Solve the Fraction Subtraction: 8/5 - 2/15 - 2/3 Step-by-Step

Fraction Subtraction with Multiple Denominators

85−215−23= \frac{8}{5}-\frac{2}{15}-\frac{2}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:02 We want to find the smallest common denominator
00:05 Therefore, we'll multiply by 3 and 5 respectively to find the common denominator 15
00:08 Remember to multiply both numerator and denominator
00:20 Let's calculate the multiplications
00:35 Subtract under the common denominator
00:39 Solve one operation at a time and continue
00:55 Reduce the fraction as much as possible
00:59 Remember to divide both numerator and denominator
01:04 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

85−215−23= \frac{8}{5}-\frac{2}{15}-\frac{2}{3}=

2

Step-by-step solution

Let's try to find the least common multiple (LCM) between 5, 15, and 3

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

In this case, the least common multiple is 15

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

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

We'll multiply the third fraction by 5

8×35×3−2×115×1−2×53×5=2415−215−1015 \frac{8\times3}{5\times3}-\frac{2\times1}{15\times1}-\frac{2\times5}{3\times5}=\frac{24}{15}-\frac{2}{15}-\frac{10}{15}

Now let's subtract:

24−2−1015=22−1015=1215 \frac{24-2-10}{15}=\frac{22-10}{15}=\frac{12}{15}

Let's divide both numerator and denominator by 3 and we get:

12:315:3=45 \frac{12:3}{15:3}=\frac{4}{5}

3

Final Answer

45 \frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find LCD of all denominators to create common base
  • Technique: Convert 85 \frac{8}{5} to 2415 \frac{24}{15} by multiplying by 3
  • Check: Verify 45=0.8 \frac{4}{5} = 0.8 equals original calculation ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of finding LCD
    Don't add 5 + 15 + 3 = 23 as your common denominator! This creates fractions that can't be properly subtracted. Always find the LCD (15) that each original denominator divides into evenly.

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 is 15 the LCD when 5, 15, and 3 are the denominators?

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The LCD is the smallest number that all denominators divide into evenly. Since 5 × 3 = 15 and 3 × 5 = 15, and 15 ÷ 15 = 1, the number 15 works perfectly for all three fractions!

Do I always subtract from left to right?

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Yes! Follow the order exactly as written: 2415−215−1015 \frac{24}{15} - \frac{2}{15} - \frac{10}{15} . This gives you 24−2−1015=1215 \frac{24-2-10}{15} = \frac{12}{15} .

How do I know when to simplify my final answer?

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Always check if the numerator and denominator share common factors. Since 12 and 15 are both divisible by 3, we get 12÷315÷3=45 \frac{12÷3}{15÷3} = \frac{4}{5} .

What if I get confused with all the conversions?

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Write each step clearly! First convert: 85=2415 \frac{8}{5} = \frac{24}{15} , 215=215 \frac{2}{15} = \frac{2}{15} , 23=1015 \frac{2}{3} = \frac{10}{15} . Then subtract the numerators: 24 - 2 - 10 = 12.

Can I use a calculator for this?

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While calculators help with arithmetic, practice the LCD method by hand first! This builds your fraction skills and helps you understand why 45=0.8 \frac{4}{5} = 0.8 .

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