# What is 51/5 as a decimal?

## Solution and how to convert 51 / 5 into a decimal

51 / 5 = 10.2

To convert 51/5 into 10.2, a student must understand why and how. Fractions and decimals represent parts of a whole, sometimes representing numbers less than 1. But in some cases, fractions make more sense, i.e., cooking or baking and in other situations decimals make more sense as in leaving a tip or purchasing an item on sale. Once we've decided the best way to represent the number, we can dive into how to convert 51/5 into 10.2

## 51/5 is 51 divided by 5

Converting fractions to decimals is as simple as long division. 51 is being divided by 5. For some, this could be mental math. For others, we should set the equation. The numerator is the top number in a fraction. The denominator is the bottom number. This is our equation! To solve the equation, we must divide the numerator (51) by the denominator (5). Here's how you set your equation:

### Numerator: 51

• Numerators are the number of parts to the equation, showed above the vinculum or fraction bar. 51 is one of the largest two-digit numbers you'll have to convert. The bad news is that it's an odd number which makes it harder to covert in your head. Values closer to one-hundred make converting to fractions more complex. Now let's explore the denominator of the fraction.

### Denominator: 5

• Denominators are the total numerical value for the fraction and are located below the fraction line or vinculum. Smaller values like 5 can sometimes make mental math easier. But the bad news is that odd numbers are tougher to simplify. Unfortunately and odd denominator is difficult to simplify unless it's divisible by 3, 5 or 7. Overall, a small denominator like 5 could make our equation a bit simpler. Next, let's go over how to convert a 51/5 to 10.2.

## Converting 51/5 to 10.2

### Step 1: Set your long division bracket: denominator / numerator

$$\require{enclose} 5 \enclose{longdiv}{ 51 }$$

Use long division to solve step one. Yep, same left-to-right method of division we learned in school. This gives us our first clue.

### Step 2: Solve for how many whole groups you can divide 5 into 51

$$\require{enclose} 00.10 \\ 5 \enclose{longdiv}{ 51.0 }$$

Since we've extended our equation we can now divide our numbers, 5 into 510 (remember, we inserted a decimal point into our equation so we we're not accidentally increasing our solution) Multiply by the left of our equation (5) to get the first number in our solution.

### Step 3: Subtract the remainder

$$\require{enclose} 00.10 \\ 5 \enclose{longdiv}{ 51.0 } \\ \underline{ 50 \phantom{00} } \\ 460 \phantom{0}$$

If you don't have a remainder, congrats! You've solved the problem and converted 51/5 into 10.2 If you still have numbers left over, continue to the next step.

### Step 4: Repeat step 3 until you have no remainder

In some cases, you'll never reach a remainder of zero. Looking at you pi! And that's okay. Find a place to stop and round to the nearest value.

### Why should you convert between fractions, decimals, and percentages?

Converting fractions into decimals are used in everyday life, though we don't always notice. Remember, they represent numbers and comparisons of whole numbers to show us parts of integers. And the same is true for percentages. So we sometimes overlook fractions and decimals because they seem tedious or something we only use in math class. But they all represent how numbers show us value in the real world. Without them, we’re stuck rounding and guessing. Here are real life examples:

### When you should convert 51/5 into a decimal

Dollars & Cents - It would be silly to use 51/5 of a dollar, but it makes sense to have $0.1019. USD is exclusively decimal format and not fractions. (Yes, yes, there was a 'half dollar' but the value is still$0.50)

### When to convert 10.2 to 51/5 as a fraction

Pizza Math - Let's say you're at a birthday party and would like some pizza. You aren't going to ask for 1/4 of the pie. You're going to ask for 2 slices which usually means 2 of 8 or 2/8s (simplified to 1/4).

### Practice Decimal Conversion with your Classroom

• If 51/5 = 10.2 what would it be as a percentage?
• What is 1 + 51/5 in decimal form?
• What is 1 - 51/5 in decimal form?
• If we switched the numerator and denominator, what would be our new fraction?
• What is 10.2 + 1/2?