Solve: Adding 2.16 and -4 1/16 with Mixed Numbers and Decimals

Q: How do I convert 1/16 to a decimal?

Divide 1 by 16: $ 1 ÷ 16 = 0.0625 $. You can also think of it as multiplying by powers of 10: $ \frac{1}{16} = \frac{625}{10000} = 0.0625 $.

Q: Why is the answer negative when I'm adding?

Because you're adding a positive number (2.16) and a larger negative number (-4.0625). When the negative number has a greater absolute value, the result is negative: think of it as owing more money than you have!

Q: Can I keep everything as fractions instead?

Yes! Convert 2.16 to $ 2\frac{4}{25} $, find a common denominator with $ -4\frac{1}{16} $, then add. But decimal conversion is usually faster for mixed problems like this.

Q: What if I get a different decimal answer?

Double-check your fraction-to-decimal conversion! $ \frac{1}{16} = 0.0625 $ exactly. Also verify your subtraction: $ 2.16 - 4.0625 = -1.90625 $.

Q: How do I know when to convert to decimals vs fractions?

When the problem mixes decimals and fractions, convert to whichever form is easier to work with. Here, since 2.16 is already decimal, converting the mixed number to decimal ($ -4.0625 $) makes the addition simpler.

Mixed Number Addition with Decimal Conversion

$(+2.16)+(-4\frac{1}{16})=$

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Understand the problem

$(+2.16)+(-4\frac{1}{16})=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the mixed number
Step 2: Add the numbers
Step 3: Determine the sign and calculate the result

Now, let's work through each step:

Step 1: Convert $-4\frac{1}{16}$ to a decimal.
The fraction $\frac{1}{16}$ is equivalent to $0.0625$ as a decimal. Therefore, the mixed number $-4\frac{1}{16}$ converts to $-4.0625$ .

Step 2: Add $+2.16$ to $-4.0625$ .
The expression becomes $2.16 + (-4.0625)$ , which is equivalent to $2.16 - 4.0625$ .

Step 3: Perform the subtraction operation.
Subtract $4.0625$ from $2.16$ :

$2.16 - 4.0625 = -1.90625$

Therefore, the solution to the problem is $-1.90625$ .

Final Answer

$-1.90625$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert mixed numbers to decimals for consistent calculation
Technique: $\frac{1}{16} = 0.0625$ makes $-4\frac{1}{16} = -4.0625$
Check: $2.16 + (-4.0625) = -1.90625$ verifies our answer ✓

Common Mistakes

Avoid these frequent errors

Adding whole and fractional parts separately
Don't calculate 2.16 + 4 = 6.16, then subtract 0.0625 = 6.0975! This ignores the negative sign on the entire mixed number. Always convert the complete mixed number first: $-4\frac{1}{16} = -4.0625$ , then add.

Practice Quiz

Test your knowledge with interactive questions

What is the additive inverse number of $$ 87 $$

FAQ

Everything you need to know about this question

How do I convert 1/16 to a decimal?

Divide 1 by 16: $1 ÷ 16 = 0.0625$ . You can also think of it as multiplying by powers of 10: $\frac{1}{16} = \frac{625}{10000} = 0.0625$ .

Why is the answer negative when I'm adding?

Because you're adding a positive number (2.16) and a larger negative number (-4.0625). When the negative number has a greater absolute value, the result is negative: think of it as owing more money than you have!

Can I keep everything as fractions instead?

Yes! Convert 2.16 to $2\frac{4}{25}$ , find a common denominator with $-4\frac{1}{16}$ , then add. But decimal conversion is usually faster for mixed problems like this.

What if I get a different decimal answer?

Double-check your fraction-to-decimal conversion! $\frac{1}{16} = 0.0625$ exactly. Also verify your subtraction: $2.16 - 4.0625 = -1.90625$ .

How do I know when to convert to decimals vs fractions?

When the problem mixes decimals and fractions, convert to whichever form is easier to work with. Here, since 2.16 is already decimal, converting the mixed number to decimal ( $-4.0625$ ) makes the addition simpler.

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