simplest form with solution!1. 1/3 × 2 1/4
The Correct Answer and Explanation is:
Answer: 13×214=13×94=912=34\frac{1}{3} \times 2\frac{1}{4} = \frac{1}{3} \times \frac{9}{4} = \frac{9}{12} = \frac{3}{4}31×241=31×49=129=43
Explanation:
To solve the expression 13×214\frac{1}{3} \times 2\frac{1}{4}31×241, first convert the mixed number 2142\frac{1}{4}241 into an improper fraction. A mixed number contains both a whole number and a fraction. To convert it:
Multiply the whole number 2 by the denominator 4, which gives 8. Then add the numerator 1. This results in 9. Place this value over the original denominator: 214=942\frac{1}{4} = \frac{9}{4}241=49
Now, multiply the fractions: 13×94\frac{1}{3} \times \frac{9}{4}31×49
When multiplying two fractions, multiply the numerators together and the denominators together: 1×93×4=912\frac{1 \times 9}{3 \times 4} = \frac{9}{12}3×41×9=129
Now, reduce 912\frac{9}{12}129 to its simplest form. To do this, find the greatest common factor (GCF) of 9 and 12, which is 3. Divide both the numerator and the denominator by 3: 9÷312÷3=34\frac{9 \div 3}{12 \div 3} = \frac{3}{4}12÷39÷3=43
Thus, the simplest form of 13×214\frac{1}{3} \times 2\frac{1}{4}31×241 is 34\frac{3}{4}43.
This method shows how multiplication involving a proper fraction and a mixed number can be handled in steps: convert to improper fractions, multiply, and simplify. The process ensures clarity and accuracy while working with fractional expressions.
