Solve: 1/10 + 3/5 - 1/2 Mixed Fraction Operations

Fraction Operations with Common Denominators

Solve the following exercise:

110+3512=? \frac{1}{10}+\frac{3}{5}-\frac{1}{2}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to find the least common denominator
00:06 Therefore, we'll multiply by 2 and 5 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:23 Let's calculate the products
00:32 Subtract under the common denominator
00:38 Let's calculate the numerator
00:45 Reduce the fraction as much as possible
00:51 Remember to divide both numerator and denominator
00:58 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

Solve the following exercise:

110+3512=? \frac{1}{10}+\frac{3}{5}-\frac{1}{2}=\text{?}

2

Step-by-step solution

To solve the exercise 110+3512 \frac{1}{10} + \frac{3}{5} - \frac{1}{2} , we must follow these steps:

Step 1: Find the Least Common Denominator (LCD).
The denominators we have are 10, 5, and 2. The LCD for these numbers is 10.

Step 2: Convert each fraction to have the common denominator of 10.
- 110 \frac{1}{10} is already with the denominator 10.
- Convert 35 \frac{3}{5} :35×22=610 \frac{3}{5} \times \frac{2}{2} = \frac{6}{10}
- Convert 12 \frac{1}{2} :
12×55=510 \frac{1}{2} \times \frac{5}{5} = \frac{5}{10}

Step 3: Perform the addition and subtraction.
Now operate: 110+610510=1+6510=210 \frac{1}{10} + \frac{6}{10} - \frac{5}{10} = \frac{1 + 6 - 5}{10} = \frac{2}{10}

Step 4: Simplify the result.
The fraction 210\frac{2}{10} simplifies to 15\frac{1}{5} because both the numerator and denominator are divisible by 2.

Therefore, the solution to the problem is 15\frac{1}{5}.

3

Final Answer

15 \frac{1}{5}

Key Points to Remember

Essential concepts to master this topic
  • LCD Method: Find least common denominator to add/subtract fractions
  • Technique: Convert 35 \frac{3}{5} to 610 \frac{6}{10} by multiplying by 22 \frac{2}{2}
  • Check: Simplify final answer - 210=15 \frac{2}{10} = \frac{1}{5} divides by 2 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators without common denominators
    Don't just add 1 + 3 - 1 = 3 and keep random denominators! This gives completely wrong results because you're adding different-sized pieces. Always convert ALL fractions to the same denominator first, then add/subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

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

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Fractions represent parts of a whole. You can only add parts when they're the same size! 110 \frac{1}{10} and 35 \frac{3}{5} are different-sized pieces, so convert them first.

How do I find the LCD of 10, 5, and 2?

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List multiples of the largest number (10): 10, 20, 30... Check if smaller numbers divide evenly. Since 5 and 2 both divide into 10, the LCD is 10!

Do I always need to simplify my final answer?

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Yes! Always check if your numerator and denominator share common factors. 210 \frac{2}{10} simplifies to 15 \frac{1}{5} because both divide by 2.

What if the LCD is really big? Is there an easier way?

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Sometimes! But using the true LCD keeps numbers smaller and calculations easier. Don't use shortcuts like multiplying all denominators together - that makes bigger, harder numbers.

Can I convert to decimals instead of finding LCD?

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You could, but fractions are often more exact. Plus, your math teacher wants to see you practice the LCD method since it works for all fraction problems!

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