Solve Mixed Number Addition: 3 5/16 + 6 5/8 Step-by-Step

Q: How do I find the common denominator between 16 and 8?

Since 16 is a multiple of 8, the common denominator is 16. To convert $ \frac{5}{8} $, multiply both numerator and denominator by 2: $ \frac{5 \times 2}{8 \times 2} = \frac{10}{16} $.

Q: Do I add the whole numbers and fractions separately?

Yes! Add whole numbers together (3 + 6 = 9) and fractions together separately ($ \frac{5}{16} + \frac{10}{16} = \frac{15}{16} $), then combine: $ 9\frac{15}{16} $.

Q: What if my fraction part becomes improper?

If your fraction is improper (numerator ≥ denominator), convert it to a mixed number and add the whole number part to your existing whole number. For example: $ 9\frac{18}{16} = 9\frac{2}{16} + 1 = 10\frac{1}{8} $.

Q: Why didn't the answer become 10 exactly?

The fractions $ \frac{5}{16} + \frac{10}{16} = \frac{15}{16} $ don't equal 1 whole. Since $ \frac{15}{16} $ is less than 1, we get $ 9\frac{15}{16} $, not 10.

Q: Should I simplify the final answer?

Always check if you can simplify! In this case, $ \frac{15}{16} $ cannot be simplified further since 15 and 16 share no common factors other than 1.

Mixed Number Addition with Common Denominators

$3\frac{5}{16}+6\frac{5}{8}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 The formula for converting a mixed fraction to a fraction

00:12 We will use this formula in our exercise and convert to fractions

00:42 Multiply to find the common denominator

00:51 Add with the common denominator

01:09 Break down 159 into 144 plus 15

01:15 Break down the fraction into a whole number and remainder

01:22 Convert from a whole fraction to a whole number

01:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3\frac{5}{16}+6\frac{5}{8}=$

Step-by-step solution

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

Step 1: Convert fractions to a common denominator.
Step 2: Add the fractions.
Step 3: Add the whole numbers and the resulting fraction.
Step 4: Simplify the result.

Now, let's work through each step:

Step 1: Convert $\frac{5}{8}$ to a fraction with denominator 16.
Currently, $\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16}$ .

Step 2: Add the fractions $\frac{5}{16}$ and $\frac{10}{16}$ .
$\frac{5}{16} + \frac{10}{16} = \frac{15}{16}$ .

Step 3: Add the whole numbers of the mixed numbers.
The whole numbers are 3 and 6, giving $3 + 6 = 9$ .

Step 4: Combine the results of steps 2 and 3 into a mixed number.
$9 + \frac{15}{16} = 9\frac{15}{16}$ .

Therefore, the solution to the problem is $9\frac{15}{16}$ , which corresponds to choice 3 in the provided options.

Final Answer

$9\frac{15}{16}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to common denominators before adding
Technique: Change $\frac{5}{8}$ to $\frac{10}{16}$ by multiplying by 2
Check: Verify $\frac{5}{16} + \frac{10}{16} = \frac{15}{16}$ and 3 + 6 = 9 ✓

Common Mistakes

Avoid these frequent errors

Adding fractions with different denominators directly
Don't add $\frac{5}{16} + \frac{5}{8} = \frac{10}{24}$ ! This gives wrong denominators and incorrect results. Always convert to the same denominator first, then add numerators only.

Practice Quiz

Test your knowledge with interactive questions

$2\frac{2}{5}+2\frac{2}{5}=$

FAQ

Everything you need to know about this question

How do I find the common denominator between 16 and 8?

Since 16 is a multiple of 8, the common denominator is 16. To convert $\frac{5}{8}$ , multiply both numerator and denominator by 2: $\frac{5 \times 2}{8 \times 2} = \frac{10}{16}$ .

Do I add the whole numbers and fractions separately?

Yes! Add whole numbers together (3 + 6 = 9) and fractions together separately ( $\frac{5}{16} + \frac{10}{16} = \frac{15}{16}$ ), then combine: $9\frac{15}{16}$ .

What if my fraction part becomes improper?

If your fraction is improper (numerator ≥ denominator), convert it to a mixed number and add the whole number part to your existing whole number. For example: $9\frac{18}{16} = 9\frac{2}{16} + 1 = 10\frac{1}{8}$ .

Why didn't the answer become 10 exactly?

The fractions $\frac{5}{16} + \frac{10}{16} = \frac{15}{16}$ don't equal 1 whole. Since $\frac{15}{16}$ is less than 1, we get $9\frac{15}{16}$ , not 10.

Should I simplify the final answer?

Always check if you can simplify! In this case, $\frac{15}{16}$ cannot be simplified further since 15 and 16 share no common factors other than 1.

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