Evaluate 5 18 × 3 4 Give your answer as a fraction in its simplest form.
The Correct Answer and Explanation is:
To evaluate the expression 5183×3415 \frac{18}{3} \times 3 \frac{4}{1}5318×314, let’s break it down step by step:
Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.
- 51835 \frac{18}{3}5318:
A mixed number is expressed as: Mixed number=Whole number+NumeratorDenominator\text{Mixed number} = \text{Whole number} + \frac{\text{Numerator}}{\text{Denominator}}Mixed number=Whole number+DenominatorNumerator So, for 51835 \frac{18}{3}5318, convert the whole part (5) into a fraction and then add the fractional part: 5=5×33=1535 = \frac{5 \times 3}{3} = \frac{15}{3}5=35×3=315 So: 5183=153+183=3335 \frac{18}{3} = \frac{15}{3} + \frac{18}{3} = \frac{33}{3}5318=315+318=333 - 3413 \frac{4}{1}314:
Similarly, for 3413 \frac{4}{1}314, we convert the whole part (3) into a fraction: 3=3×11=313 = \frac{3 \times 1}{1} = \frac{3}{1}3=13×1=13 Thus: 341=31+41=713 \frac{4}{1} = \frac{3}{1} + \frac{4}{1} = \frac{7}{1}314=13+14=17
Step 2: Multiply the Fractions
Now that we have the fractions 333\frac{33}{3}333 and 71\frac{7}{1}17, we can multiply them together:333×71=33×73×1=2313\frac{33}{3} \times \frac{7}{1} = \frac{33 \times 7}{3 \times 1} = \frac{231}{3}333×17=3×133×7=3231
Step 3: Simplify the Fraction
Finally, simplify the fraction 2313\frac{231}{3}3231 by dividing the numerator (231) by the denominator (3):2313=77\frac{231}{3} = 773231=77
Final Answer:
Thus, the result of 5183×3415 \frac{18}{3} \times 3 \frac{4}{1}5318×314 is:777777
