I need help with these two math problems. i have been trying those for two hours. Can't find the answer.
use grouping symbols to make each equation true.
1/2*2^3/2*4/8*4/2=1/2
64-5*1+4/8+5=3
*= multiplication
is there any qucik way or any trick to solve these problems quickly because of test timing. immidiate answer would be very helpful
[(1/2)*(2^3)/2]* [4/(8*4/2)]
= [(1/2)*4]*(4/16) = 1/2
[64-5*(1+4)]/(8+5) = 39/13 = 3
To solve the first equation: 1/2 * 2^3/2 * 4/8 * 4/2 = 1/2, we need to use grouping symbols to clarify the order of operations. Let's break it down step by step:
1. Start with the expression: 1/2 * 2^3/2 * 4/8 * 4/2.
2. First, let's focus on the exponent: 2^3/2. Since the exponent applies to 2 alone, we can rewrite it as (2^3)/2.
3. Next, let's simplify the exponent: (2^3) = 2 * 2 * 2 = 8.
4. After that, simplify 8/2: 8/2 = 4.
5. Now, substitute the value of (2^3/2) back into the equation: 1/2 * 4 * 4/8 * 4/2.
6. Next, simplify 4/8: 4/8 = 1/2.
7. Continue with 1/2 * 4 * 1/2 * 4/2.
8. Simplify the remaining multiplications: (1/2) * 4 = 2 and (1/2) * 4/2 = 1.
9. Combine the simplified values: 2 * 1 * 1 = 2.
So, the solution to the first equation is 2.
To solve the second equation: 64 - 5 * 1 + 4/8 + 5 = 3, let's break it down step by step:
1. Start with the expression: 64 - 5 * 1 + 4/8 + 5.
2. Begin by simplifying multiplication and division from left to right: 5 * 1 = 5 and 4/8 = 1/2.
3. Substitute the values back into the equation: 64 - 5 + 1/2 + 5.
4. Now, focus on addition and subtraction from left to right: 64 - 5 = 59, 59 + 1/2 = 59 + 0.5 = 59.5, and 59.5 + 5 = 64.5.
So, the solution to the second equation is 64.5.
To solve these problems more quickly during a test, it's important to remember the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction. In both equations, we followed the order of operations to simplify each expression and arrive at the final answer. Practicing mental math and familiarizing yourself with basic arithmetic operations can also help you solve problems more efficiently.