Solve the Fraction Expression: 9/10 - 4/5 + 1/2

Fraction Operations with Mixed Denominators

Solve the following exercise:

91045+12=? \frac{9}{10}-\frac{4}{5}+\frac{1}{2}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this math problem together.
00:11 First, we need to find the least common denominator.
00:14 We'll multiply by 2 and 5 to achieve the common denominator of 10.
00:19 Don't forget! Multiply both the numerator, and the denominator, for each fraction.
00:32 Now, let's do the multiplications.
00:40 Add the fractions under this common denominator.
00:48 Calculate the numerator, one step at a time.
00:53 And that's how we find the solution to this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

91045+12=? \frac{9}{10}-\frac{4}{5}+\frac{1}{2}=\text{?}

2

Step-by-step solution

To solve the expression 91045+12 \frac{9}{10} - \frac{4}{5} + \frac{1}{2} , we first seek a common denominator for the fractions. The denominators are 10, 5, and 2.

The least common multiple of these numbers is 10, as it is the smallest number that all denominators divide perfectly.

  • Convert 45 \frac{4}{5} to a fraction with a denominator of 10: 45=4×25×2=810 \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} .
  • Convert 12 \frac{1}{2} to a fraction with a denominator of 10: 12=1×52×5=510 \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} .

Now, the expression becomes 910810+510 \frac{9}{10} - \frac{8}{10} + \frac{5}{10} .

Perform the operations:

  • Subtract: 910810=110 \frac{9}{10} - \frac{8}{10} = \frac{1}{10} .
  • Add: 110+510=610 \frac{1}{10} + \frac{5}{10} = \frac{6}{10} .

Thus, the value of the expression is 610 \frac{6}{10} .

The correct answer is 610\frac{6}{10}.

3

Final Answer

610 \frac{6}{10}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator: Find LCD of all fractions before adding or subtracting
  • Convert Fractions: Change 45 \frac{4}{5} to 810 \frac{8}{10} and 12 \frac{1}{2} to 510 \frac{5}{10}
  • Verify Answer: Check that 910810+510=610 \frac{9}{10} - \frac{8}{10} + \frac{5}{10} = \frac{6}{10}

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions without finding common denominators
    Don't add numerators and denominators separately like 91045=55 \frac{9}{10} - \frac{4}{5} = \frac{5}{5} = wrong answer! This ignores that fractions need the same denominator to be combined. Always convert all fractions to the same denominator first, then add or subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

\( \frac{3}{4}:\frac{5}{6}=\text{?} \)

FAQ

Everything you need to know about this question

How do I find the least common denominator quickly?

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Look at your denominators (10, 5, and 2). Find the smallest number that all of them divide into evenly. Since 10 ÷ 10 = 1, 10 ÷ 5 = 2, and 10 ÷ 2 = 5, the LCD is 10!

Why can't I just add the numerators and denominators separately?

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Fractions represent parts of a whole. You can only combine parts when they're the same size (same denominator). It's like trying to add 12 \frac{1}{2} pizza slice with 14 \frac{1}{4} pizza slice - you need equal-sized pieces first!

Do I need to simplify my final answer?

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Yes, always check if your answer can be simplified! 610 \frac{6}{10} can be reduced to 35 \frac{3}{5} by dividing both numerator and denominator by their greatest common factor (2).

What if some fractions already have the same denominator?

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Lucky you! You can work with those fractions immediately. In this problem, 910 \frac{9}{10} already has denominator 10, so you only need to convert the others to tenths.

How do I convert a fraction to have a different denominator?

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Multiply both the numerator and denominator by the same number. For 45 \frac{4}{5} to tenths: multiply by 2 to get 810 \frac{8}{10} . This keeps the fraction's value the same!

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