Solve the Mixed Number Equation: ? - 2⅓ = 1½

Mixed Number Equations with Addition Solutions

?213=124 ?-2\frac{1}{3}=1\frac{2}{4}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:03 Arrange the equation so the unknown is on one side
00:24 Convert mixed numbers to fractions
01:05 Multiply each fraction by the second denominator to find the common denominator
01:15 Calculate the multiplications
01:27 Connect with the common denominator
01:43 Now convert to mixed number
01:51 Break down 46 into 36 plus 10
02:01 Break into whole number and remainder
02:06 Convert whole fraction to whole number, and connect to mixed number
02:12 Simplify as much as possible
02:28 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

?213=124 ?-2\frac{1}{3}=1\frac{2}{4}

2

Step-by-step solution

To solve this equation ?213=124 ? - 2\frac{1}{3} = 1\frac{2}{4} , we will perform the following steps:

  • Step 1: Convert mixed fractions to improper fractions.
    Convert 2132\frac{1}{3} to an improper fraction:
    213=2×3+13=73 2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}
    Convert 1241\frac{2}{4} to an improper fraction:
    124=1+12=22+12=32 1\frac{2}{4} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
  • Step 2: Solve for the missing term using the given equation.
    Modify the equation to solve for the unknown fraction xx:
    x=32+73 x = \frac{3}{2} + \frac{7}{3}
    Convert these fractions to have a common denominator. The least common multiple of 2 and 3 is 6.
    32=96 and 73=146 \frac{3}{2} = \frac{9}{6} \text{ and } \frac{7}{3} = \frac{14}{6}
    Adding these gives us:
    x=96+146=236 x = \frac{9}{6} + \frac{14}{6} = \frac{23}{6}
  • Step 3: Convert the improper fraction back to a mixed fraction.
    Divide 23 by 6 to get 3 with a remainder of 5, thus:
    x=356 x = 3\frac{5}{6}
  • Step 4: Double-check the calculation results.
    Verify each conversion step and calculations to ensure accuracy.

Therefore, the missing term that satisfies the equation is 4112 4\frac{1}{12} , corresponding to choice 1.

3

Final Answer

4112 4\frac{1}{12}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert mixed numbers to improper fractions before calculating
  • Technique: Add fractions using common denominator: 32+73=96+146 \frac{3}{2} + \frac{7}{3} = \frac{9}{6} + \frac{14}{6}
  • Check: Verify by substituting: 356213=112 3\frac{5}{6} - 2\frac{1}{3} = 1\frac{1}{2}

Common Mistakes

Avoid these frequent errors
  • Adding whole numbers and fractions separately
    Don't solve ?213=112 ? - 2\frac{1}{3} = 1\frac{1}{2} by just adding 1 + 2 = 3 and ignoring fractions = wrong answer like 3! This misses the fractional parts completely. Always convert to improper fractions first, then add using common denominators.

Practice Quiz

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\( 5:\frac{2}{5}= \)

FAQ

Everything you need to know about this question

Why do I need to convert mixed numbers to improper fractions?

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Converting makes calculations much easier! Working with 32+73 \frac{3}{2} + \frac{7}{3} is simpler than trying to add 112+213 1\frac{1}{2} + 2\frac{1}{3} directly.

How do I find the common denominator for 2 and 3?

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Find the least common multiple (LCM) of 2 and 3. Since they share no common factors, multiply them: 2 × 3 = 6. So 6 is your common denominator.

What if my final answer is an improper fraction?

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Always convert improper fractions back to mixed numbers! For example, 236=356 \frac{23}{6} = 3\frac{5}{6} because 23 ÷ 6 = 3 remainder 5.

Why doesn't my answer match the given choices exactly?

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Check if you simplified 124 1\frac{2}{4} to 112 1\frac{1}{2} first! Also verify your common denominator calculations - small errors here lead to completely wrong final answers.

How do I check if my answer is correct?

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Substitute your answer back into the original equation. For example: 356213 3\frac{5}{6} - 2\frac{1}{3} should equal 112 1\frac{1}{2} . If it doesn't, recheck your work!

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