Simplify $6\frac{1}{12} − 2 ¾ + 1 ½$

Analysis

To solve this expression, we need to perform addition and subtraction on mixed fractions. The best approach is to convert the mixed fractions into improper fractions, find a common denominator, and then simplify the result.

Concept

A mixed fraction $a \frac{b}{c}$ is equivalent to $\frac{(a \times c) + b}{c}$. Once all terms are in improper fraction form, we find the Least Common Multiple (LCM) of the denominators to combine them.

Step-by-Step Solution

Step 1: Convert mixed fractions to improper fractions.

• $6 \frac{1}{12} = \frac{(6 \times 12) + 1}{12} = \frac{72 + 1}{12} = \frac{73}{12}$
• $2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$
• $1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$

Step 2: Rewrite the expression. The expression becomes: $\frac{73}{12} - \frac{11}{4} + \frac{3}{2}$

Step 3: Find the LCM of the denominators (12, 4, and 2). The LCM of 12, 4, and 2 is 12.

Step 4: Adjust the fractions to have the denominator 12.

• $\frac{73}{12}$ remains $\frac{73}{12}$
• $\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}$
• $\frac{3}{2} = \frac{3 \times 6}{2 \times 6} = \frac{18}{12}$

Step 5: Perform the arithmetic. $\frac{73}{12} - \frac{33}{12} + \frac{18}{12} = \frac{73 - 33 + 18}{12}$ $= \frac{40 + 18}{12} = \frac{58}{12}$

Step 6: Simplify the fraction. Divide both numerator and denominator by 2: $\frac{58 \div 2}{12 \div 2} = \frac{29}{6}$

Step 7: Convert back to a mixed fraction. $29 \div 6 = 4$ remainder $5$. So, $\frac{29}{6} = 4 \frac{5}{6}$

Conclusion

Comparing our result to the given options, we find that it matches option B.

Exam Tip

When dealing with mixed fractions in JAMB, you can also solve them by separating the whole numbers and the fractions: $(6 - 2 + 1) + (\frac{1}{12} - \frac{3}{4} + \frac{1}{2})$. This often keeps the numbers smaller and reduces the risk of calculation errors!