Can you please explain step by step on how to do each of these two problems below? And then tell me whether it involves an arithmetic sequence or a geometric sequence I also need the work shown out on both problems
thank you.
Perform the indicated operations and reduce the answer to lowest terms.
(-3/4) ÷ (5/8)
(9/14 ÷ 3/7) × ½
dividion is the reciprocal of multiplication.
-3/4 divided by 5/8=(-3/4)*(8/5)=-6/5
on the second, do the same...
9/14 * 7/3 * 1/2=21/28 check that.
(-3/4) ÷ (5/8)
(-3/4) * (8/5) = -24/20 = -1 4/20 = -1 1/5
(9/14 ÷ 3/7) × ½
[(9/14) * (7/3)] * 1/2
(63/42) * 1/2 = 63/84 = 3/4
Sure! I'd be happy to help you with both of these problems step by step.
Problem 1:
To simplify the expression (-3/4) ÷ (5/8), we need to divide the numerator of the first fraction by the denominator of the second fraction. Here's how you can do it:
Step 1: Rewrite the division as multiplication by the reciprocal.
Reciprocal means flipping the fraction upside down. So, the expression becomes (-3/4) × (8/5).
Step 2: Multiply the numerators and the denominators.
(-3 × 8) / (4 × 5) = -24/20.
Step 3: Reduce the fraction to its lowest terms.
To reduce the fraction, find the greatest common factor (GCF) of the numerator and the denominator, and then divide both by the GCF. In this case, the GCF of 24 and 20 is 4.
(-24 ÷ 4) / (20 ÷ 4) = -6/5.
Therefore, the simplified form of (-3/4) ÷ (5/8) is -6/5.
Now, let's move to the second problem.
Problem 2:
To solve (9/14 ÷ 3/7) × ½, we need to first divide the two fractions inside the parentheses and then multiply the result by 1/2. Here's how:
Step 1: Simplify the division inside the parentheses.
To divide fractions, multiply the first fraction (9/14) by the reciprocal of the second fraction (3/7).
(9/14) ÷ (3/7) = (9/14) × (7/3).
Step 2: Multiply the numerators and the denominators.
(9 × 7) / (14 × 3) = 63/42.
Step 3: Reduce the fraction to its lowest terms.
The GCF of 63 and 42 is 21.
(63 ÷ 21) / (42 ÷ 21) = 3/2.
Step 4: Multiply the result by 1/2.
(3/2) × (1/2) = 3/4.
Therefore, the simplified form of (9/14 ÷ 3/7) × ½ is 3/4.
Now, let's determine if each of the problems involves an arithmetic sequence or a geometric sequence.
In both of these problems, we are dealing with simple arithmetic operations (addition, subtraction, multiplication, and division) in order to simplify the fractions. There is no pattern of increasing or decreasing values or any common ratio involved, which means that neither of these problems represents either an arithmetic sequence or a geometric sequence.
I hope this explanation helps you understand how to solve these problems step by step!