Determine the value of 7/6 of (3 1/3 -2 1/4)+5 1/8÷3/16-1/2
First, we need to simplify the expression inside the parentheses:
3 1/3 - 2 1/4
= (10/3) - (9/4) (converting mixed fractions to improper fractions)
= (40/12) - (27/12) (getting a common denominator)
= 13/12
Now, we can calculate 7/6 of (13/12):
(7/6) × (13/12)
= (91/72)
Next, we need to simplify the expression after the plus sign:
5 1/8 ÷ 3/16 - 1/2
= 41/8 ÷ 3/16 - 1/2 (converting mixed fractions to improper fractions)
= 41/8 × 16/3 - 1/2 (dividing by a fraction is the same as multiplying by its reciprocal)
= 82/3 - 1/2
= (164/6) - (3/6) (getting a common denominator)
= 161/6
Finally, we can add the two simplified expressions:
(91/72) + (161/6)
= (13/72) + (26/72) + (241/72) (getting a common denominator)
= 280/72
= 35/9
Therefore, the value of the expression is 35/9.
To determine the value of the expression, let's break it down step-by-step:
Step 1: Simplify the expression within the parentheses.
3 1/3 - 2 1/4:
To subtract mixed numbers, we need to find a common denominator.
The common denominator of 3 and 4 is 12.
3 1/3 = (3 * 3)/3 + 1/3 = 9/3 + 1/3 = 10/3
2 1/4 = (2 * 4)/4 + 1/4 = 8/4 + 1/4 = 9/4
Now we can subtract: (10/3) - (9/4)
To subtract fractions, we need to have a common denominator.
The common denominator of 3 and 4 is 12.
(10/3) = (10/3) * (4/4) = 40/12
(9/4) = (9/4) * (3/3) = 27/12
Now we can subtract: (40/12) - (27/12) = 13/12
So, 7/6 * (3 1/3 - 2 1/4) becomes 7/6 * 13/12.
Step 2: Simplify the expression 5 1/8 ÷ 3/16.
To divide mixed numbers, we need to convert the mixed numbers into improper fractions.
5 1/8 = (5 * 8)/8 + 1/8 = 40/8 + 1/8 = 41/8
3/16 = 3/16
Now we can divide: (41/8) ÷ (3/16)
To divide fractions, we can multiply the first fraction by the reciprocal of the second.
(41/8) * (16/3) = (41 * 16) / (8 * 3) = 656/24
So, 5 1/8 ÷ 3/16 becomes 656/24.
Step 3: Simplify the expression 7/6 * 13/12 + 656/24 - 1/2.
Now that we have simplified the individual parts, we can add these fractions.
(7/6) * (13/12) = (7 * 13) / (6 * 12) = 91/72
656/24 - 1/2 = (656/24) - (12/24) = (656 - 12) / 24 = 644/24
Now let's add the fractions:
91/72 + 644/24 = (91 * 3) / (72 * 3) + 644/24 = 273/216 + 644/24
To add the fractions, we need a common denominator, which is 216.
273/216 + 644/24 = (273 * 4) / (216 * 4) + 644/24 = 1092/864 + 644/24
Now, let's convert 1092/864 to have the same denominator as 644/24:
1092/864 = (1092 * 3) / (864 * 3) = 3276/2592
Now, we can add the fractions:
3276/2592 + 644/24 = (3276 + 2592 * 107) / (2592 * 107) = 61972/277344
So, the simplified value of the expression 7/6 * (3 1/3 - 2 1/4) + 5 1/8 ÷ 3/16 - 1/2 is 61972/277344.
To determine the value of the expression 7/6 of (3 1/3 -2 1/4) + 5 1/8 ÷ 3/16 - 1/2, we will break it down step by step.
Step 1: Simplify the within-parentheses expression (3 1/3 - 2 1/4).
To do this, we need to convert the mixed numbers into improper fractions:
3 1/3 = 10/3
2 1/4 = 9/4
Now, we subtract these fractions:
10/3 - 9/4
To subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 4 is 12.
10/3 = (10/3) * (4/4) = 40/12
9/4 = (9/4) * (3/3) = 27/12
Now, we subtract:
40/12 - 27/12 = 13/12
Step 2: Calculate 7/6 of 13/12.
To calculate a fraction of a fraction, we multiply the numerators and denominators:
(7/6) * (13/12) = (7 * 13) / (6 * 12) = 91 / 72
Step 3: Simplify 5 1/8 ÷ 3/16.
Again, we need to convert the mixed number into an improper fraction:
5 1/8 = 41/8
Now, we divide by the fraction 3/16:
(41/8) ÷ (3/16)
To divide fractions, we multiply by the reciprocal of the dividend (the fraction we're dividing by). So, we need to divide by (3/16), which means multiplying by (16/3):
(41/8) * (16/3) = (41 * 16) / (8 * 3) = 656 / 24
Step 4: Subtract 1/2.
Now, we subtract 1/2 from the result obtained in Step 3:
656/24 - 1/2
To subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 24 and 2 is 24.
656/24 = (656/24) * (1/1) = 656/24
1/2 = (1/2) * (12/12) = 12/24
Now, we subtract:
656/24 - 12/24 = 644/24
Step 5: Simplify the final fraction.
To simplify the fraction 644/24, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 4:
644/24 = (644/4) / (24/4) = 161/6
Therefore, the value of the expression 7/6 of (3 1/3 -2 1/4) + 5 1/8 ÷ 3/16 - 1/2 is 161/6.