Simplify and Solve: Combining Fractions and Decimals in 6 4/5x + 7 1/2x + 4 1/3x * 7.3x = ?

Q: Why do I multiply the x terms instead of adding them?

When you see $ 4\frac{1}{3}x \cdot 7.3x $, you're multiplying x times x, which gives you $ x^2 $! The coefficients multiply too: $ 4\frac{1}{3} \times 7.3 $.

Q: How do I convert mixed numbers to work with decimals?

You can either convert mixed numbers to improper fractions or decimals. For example, $ 6\frac{4}{5} = 6.8 $ and $ 7\frac{1}{2} = 7.5 $. Choose whichever feels easier!

Q: What's the difference between x and x² terms?

x terms are linear (first degree) and x² terms are quadratic (second degree). You can only combine like terms, so 14.3x and $ 31\frac{19}{30}x^2 $ stay separate!

Q: How do I check if this answer is right?

Substitute a test value for x (like x = 1) into both the original expression and your final answer. If they give the same result, you're correct!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:06 We'll use the formula to convert a mixed fraction to a fraction

00:11 We'll use this formula in our exercise

00:38 We'll convert a decimal fraction to a fraction and substitute in the exercise

01:00 Let's calculate the numerators

01:23 Multiply each fraction by the second denominator to find the common denominator

01:33 When multiplying fractions, be sure to multiply numerator by numerator and denominator by denominator

01:43 Let's calculate the products

01:54 We'll use long multiplication to calculate the product

02:00 Each time we'll multiply and substitute accordingly

02:40 Let's combine the fractions with the common denominator

03:07 Dividing by 10 is actually moving the decimal point one place

03:10 Let's substitute in our exercise

03:21 Let's break down 949 into 930 plus 19

03:31 Let's break down the fraction into a whole number and remainder

03:42 Let's convert the whole fraction to a whole number

03:50 Let's combine into a mixed fraction

03:56 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

$6\frac{4}{5}x+7\frac{1}{2}x+4\frac{1}{3}x\cdot7.3x=\text{?}$

2

Step-by-step solution

To solve this problem, we need to follow a systematic approach:

Step 1: Convert all mixed numbers into improper fractions.
Step 2: Carry out the multiplication between the terms $4\frac{1}{3}x \cdot 7.3x$ .
Step 3: Combine the terms by adding the coefficients of $x$ and $x^2$ .

Let's proceed with these steps:
Step 1: Convert mixed numbers to improper fractions.
$6\frac{4}{5}x = \left(\frac{34}{5}\right)x$ $7\frac{1}{2}x = \left(\frac{15}{2}\right)x$ $4\frac{1}{3} = \frac{13}{3}$ Step 2: Compute the multiplication and product.
$\left(\frac{13}{3}\right)x \cdot 7.3x = \left(\frac{13}{3} \cdot 7.3\right)x^2 = \left(\frac{94.9}{3}\right)x^2$ Approximate $\frac{94.9}{3} = 31.633...$ or convert to a fraction $31\frac{19}{30}$ .
Step 3: Combine all like terms by their variables.
$\left(\frac{34}{5}\right)x + \left(\frac{15}{2}\right)x + 31\frac{19}{30}x^2$ Converting to decimal form: $6.8x + 7.5x = 14.3x$ Thus, the final expression combines neatly as:
$14.3x + 31\frac{19}{30}x^2$

After reviewing the steps and calculations, the solution to the expression is $14.3x + 31\frac{19}{30}x^2$ .

3

Final Answer

$14.3x+31\frac{19}{30}x^2$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Multiplication before addition for $4\frac{1}{3}x \cdot 7.3x$
Technique: Convert mixed numbers to improper fractions: $6\frac{4}{5} = \frac{34}{5}$
Check: Verify by combining like terms separately: 14.3x + quadratic term ✓

Common Mistakes

Avoid these frequent errors

Adding all coefficients together
Don't add 6.8 + 7.5 + 4.33 + 7.3 = 25.93x! This ignores that multiplication creates an x² term, not another x term. Always follow order of operations: multiply $4\frac{1}{3}x \cdot 7.3x$ first to get $31\frac{19}{30}x^2$ , then add only the x terms together.

Practice Quiz

Test your knowledge with interactive questions

$3x+4x+7+2=\text{?}$

FAQ

Everything you need to know about this question

Why do I multiply the x terms instead of adding them?

+

When you see $4\frac{1}{3}x \cdot 7.3x$ , you're multiplying x times x, which gives you $x^2$ ! The coefficients multiply too: $4\frac{1}{3} \times 7.3$ .

How do I convert mixed numbers to work with decimals?

+

You can either convert mixed numbers to improper fractions or decimals. For example, $6\frac{4}{5} = 6.8$ and $7\frac{1}{2} = 7.5$ . Choose whichever feels easier!

What's the difference between x and x² terms?

+

x terms are linear (first degree) and x² terms are quadratic (second degree). You can only combine like terms, so 14.3x and $31\frac{19}{30}x^2$ stay separate!

Why is my final answer a mixed number and decimal?

+

That's totally normal! The coefficient of x became a clean decimal (14.3), while the coefficient of x² stayed as a mixed number $31\frac{19}{30}$ . Both forms are mathematically correct.

How do I check if this answer is right?

+

Substitute a test value for x (like x = 1) into both the original expression and your final answer. If they give the same result, you're correct!

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Simplify and Solve: Combining Fractions and Decimals in 6 4/5x + 7 1/2x + 4 1/3x * 7.3x = ?

Algebraic Simplification with Mixed Numbers

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