simplify 24÷1/2+5/8*6/7

24 divided by 1/2 = 24 * 2 = 48

5/8 * 6/7 = 30/56

Take it from there.

21/4

To simplify the expression 24 ÷ (1/2) + (5/8) * (6/7), we will follow the order of operations (also known as PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Step 1: Simplify the division 24 ÷ (1/2) first.
To divide by a fraction, we can multiply by its reciprocal (flipping the numerator and denominator). So, we have 24 ÷ (1/2) = 24 * (2/1) = 24 * 2 = 48.

Step 2: Simplify the multiplication (5/8) * (6/7).
Multiply the numerators together (5 * 6 = 30) and multiply the denominators together (8 * 7 = 56). So, (5/8) * (6/7) = 30/56.

Step 3: Perform addition 48 + 30/56.
To add fractions, we need a common denominator. The least common multiple (LCM) of 56 is 56 itself. We can convert the whole number 48 to a fraction by putting it over 1 (48/1). Then, we can add the fractions: (48/1) + (30/56) = (48 * 56)/(1 * 56) + (30 * 1)/(56 * 1) = 2688/56 + 30/56 = (2688 + 30)/56 = 2718/56.

Step 4: Simplify the fraction 2718/56.
To simplify a fraction, we can find the greatest common divisor (GCD) of the numerator and denominator and divide them both by it. In this case, the GCD of 2718 and 56 is 2. So, we divide both numbers by 2: 2718/56 = (2718 ÷ 2) / (56 ÷ 2) = 1359/28.

Therefore, the simplified expression is 1359/28.