simplify one half plus two thirds divided by three fourths
If you verbalize an arithmetic calculation rather than using symbols, you lose the correct sequence of operations
e.g. If I say
What is 3 plus 8 divided by 4
is it (3+8)/4 or 3 + 8/4 ? different answers!
I will suppose it is the usual BEDMAS rule
1/2 + (2/3) ÷ (3/4)
= 1/2 + (2/3)(4/3)
= 1/2 + 8/9
= 9/18 + 16/18
= 25/18
its PEMDAS btw :)) not BEMDAS
To simplify the expression (1/2 + 2/3) ÷ (3/4), follow these steps:
Step 1: Find a common denominator for 2/3 and 3/4, which is 12. Multiply the numerator and denominator of 2/3 by 4, and the numerator and denominator of 3/4 by 3. This gives us (8/12 + 9/12) ÷ (9/12).
Step 2: Now that the fractions have the same denominator, we can add the numerators. 8/12 + 9/12 equals 17/12. The expression becomes 17/12 ÷ (9/12).
Step 3: To divide fractions, multiply the first fraction by the reciprocal (or inverse) of the second fraction. This means we'll multiply 17/12 by 12/9. Cancel out any common factors between the numerators and denominators, if possible.
Step 4: Simplify the multiplication. Multiply the numerators (17 * 12) and the denominators (12 * 9). The result is (204/108).
Step 5: Simplify the fraction. Divide both the numerator and denominator by their greatest common divisor (GCD), which is 12 in this case. 204/12 reduces to 17/9.
So, the simplified expression for (1/2 + 2/3) ÷ (3/4) is 17/9.
To simplify one half plus two thirds divided by three fourths, you need to follow the correct order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
Let's break down the steps:
Step 1: Simplify the addition within the parentheses.
To add one half and two thirds, you need to find a common denominator for the fractions. The least common multiple (LCM) of 2 and 3 is 6.
One half is equivalent to three sixths (multiply the numerator and the denominator by 3), and two thirds is equivalent to four sixths (multiply the numerator and the denominator by 2).
Therefore, one half plus two thirds becomes:
3/6 + 4/6 = 7/6
Step 2: Simplify the division.
To divide by three fourths, you need to multiply by the reciprocal of three fourths. The reciprocal of a fraction is obtained by switching the numerator and the denominator.
The reciprocal of three fourths is four thirds (switch 3 and 4 to get 4/3).
Therefore, 7/6 divided by three fourths becomes:
7/6 * 4/3 = 28/18
Step 3: Simplify the fraction.
To simplify 28/18, see if there is a common factor between the numerator and denominator that can be canceled out. In this case, both 28 and 18 can be divided by 2.
Dividing both the numerator and the denominator by 2 gives us:
28/18 = (28 ÷ 2) / (18 ÷ 2) = 14/9
So, one half plus two thirds divided by three fourths simplifies to 14/9.