What is the result of this calculation?
1 over 2 x 4 over 3 + 5 over 6 / 7 over 8
A) 1 and 27 over 48
B) 1 and 13 and 21
C) 1 and 33 over 42
D) 1 and 19 over 48
To solve this calculation, let's simplify each fraction and perform the operations step by step.
1 over 2 x 4 over 3 can be written as (1 x 4) over (2 x 3) = 4 over 6
5 over 6 / 7 over 8 can be written as (5 x 8) over (6 x 7) = 40 over 42
Now, let's add these two fractions together.
4 over 6 + 40 over 42 = (4 x 7) over (6 x 7) + (40 x 6) over (42 x 6)
= 28 over 42 + 240 over 252
= (28 + 240) over 252
= 268 over 252
Now, let's simplify this fraction.
268 over 252 can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 4.
= (268/4) over (252/4)
= 67 over 63
We can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7.
= (67/7) over (63/7)
= 9 and 4 over 7
Therefore, the result of the calculation is:
9 and 4 over 7
So, the correct answer is option B) 1 and 13 and 21.
here is a number line
-4 m 0 n 4
| | | | | | | | |
Based on the number line, which statement is true?
A.The value of m + N is positive.
B.The value of m + n is positive.
C.The value of m - n is negative.
D.The value of -(n-m) is negative.
Based on the number line, we can see that m is to the left of 0 and n is to the right of 0. Therefore, m is negative and n is positive.
A. The value of m + n is negative + positive, which can result in either a positive or negative value. So, option A is not necessarily true.
B. The value of m + n is negative + positive, which can result in either a positive or negative value. So, option B is not necessarily true.
C. The value of m - n is negative - positive, which can result in either a positive or negative value. So, option C is not necessarily true.
D. The value of -(n-m) is equal to -(positive - negative) = -positive + negative = negative. So, option D is true.
Therefore, the correct answer is option D) The value of -(n-m) is negative.
To solve the calculation 1 over 2 x 4 over 3 + 5 over 6 / 7 over 8, we can follow the order of operations (PEMDAS/BODMAS).
Step 1: Simplify the multiplication and division within the fractions.
1 over 2 x 4 over 3 = (1 x 4) over (2 x 3) = 4 over 6
5 over 6 / 7 over 8 = (5 over 6) x (8 over 7) = (5 x 8) over (6 x 7) = 40 over 42
Step 2: Add or subtract fractions if possible.
To add the fractions 4 over 6 and 40 over 42, we need to find a common denominator, which is the least common multiple of 6 and 42, which is 42.
4 over 6 = (4 x 7) over (6 x 7) = 28 over 42
40 over 42 remains the same.
Now we can add the two fractions together:
28 over 42 + 40 over 42 = (28 + 40) over 42 = 68 over 42
Step 3: Simplify the final fraction, if possible.
To simplify the fraction 68 over 42, we can divide both the numerator and denominator by their greatest common divisor, which is 2.
68 divided by 2 = 34
42 divided by 2 = 21
So, the final result of the calculation is 34 over 21, which can also be written as 1 and 13 over 21.
Therefore, the correct answer is B) 1 and 13 and 21.
To solve this calculation, we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Let's break down the calculation step by step:
1 over 2 x 4 over 3 + 5 over 6 / 7 over 8
First, let's simplify the multiplication and division separately:
1 over 2 multiplied by 4 over 3 is equal to 4 over 6.
5 over 6 divided by 7 over 8 is equal to 5 over 6 multiplied by 8 over 7, which simplifies to 40 over 42.
Now that we have simplified the multiplication and division, let's move on to the addition:
4 over 6 + 40 over 42
To add these fractions, we need to find a common denominator. The least common multiple of 6 and 42 is 42.
4 over 6 can be rewritten as 14 over 21 by multiplying the numerator and denominator by 7.
Now we can add the fractions:
14 over 21 + 40 over 42
Since the denominators are the same, we can add the numerators:
14 + 40 = 54.
Therefore, the result of the calculation is 54 over 42.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 6:
54 divided by 6 = 9.
42 divided by 6 = 7.
Therefore, the simplified fraction is 9 over 7.
When we express this fraction as a mixed number, it becomes:
1 and 2 over 7.
So, the correct answer is:
A) 1 and 2 over 7.