What is the result of this calculation? 1/2 ⋅ 4/3 + 5/6 ÷ 7/8
To solve this calculation, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). However, there are no parentheses or exponents in this calculation, so we can proceed with multiplication and division.
1/2 ⋅ 4/3 equals (1/2) * (4/3) = 4/6 = 2/3
Now, we can rewrite the calculation as:
2/3 + 5/6 ÷ 7/8
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:
5/6 ÷ 7/8 equals (5/6) * (8/7) = 40/42 = 20/21
Now, the calculation becomes:
2/3 + 20/21
To add fractions, they need to have a common denominator. In this case, the least common denominator (LCD) is 63. To find a common denominator, we need to multiply the numerator and denominator of each fraction by the same value that will result in the LCD.
2/3 * 21/21 = 42/63
20/21 * 3/3 = 60/63
Now, the calculation becomes:
42/63 + 60/63 = 102/63
The result of this calculation is 102/63, which is an improper fraction. It can be simplified to 2 and 18/63, or further reduced to 2 and 6/21, or even 2 and 2/7.