Solve the Expression: 5/9 + 4/9 + 8 Step by Step

Q: Why don't I add the denominators when they're the same?

The denominator tells us what size pieces we're working with. When adding $ \frac{5}{9} + \frac{4}{9} $, we're adding 5 ninths plus 4 ninths, which gives us 9 ninths total - still the same size pieces!

Q: How do I add the whole number 8 to my fraction result?

First simplify your fraction completely. Since $ \frac{9}{9} = 1 $, you just add 1 + 8 = 9. Always convert improper fractions to mixed numbers or whole numbers first!

Q: What if the fractions don't simplify to a whole number?

No problem! You'd get a mixed number as your final answer. For example, if you had $ \frac{7}{9} + 8 $, your answer would be $ 8\frac{7}{9} $.

Q: Do I always work left to right with addition?

With addition, you can actually work in any order due to the commutative property! However, it's usually easier to add fractions first, then add whole numbers to keep your work organized.

Q: How can I check if my answer is reasonable?

Estimate first! $ \frac{5}{9} $ and $ \frac{4}{9} $ are both close to $ \frac{1}{2} $, so together they're about 1. Adding 8 gives approximately 9, which matches our exact answer!

Fraction Addition with Mixed Numbers

$\frac{5}{9}+\frac{4}{9}+8=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the problem together.

00:12 First, we add fractions that have the same denominator.

00:18 Next, we convert the fraction into a whole number.

00:22 And that's our solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{5}{9}+\frac{4}{9}+8=$

Step-by-step solution

Since there is an addition operation between fractions with a common denominator, we can combine them into a single fraction:

$\frac{5+4}{9}+8=$

We solve the exercise in the numerator and obtain:

$\frac{9}{9}+8=1+8=9$

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Common Denominators: Add fractions with same denominator by adding numerators
Technique: $\frac{5}{9} + \frac{4}{9} = \frac{9}{9} = 1$
Check: Verify that $1 + 8 = 9$ matches the given answer ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add $\frac{5}{9} + \frac{4}{9} = \frac{9}{18}$ ! This changes the value completely and gives a wrong final answer of 8.5 instead of 9. Always keep the common denominator unchanged and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

Why don't I add the denominators when they're the same?

The denominator tells us what size pieces we're working with. When adding $\frac{5}{9} + \frac{4}{9}$ , we're adding 5 ninths plus 4 ninths, which gives us 9 ninths total - still the same size pieces!

How do I add the whole number 8 to my fraction result?

First simplify your fraction completely. Since $\frac{9}{9} = 1$ , you just add 1 + 8 = 9. Always convert improper fractions to mixed numbers or whole numbers first!

What if the fractions don't simplify to a whole number?

No problem! You'd get a mixed number as your final answer. For example, if you had $\frac{7}{9} + 8$ , your answer would be $8\frac{7}{9}$ .

Do I always work left to right with addition?

With addition, you can actually work in any order due to the commutative property! However, it's usually easier to add fractions first, then add whole numbers to keep your work organized.

How can I check if my answer is reasonable?

Estimate first! $\frac{5}{9}$ and $\frac{4}{9}$ are both close to $\frac{1}{2}$ , so together they're about 1. Adding 8 gives approximately 9, which matches our exact answer!

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