(4¾-1⅚)÷1 1/24×(1⅔+2½)
First, we need to simplify the expression inside the parenthesis:
1⅔ + 2½ = 5/3 + 5/2 (we need to find a common denominator)
= 10/6 + 15/6
= 25/6
Now we can substitute this in the original expression:
(4¾ - 1⅚) ÷ 1 1/24 × (1⅔ + 2½)
= (19/4 - 7/6) ÷ 1 1/24 × 25/6
Next, we need to convert the mixed number into an improper fraction:
1 1/24 = (24/24) + (1/24)
= 25/24
Now, we can multiply the dividend by the reciprocal of the divisor, which is the same as dividing by the divisor:
(19/4 - 7/6) ÷ 1 1/24 × 25/6
= (19/4 - 7/6) × 24/25
To simplify this fraction, we need to find a common denominator:
19/4 = 114/24
7/6 = 28/24
So, the expression becomes:
= (114/24 - 28/24) × 24/25
= (86/24) × (24/25)
= 86/25
Therefore, (4¾ - 1⅚) ÷ 1 1/24 × (1⅔ + 2½) = 86/25.
To solve the expression (4¾-1⅚)÷1 1/24×(1⅔+2½), let's break it down step-by-step:
Step 1: Simplify the subtraction, (4¾-1⅚):
To subtract fractions, we need a common denominator.
Converting 4¾ to an improper fraction:
4¾ = (4 x 4) + 3 = 19/4
Converting 1⅚ to an improper fraction:
1⅚ = (1 x 6) + 1 = 7/6
Subtracting the fractions:
19/4 - 7/6 = (19/4) * (6/6) - (7/6) * (4/4)
= (114/24) - (28/24)
= 86/24
Step 2: Simplify the multiplication, 1 1/24 × (1⅔ + 2½):
Let's calculate the sum inside the parentheses first.
Converting 1⅔ to an improper fraction:
1⅔ = (1 x 3) + 2 = 5/3
Converting 2½ to an improper fraction:
2½ = (2 x 2) + 1 = 5/2
Adding the fractions inside the parentheses:
5/3 + 5/2 = (5/3) * (2/2) + (5/2) * (3/3)
= (10/6) + (15/6)
= 25/6
Now, we can multiply by 1 1/24:
Converting 1 1/24 to an improper fraction:
1 1/24 = (1 x 24) + 1 = 25/24
Multiplying the fractions:
25/24 * 25/6 = (25*25)/(24*6)
= 625/144
Step 3: Divide the result from Step 1 by the result from Step 2:
(86/24) ÷ (625/144)
To divide fractions, we multiply by the reciprocal of the second fraction:
(86/24) * (144/625) = (86*144)/(24*625)
= 12,384/15,000
This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, 48:
12,384 ÷ 48 = 258
15,000 ÷ 48 = 312.5
Therefore, the simplified result is:
258/312.5