Solve: 7/5 - 2/15 - 2/3 Using Fraction Subtraction

Fraction Subtraction with Mixed Denominators

7521523= \frac{7}{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 least common denominator
00:05 Therefore we'll multiply by 3 and 5 respectively to find the common denominator
00:08 Remember to multiply both numerator and denominator
00:22 Let's calculate the multiplications
00:40 Subtract under the common denominator
00:48 Calculate the numerator
00:54 Reduce the fraction as much as possible
01:00 Remember to divide both numerator and denominator
01:03 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

7521523= \frac{7}{5}-\frac{2}{15}-\frac{2}{3}=

2

Step-by-step solution

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

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

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 3

We'll multiply the second fraction by 1

We'll multiply the third fraction by 5

7×35×32×115×12×53×5=21152151015 \frac{7\times3}{5\times3}-\frac{2\times1}{15\times1}-\frac{2\times5}{3\times5}=\frac{21}{15}-\frac{2}{15}-\frac{10}{15}

Now let's subtract:

2121015=191015=915 \frac{21-2-10}{15}=\frac{19-10}{15}=\frac{9}{15}

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

9:315:3=35 \frac{9:3}{15:3}=\frac{3}{5}

3

Final Answer

35 \frac{3}{5}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find common denominator that divides into all denominators
  • Technique: Convert 75 \frac{7}{5} to 2115 \frac{21}{15} by multiplying by 3
  • Check: Verify 35=0.6 \frac{3}{5} = 0.6 equals original calculation result ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of finding LCD
    Don't just add 5 + 15 + 3 = 23 as the common denominator! This creates wrong fractions that don't equal the originals. Always find the LCD by identifying the smallest number divisible by all denominators.

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

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

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List multiples of the largest denominator (15): 15, 30, 45... Check if smaller denominators divide evenly: 15 ÷ 5 = 3 ✓, 15 ÷ 3 = 5 ✓. So LCD = 15!

Why do I multiply the whole fraction, not just the denominator?

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You must multiply both numerator and denominator by the same number to keep the fraction's value unchanged. 75=7×35×3=2115 \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15}

What if my final answer can be simplified?

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Always simplify! 915 \frac{9}{15} becomes 35 \frac{3}{5} by dividing both parts by their GCD (3). Simplified fractions are the expected final answer.

Can I subtract fractions left to right in any order?

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Be careful with order! 7521523 \frac{7}{5} - \frac{2}{15} - \frac{2}{3} means subtract the second fraction, then subtract the third. Work left to right: 2121015 \frac{21-2-10}{15}

How do I check if my LCD is correct?

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Your LCD should be divisible by every original denominator. Test: 15 ÷ 5 = 3, 15 ÷ 15 = 1, 15 ÷ 3 = 5. All whole numbers means 15 works!

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