Solve the Expression: 13⋅2x÷(4a⋅5/z) Step-by-Step

Q: Why do we convert division to multiplication?

Division by a fraction is the same as multiplying by its reciprocal. So $ :\frac{5}{z} $ becomes $ \times\frac{z}{5} $, which is much easier to work with!

Q: How do I know when to factor numbers in denominators?

Factor denominators when you can cancel common factors with the numerator. Here, factoring 4 as 2×2 lets us cancel the 2 from the numerator $ 13\times2x $.

Q: What does the colon symbol mean in this expression?

The colon : means division. So $ 13\cdot2x:(4a\cdot\frac{5}{z}) $ means we're dividing the first part by the second part.

Q: Why is the final answer written as 1.3 instead of 13/10?

Both forms are correct! $ \frac{13}{10} = 1.3 $. The decimal form 1.3 is often preferred because it's easier to read and understand.

Q: How do I check if my variable placement is correct?

Look at the original expression structure. Since x was in the numerator and a,z had different positions, the final answer should have x and z in numerator, a in denominator.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's write division as a fraction, and keep the last division

00:21 Let's break down 4 into factors 2 and 2

00:30 Division is also multiplication by the reciprocal

00:36 Let's reduce what we can

00:43 Note to multiply denominator by denominator and numerator by numerator

00:52 Let's calculate 13 divided by 10

00:56 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$13\cdot2x:(4a\cdot\frac{5}{z})=\text{?}$

2

Step-by-step solution

Firstly, let's rewrite the exercise as a fraction:

$\frac{13\times2x}{4a}:\frac{5}{z}=$

Next, we'll factor out the 4 from the denominator of the first fraction into a smaller multiplication exercise and invert the second fraction to create a multiplication exercise:

$\frac{13\times2x}{2\times2\times a}\times\frac{z}{5}=$

We'll now reduce the 2 in the numerator and denominator of the first fraction:

$\frac{13\times x}{2\times a}\times\frac{z}{5}=$

We'll then multiply the two multiplication exercises:

$\frac{13\times x\times z}{2\times a\times5}=\frac{13xz}{10a}$

Finally, we divide 13 by 10 to get:

$1.3\frac{xz}{a}$

3

Final Answer

$1.3\frac{xz}{a}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Convert division by fraction to multiplication by reciprocal
Technique: Factor denominators like 4a = 2×2×a to simplify
Check: Substitute variables to verify $1.3\frac{xz}{a}$ format ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling division by fractions
Don't divide by $\frac{5}{z}$ directly = confusion with fraction operations! This leads to wrong placement of variables in numerator/denominator. Always convert division by a fraction to multiplication by its reciprocal: $:\frac{5}{z} = \times\frac{z}{5}$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do we convert division to multiplication?

+

Division by a fraction is the same as multiplying by its reciprocal. So $:\frac{5}{z}$ becomes $\times\frac{z}{5}$ , which is much easier to work with!

How do I know when to factor numbers in denominators?

+

Factor denominators when you can cancel common factors with the numerator. Here, factoring 4 as 2×2 lets us cancel the 2 from the numerator $13\times2x$ .

What does the colon symbol mean in this expression?

+

The colon : means division. So $13\cdot2x:(4a\cdot\frac{5}{z})$ means we're dividing the first part by the second part.

Why is the final answer written as 1.3 instead of 13/10?

+

Both forms are correct! $\frac{13}{10} = 1.3$ . The decimal form 1.3 is often preferred because it's easier to read and understand.

How do I check if my variable placement is correct?

+

Look at the original expression structure. Since x was in the numerator and a,z had different positions, the final answer should have x and z in numerator, a in denominator.

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Solve the Expression: 13⋅2x÷(4a⋅5/z) Step-by-Step

Algebraic Expressions with Complex Division

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we convert division to multiplication?

How do I know when to factor numbers in denominators?

What does the colon symbol mean in this expression?

Why is the final answer written as 1.3 instead of 13/10?

How do I check if my variable placement is correct?

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