Solve Fraction Expression: 1/3 + 7/15 - 2/5 Step-by-Step

Fraction Addition with Mixed Denominators

13+71525= \frac{1}{3}+\frac{7}{15}-\frac{2}{5}=

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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 5 and 3 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:21 Let's calculate the products
00:32 Subtract under the common denominator
00:39 Calculate the numerator
00:47 Reduce the fraction as much as possible
00:52 Remember to divide both numerator and denominator
00:59 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+71525= \frac{1}{3}+\frac{7}{15}-\frac{2}{5}=

2

Step-by-step solution

Let's try to find the lowest common denominator between 3, 15, and 5

To find the lowest common denominator, we need to find a number that is divisible by 3, 15, and 5

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

1×53×5+7×115×12×35×3=515+715615 \frac{1\times5}{3\times5}+\frac{7\times1}{15\times1}-\frac{2\times3}{5\times3}=\frac{5}{15}+\frac{7}{15}-\frac{6}{15}

Now we'll add and then subtract:

5+7615=12615=615 \frac{5+7-6}{15}=\frac{12-6}{15}=\frac{6}{15}

We'll divide both numerator and denominator by 3 and get:

6:315:3=25 \frac{6:3}{15:3}=\frac{2}{5}

3

Final Answer

25 \frac{2}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find LCD of all denominators before adding or subtracting
  • Technique: Convert 13 \frac{1}{3} to 515 \frac{5}{15} when LCD is 15
  • Check: Verify 25=0.4 \frac{2}{5} = 0.4 matches decimal conversion ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 13+715 \frac{1}{3} + \frac{7}{15} as 818 \frac{8}{18} = wrong answer! This ignores that fractions need common denominators. Always find the LCD first, then convert all fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

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! 13 \frac{1}{3} means 1 piece of size 1/3, while 715 \frac{7}{15} means 7 pieces of size 1/15. They're different sizes!

How do I find the LCD of 3, 15, and 5?

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Look for the smallest number that all denominators divide into evenly. Since 15 = 3×5, the number 15 works for all three denominators: 15÷3=5, 15÷15=1, 15÷5=3.

What if I get a different LCD than 15?

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Any common multiple works, but using the smallest one keeps your numbers manageable. For example, 30 would work too, but you'd get 1230 \frac{12}{30} instead of 25 \frac{2}{5} .

Do I always need to simplify my final answer?

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Yes, always simplify! 615 \frac{6}{15} and 25 \frac{2}{5} are equal, but 25 \frac{2}{5} is in simplest form. Divide both numerator and denominator by their greatest common factor.

What if I make an error when converting fractions?

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Double-check each conversion: 13=1×53×5=515 \frac{1}{3} = \frac{1×5}{3×5} = \frac{5}{15} . The original fraction should equal your converted fraction when you simplify it back.

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