(2/3 + 3/4) × (3/6 + 4/9)
2 answers:
2/3 + 3/4
= 2 × 4/3 × 4 + 3 × 3/4 × 3
= 8/12 + 9/12
= 8 + 9/12
= 17/12
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. In practice, it is enough to find the common denominator by multiplying the denominators: 3 × 4 = 12. In the next intermediate step, the fraction result cannot be further simplified by canceling.
Add: 3/6 + 4/9
= 3 × 3/6 × 3 + 4 × 2/9 × 2
= 9/18 + 8/18
= 9 + 8/18
= 17/18
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 9) = 18. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 9 = 54. In the next intermediate step, the fraction result cannot be further simplified by canceling.
2 = 17/12 × 17/18
= 17 × 17/12 × 18
= 289/216
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(289, 216) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.
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We are given that there are a total of 78 students. If we set the following variables:
Then, the sum of all of these must be 78, that is:
Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:
Simplifying:
Now we solve for P by subtracting 62 on both sides:
Therefore, there are 16 students in physics