Least To Greatest Fraction Calculator

Ordering fractions with our least to greatest fraction calculator has never been easier, especially when you’ve got fractions, decimals, and percentages all mixed.

Not sure where to start? Well, that’s where Omni’s least to greatest decimal and fraction calculator comes in handy. It sorts out any combination of numbers, and we’ve made sure you won’t just get the answer but a full step-by-step explanation, so you know exactly what’s going on! Just enter your numbers, pick the order you want, and let it do its thing.

Keep scrolling to read more about:

• Comparing fractions;
• How to find the LCD of a set of fractions;
• How to order fractions from least to greatest; and
• Ordering fractions from greatest to least.

When comparing fractions that have different denominators, or even mixed numbers, decimals, or percentages, you’ve got a couple of solid options: either convert them all into decimals or find the lowest common denominator (LCD): the smallest number that is a multiple of all the denominators. Our least to greatest fraction calculator uses both methods; let’s walk through each one.

Method 1: Convert to decimals

This way works pretty well if your numbers include a mix of fractions, decimals, and percentages.

Here’s what you do:

1. Convert each fraction to decimal form.
2. Compare those decimals and order them from least to greatest in ascending order.
3. Connect decimals back to the original numbers you started with.

Let’s take as an example: $\frac{1}{3}, 75 \%, 0.5, 1 \frac{1}{4}$, and order fractions smallest to largest.

1. Convert numbers to decimals:

   $\frac{1}{3} = 0.3333$

   $75\% = 0.75$

   $0.5 = 0.5$

   $1 \frac{1}{4} = 1.25$
   
   

2. Order the decimals from least to greatest:

   $0.3333 < 0.5 < 0.75 < 1.25$
   
   

3. Match back to original inputs:

   $\frac{1}{3} < 0.5 < 75\% < 1 \frac{1}{4}$

Method 2: Finding the LCD of fractions

This approach tends to work best when all inputs are fractions or mixed numbers.

Here’s how you do it:

1. Change any mixed numbers into improper fractions or use the dedicated mixed number to improper fraction calculator.
2. Find the lowest common denominator (LCD) by calculating least common multiple of all denominators in your set.
3. Rewrite each fraction using that LCD.
4. Order by numerator and match back to the original numbers.

Let‘s order $\frac{3}{4}, \frac{1}{3}, 1 \frac{5}{6}$ from least to greatest.

1. Convert mixed numbers to improper fractions:

   • $\frac{3}{4}$ and $\frac{1}{3}$ are already proper fractions;
   • $1 \frac{5}{6}$ → multiply whole number $1$ by denominator $6$ to get $6$, then add numerator $5$, which gives $\frac{11}{6}$; and
   • All inputs as fractions: $\frac{3}{4}, \frac{1}{3}, \frac{11}{6}$.

2. Find the LCD of 3, 4, and 6:

   $\mathrm{LCD} = 12$
   
   

3. Rewrite each fraction using LCD = 12:

   $\frac{3}{4} = \frac{9}{12}$

   $\frac{1}{3} = \frac{4}{12}$

   $\frac{11}{6} = \frac{22}{12}$
   
   

4. Order by numerator from least to greatest:

   $\frac{4}{12} < \frac{9}{12} < \frac{22}{12}$
   
   

5. Match back to original inputs:

   $\frac{1}{3}< \frac{3}{4} < 1 \frac{5}{6}$

Ordering fractions from greatest to least is pretty much the same as doing it from least to greatest; you can use the same two methods, then simply switch the order around, or give our least to greatest fraction calculator a try!

Let’s order the set of $\frac{1}{3}, 75\%, 0.5, 1 \frac{1}{4}$ from greatest to least:

1. Change each value into a decimal:

   $\frac{1}{3} = 0.3333$

   $75\% = 0.75$

   $0.5 = 0.5$

   $1 \frac{1}{4} = 1.25$

   If you want to convert in the other direction, check our decimal to fraction calculator.
   
   

2. Put them in order from greatest to least (descending order):

   $1.25 > 0.75 > 0.5 > 0.3333$
   
   

3. Match those back up with what you started with:

   $1 \frac{1}{4} > 75\% > 0.5 > \frac{1}{3}$

Sometimes you need to decide at a glance which set of fractions is ordered from least to greatest, or the other way around. For example, let's check if $\frac{3}{4}, \frac{1}{2}, \frac{1}{4}$ are ordered from greatest to least?

A handy trick is to change each fraction into a decimal first:

$\frac{3}{4} = 0.75$

$\frac{1}{2} = 0.5$

$\frac{1}{4} = 0.25$

Then, just see whether the sequence is consistently increasing or decreasing:

$0.75 > 0.5 > 0.25$ ← the set is arranged properly, going from the greatest down to the least.

Both methods above are useful for comparing fractions and determining which fraction is larger, smaller, or equal. It’s especially helpful when you need to put the fractions in order from least to greatest or in reverse. The key challenge is that fractions with different denominators aren’t easy to compare right off the bat. Take $\frac{3}{8}$ and $\frac{1}{3}$, for example; they don’t share a common reference point.

Method 1:

1. Divide the numerator by the denominator to get a decimal.
2. Then you can compare those directly.

In this case, $3$ divided by $8$ is $0.375$, and $1$ divided by $3$ is about $0.3333$.

Since $0.375$ is bigger than $0.3333$, $\frac{3}{8}$ is larger than $\frac{1}{3}$.

Method 2:

1. Find the LCD, which is the smallest number that both denominators go into evenly. For $8$ and $3$, it’s $24$.
2. Then, turn both fractions into ones with that denominator: $\frac{3}{8}$ becomes $\frac{9}{24}$, and $\frac{1}{3}$ becomes $\frac{8}{24}$.
3. Now, just compare the numerators; $9$ is bigger than $8$, so $\frac{3}{8}$ is bigger than $\frac{1}{3}$.

Using our least to greatest fraction calculator is as simple as it gets; just follow these steps:

1. Type in your fractions, mixed numbers, decimals, or percentages separated by commas.
2. Choose the order: least to greatest or greatest to least.
3. Omni’s least to greatest decimal and fraction calculator will quickly sort your fractions and show them back to you in whatever order you picked.
4. If you’re curious about how it all works, click I want to see the step-by-step solution! to check out the step-by-step breakdown.