 × 100)% = 25%;
• ⁷/₈ = 0.875 = 0.875 × 100% = (0.875 × 100)% = 87.5%
• ^1.3/_9.4 ≈ 0.138297 = 0.138297 × 100% = (0.138297 × 100)% = 13.8297%
• 4.3 = 4.3 × 100% = (4.3 × 100)% = 430%;

Write 26 As A Fraction