Question

Help 8/9*(2 1/4)² - 3/7:3 3/7+5/6 :3 1/3

Answer 1

2 1/4²=9/4*9/4=81/16 8/9*81/16=9/2=4,5

3/7:3 3/7=3/7:24/7=3/7*7/24=1/8=0,125

5/6:3 1/3=5/6:10/3=5/6*3/10=1/4=0,25

4,5-0,125+0,25=4,625

другое решение 4 5/10-1/8+1/4=4 1/2-1/8+1/4=4 4/8-1/8+2/8=4 5/8=4,625

Answer 2

Sure, let's break down the expression step by step:

1. Evaluate the expression inside the parentheses first. 2 1/4 = 2 + 1/4 = 9/4 Now, square 9/4: (9/4)^2 = (9/4) * (9/4) = 81/16

2. Evaluate the multiplication: 8/9 * (81/16) = 8/9 * 81/16

To multiply fractions, simply multiply the numerators together and the denominators together: (8 * 81) / (9 * 16) = 648 / 144

Now, let's simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator, which is 36: 648 ÷ 36 = 18 144 ÷ 36 = 4

So, the fraction becomes: 18/4

Next, let's proceed with the division on the right side of the expression: 3/7 ÷ 3 3/7

To divide fractions, multiply by the reciprocal of the second fraction: 3/7 * 7/24

Now, multiply the numerators together and the denominators together: (3 * 7) / (7 * 24) = 21/168

The fraction 21/168 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 21: 21 ÷ 21 = 1 168 ÷ 21 = 8

So, the fraction becomes: 1/8

Now, let's proceed with the division on the left side of the expression: 5/6 ÷ 3 1/3

To divide fractions, multiply by the reciprocal of the second fraction: 5/6 * 3/10

Now, multiply the numerators together and the denominators together: (5 * 3) / (6 * 10) = 15/60

The fraction 15/60 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 15: 15 ÷ 15 = 1 60 ÷ 15 = 4

So, the fraction becomes: 1/4

Finally, let's finish the overall calculation: 18/4 - 1/8 + 1/4

To add and subtract fractions, they need to have the same denominator. Since 4 and 8 share 4 as a common multiple, we can rewrite 1/8 as 2/8: 18/4 - 2/8 + 1/4

Now, all fractions have the same denominator, so we can combine them: 18/4 - 2/8 + 2/8 (18 - 2 + 2) / 4 18/4 9/2

So, the final result of the expression is 9/2 or 4.5.