Solve the Fraction Equation: 7/10 - 2/6 Subtraction Problem

Fraction Subtraction with Different Denominators

Solve the following equation:

71026= \frac{7}{10}-\frac{2}{6}=

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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 30
00:08 Remember to multiply both numerator and denominator
00:17 Let's calculate the multiplications
00:28 Subtract under the common denominator
00:32 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 equation:

71026= \frac{7}{10}-\frac{2}{6}=

2

Step-by-step solution

Let's first identify the lowest common denominator between 10 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 10 and 6.

In this case, the common denominator is 30.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 30.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 5

7×310×32×56×5=21301030 \frac{7\times3}{10\times3}-\frac{2\times5}{6\times5}=\frac{21}{30}-\frac{10}{30}

Now let's subtract:

211030=1130 \frac{21-10}{30}=\frac{11}{30}

3

Final Answer

1130 \frac{11}{30}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find common denominator before subtracting unlike fractions
  • Technique: Convert 710 \frac{7}{10} to 2130 \frac{21}{30} and 26 \frac{2}{6} to 1030 \frac{10}{30}
  • Check: Verify LCD is correct: 30 ÷ 10 = 3, 30 ÷ 6 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting numerators and denominators separately
    Don't subtract 7-2=5 and 10-6=4 to get 54 \frac{5}{4} = wrong answer! This ignores that fractions represent parts of different wholes. Always find the LCD first to make denominators the same before subtracting.

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 10 and 6?

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List multiples of each number: 10: 10, 20, 30, 40... and 6: 6, 12, 18, 24, 30... The first common multiple is 30, so that's your LCD!

Why can't I just subtract the fractions as they are?

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You can only add or subtract fractions when they have the same denominator. Think of it like trying to subtract 7 apples from 2 oranges - you need the same "unit" first!

What if I simplified 2/6 to 1/3 first?

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That's actually a great idea! 26=13 \frac{2}{6} = \frac{1}{3} , so you'd solve 71013 \frac{7}{10} - \frac{1}{3} . The LCD of 10 and 3 is still 30, giving the same answer.

How do I know what to multiply each fraction by?

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Divide the LCD by each denominator: 30 ÷ 10 = 3 and 30 ÷ 6 = 5. So multiply the first fraction by 3 and the second by 5.

Can I reduce my final answer further?

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1130 \frac{11}{30} is already in lowest terms because 11 and 30 share no common factors other than 1. You're done!

What if I get the LCD wrong?

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If you pick a number that's too small (like 15), it won't work as a common denominator. If it's too big (like 60), you'll still get the right answer, just with more work!

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