Solve the Mixed Number Equation: ? - 2⅓ = 1½

Question

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

Video Solution

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.

Answer

4112 4\frac{1}{12}