1/2*4/3+5/6÷7/8
To simplify the given expression, follow the order of operations (PEMDAS/BODMAS):
1/2 * 4/3 + 5/6 ÷ 7/8
First, simplify the division:
5/6 ÷ 7/8 = 5/6 * 8/7 = (5*8)/(6*7) = 40/42
Now, perform the multiplication and addition:
1/2 * 4/3 + 40/42 = (1*4)/(2*3) + 40/42 = 4/6 + 40/42
To add these fractions, the denominators must be the same. The least common denominator for 6 and 42 is 42.
4/6 = (4*7)/(6*7) = 28/42
Now, the expression becomes:
28/42 + 40/42
To add two fractions with the same denominator, simply add the numerators while keeping the denominator the same:
(28 + 40) / 42 = 68/42
The final simplified result is 68/42, which can also be reduced to 34/21.
To solve the expression 1/2 * 4/3 + 5/6 ÷ 7/8 step-by-step, follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and simplify the calculations.
First, let's tackle the division: 5/6 ÷ 7/8:
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction, so we have:
5/6 * 8/7
Now, multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
(5 * 8) / (6 * 7) = 40/42
Next, let's proceed with the multiplication: 1/2 * 4/3:
Multiply the numerators and denominators:
(1 * 4) / (2 * 3) = 4/6
Now, the expression becomes:
4/6 + 40/42
To add or subtract fractions, we need a common denominator. In this case, the least common denominator is 6. We need to find equivalent fractions for both fractions with the denominator of 6:
4/6 + (40/42 * 6/6)
Multiply the numerator and denominator of 40/42 by 6:
4/6 + (40 * 6) / (42 * 6) = 4/6 + 240/252
Simplify the fraction 240/252 by dividing the numerator and denominator by their greatest common divisor, which is 12:
4/6 + (240/12) / (252/12) = 4/6 + 20/21
Now, we can combine the fractions:
4/6 + 20/21 = (4*21 + 20*6) / (6*21) = (84 + 120) / 126 = 204 / 126
Finally, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (6):
204 / 126 = (6*34) / (6*21) = 34 / 21
Therefore, the expression 1/2 * 4/3 + 5/6 ÷ 7/8 simplifies to 34/21.
To simplify this expression, you'll need to follow the order of operations: Parentheses, Exponents, Multiplication/Division (from left to right), and Addition/Subtraction (from left to right), often remembered as PEMDAS/BODMAS.
Let's break down the steps:
Step 1: Simplify the multiplication/division within the expression.
Start with the multiplication:
1/2 * 4/3 = (1 * 4) / (2 * 3) = 4/6 = 2/3
Next, the division:
5/6 ÷ 7/8 = (5/6) * (8/7) = (5 * 8) / (6 * 7) = 40/42 = 20/21
Now our expression becomes:
2/3 + 20/21
Step 2: Simplify the addition.
To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 3 and 21 is 21.
To make the denominators the same, we'll multiply the numerator and denominator of the first fraction by 7, and multiply the numerator and denominator of the second fraction by 3:
(2/3) * (7/7) + (20/21) * (3/3) = 14/21 + 60/63
Now that the denominators are the same, we can add the numerators:
14/21 + 60/63 = (14 + 60) / 21 = 74/21
Therefore, the simplified expression is 74/21.