Solve Mixed Number Division: (45 7/15) ÷ 9 Step-by-Step

Q: Why do I need to convert the mixed number to an improper fraction first?

Converting to an improper fraction like $ \frac{682}{15} $ creates one single fraction that's much easier to work with. Trying to divide mixed numbers directly often leads to errors and confusion!

Q: How do I remember the rule for dividing fractions?

Think "Keep, Change, Flip": Keep the first fraction, change division to multiplication, flip the second fraction. So $ \frac{682}{15} ÷ \frac{9}{1} $ becomes $ \frac{682}{15} × \frac{1}{9} $!

Q: Why is my answer a fraction instead of a mixed number?

Both forms are correct! $ \frac{682}{135} $ equals approximately 5.05, which could also be written as $ 5\frac{7}{135} $. The improper fraction form is often preferred in algebra.

Q: How do I know if the signs are correct?

Use the sign rule: positive ÷ positive = positive. Since both $ +45\frac{7}{15} $ and $ +9 $ are positive, your answer must be positive too!

Q: Can I simplify this fraction further?

Check if 682 and 135 share any common factors. Since 682 = 2 × 341 and 135 = 3³ × 5, they don't share common factors, so $ \frac{682}{135} $ is already in lowest terms!

Mixed Number Division with Positive Fractions

Solve the following expression:

$(+45\frac{7}{15}):(+9)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together.

00:10 Remember, when you divide a positive number by another positive number, the result is always positive.

00:36 First, change any mixed fractions into regular fractions.

00:45 Now, use long multiplication to find the product. Take your time.

01:12 Rewrite the division as multiplication using the reciprocal.

01:17 Switch the numerator with the denominator. This is an important step.

01:24 Multiply the numerators together, and then multiply the denominators together.

01:31 Again, use long multiplication to calculate if needed.

01:40 And there you have it! That's how we solve the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$(+45\frac{7}{15}):(+9)=$

Step-by-step solution

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, let's convert each mixed fraction to an improper fraction as follows:

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

$45\frac{7}{15}=\frac{45\times15+7}{15}=$

Let's solve the multiplication in the numerator:

$45\\\times15\\675$

We should obtain the following:

$\frac{675+7}{15}=\frac{682}{15}$

Now our division problem between the fractions looks like this:

$\frac{682}{15}:\frac{9}{1}=$

Let's convert the division to multiplication, and don't forget to switch between numerator and denominator:

$\frac{682}{15}\times\frac{1}{9}=$

Let's combine everything into one problem:

$\frac{682\times1}{15\times9}=$

Let's solve the problem in the numerator:

$15\\\times9\\135$

And the result is:

$\frac{682}{135}$

Final Answer

$\frac{682}{135}$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by positive equals positive result
Technique: Convert $45\frac{7}{15}$ to $\frac{682}{15}$ before dividing
Check: $\frac{682}{135} \times 9 = \frac{682}{15} = 45\frac{7}{15}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing mixed numbers without converting to improper fractions
Don't try to divide 45 7/15 by 9 as separate parts = wrong answer! This leads to confusion and incorrect calculations. Always convert mixed numbers to improper fractions first, then apply division rules.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction first?

Converting to an improper fraction like $\frac{682}{15}$ creates one single fraction that's much easier to work with. Trying to divide mixed numbers directly often leads to errors and confusion!

How do I remember the rule for dividing fractions?

Think "Keep, Change, Flip": Keep the first fraction, change division to multiplication, flip the second fraction. So $\frac{682}{15} ÷ \frac{9}{1}$ becomes $\frac{682}{15} × \frac{1}{9}$ !

Why is my answer a fraction instead of a mixed number?

Both forms are correct! $\frac{682}{135}$ equals approximately 5.05, which could also be written as $5\frac{7}{135}$ . The improper fraction form is often preferred in algebra.

How do I know if the signs are correct?

Use the sign rule: positive ÷ positive = positive. Since both $+45\frac{7}{15}$ and $+9$ are positive, your answer must be positive too!

Can I simplify this fraction further?

Check if 682 and 135 share any common factors. Since 682 = 2 × 341 and 135 = 3³ × 5, they don't share common factors, so $\frac{682}{135}$ is already in lowest terms!

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