Solve for the Missing Fraction in 5×17-112-?/14=-27.5

Linear Equations with Mixed Operations

What is the missing number in the equation?

5×17−112−?14=−27.5 5\times17-112-\frac{?}{14}=-27.5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:14 Begin by solving any operations inside parentheses. They come first.
00:28 Next, work through the problem from left to right. One step at a time.
00:44 To get the variable by itself, add twenty-seven to both sides.
01:05 Finally, multiply both sides by fourteen. And that's how we solve it!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the missing number in the equation?

5×17−112−?14=−27.5 5\times17-112-\frac{?}{14}=-27.5

2

Step-by-step solution

We place the multiplication exercise inside of the parenthesis:

(5×17)−112−x14=−27.5 (5\times17)-112-\frac{x}{14}=-27.5

We solve the multiplication exercise and then subtract:

85−112−x14=−27.5 85-112-\frac{x}{14}=-27.5

−27−x14=−27.5 -27-\frac{x}{14}=-27.5

We swap sections:

−x14=−27.5+27 -\frac{x}{14}=-27.5+27

−x14=−12 -\frac{x}{14}=-\frac{1}{2}

We multiply by 14:

−x=−12×14 -x=-\frac{1}{2}\times14

−x=−7 -x=-7

We multiply by -1

x=7 x=7

3

Final Answer

7 7

Key Points to Remember

Essential concepts to master this topic
  • Order: Follow PEMDAS - multiplication first, then subtraction operations
  • Technique: Isolate fraction term: -x/14 = -0.5, then multiply by -14
  • Check: Substitute x = 7: 5×17 - 112 - 7/14 = -27.5 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations with mixed terms
    Don't solve left to right without following PEMDAS = wrong intermediate values! This creates calculation errors that compound. Always do multiplication (5×17) first, then work with the resulting subtraction and fraction terms in proper sequence.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do we need parentheses around 5×17?

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The parentheses help clarify the order of operations. While multiplication comes before subtraction anyway, showing (5×17) makes it clear we get 85 first, then subtract 112.

How do I handle the negative fraction term?

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Treat −x14 -\frac{x}{14} as a single unit. When isolating it, remember that subtracting a fraction is the same as adding its opposite.

Why did -27.5 + 27 become -1/2?

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Because -27.5 = -27 - 0.5, so -27.5 + 27 = -0.5. Converting to fraction form: -0.5 = −12 -\frac{1}{2} .

Can I solve this without converting to fractions?

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Yes! You could keep everything as decimals: −x14=−0.5 -\frac{x}{14} = -0.5 , so x = 0.5 × 14 = 7. Both methods work perfectly.

What if I get a different answer when checking?

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Double-check your arithmetic at each step. The most common errors happen in the multiplication step (5×17) or when handling the negative signs.

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