Question

1/2 x 4/3 + 5/6 / 7/8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression, we can follow the order of operations (PEMDAS/BODMAS).

First, let's perform the multiplication:
1/2 * 4/3 = (1 * 4) / (2 * 3) = 4/6 = 2/3

Now, let's perform the division:
5/6 / 7/8 = (5/6) * (8/7) = (5 * 8) / (6 * 7) = 40/42 = 20/21

Now, let's add the results:
2/3 + 20/21

To add the fractions, we need a common denominator. The least common multiple (LCM) of 3 and 21 is 21.

2/3 + 20/21 = (2 * 7) / (3 * 7) + 20/21 = 14/21 + 20/21 = 34/21

Therefore, 1/2 x 4/3 + 5/6 / 7/8 simplifies to 34/21.

Answer 2

34/21 simplified

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the fraction 34/21, we can find the greatest common divisor (GCD) of the numerator (34) and denominator (21) and divide both by the GCD.

The GCD of 34 and 21 is 1.

Dividing both the numerator and denominator by 1:

34/1 / 21/1 = 34/21

Therefore, 34/21 is already in simplified form.

Answer 4

34/21 as a mixed number

Answer 5

[AI-generated answer — Bot GPT 3.5]

To convert the improper fraction 34/21 to a mixed number, we divide the numerator (34) by the denominator (21) and express the result as a whole number with a proper fraction.

34 ÷ 21 = 1 remainder 13

So, the whole number part is 1, and the fraction part is 13/21.

Therefore, 34/21 as a mixed number is 1 and 13/21.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To solve this expression step-by-step, we need to follow the order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction.

Let's simplify the expression:

Step 1: Multiply 1/2 by 4/3
To multiply fractions, we simply multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
(1/2) x (4/3) = (1 x 4) / (2 x 3) = 4/6

Step 2: Divide 5/6 by 7/8
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(5/6) ÷ (7/8) = (5/6) x (8/7) = (5 x 8) / (6 x 7) = 40/42

Now, we have:

4/6 + 40/42

Step 3: Find a common denominator
To add or subtract fractions, we need to have a common denominator. In this case, we can use 6 as our common denominator.

Step 4: Convert the fractions to have the same denominator
(4/6) = (4 x 1)/(6 x 1) = 4/6
(40/42) = (40 x 7)/(42 x 7) = 280/294

Now, we have:

4/6 + 280/294

Step 5: Add the fractions
To add fractions, we add the numerators together and keep the same denominator.
4/6 + 280/294 = (4/6) + (280/294) = (2/3) + (40/49)

Step 6: Find a common denominator again
We can use 3 as our common denominator.

Step 7: Convert the fractions to have the same denominator
(2/3) = (2 x 1)/(3 x 1) = 2/3
(40/49) = (40 x 3)/(49 x 3) = 120/147

Now, we have:

2/3 + 120/147

Step 8: Add the fractions
2/3 + 120/147 = (2/3) + (120/147) = (98/147) + (120/147)

Step 9: Simplify the fraction
98/147 + 120/147 = (98 + 120) / 147 = 218/147

The simplified expression is 218/147.

Answer 7

[AI-generated answer — Explain Bot]

To simplify the expression 1/2 x 4/3 + 5/6 / 7/8, we need to apply the order of operations.

Step 1: Simplify the division
To divide fractions, we can flip the second fraction (the divisor) and multiply it by the first fraction (the dividend). So, let's simplify 5/6 divided by 7/8:

5/6 ÷ 7/8 = 5/6 x 8/7

Step 2: Multiply the fractions
To multiply fractions, we multiply their numerators together and their denominators together. Let's multiply 1/2 by 4/3:

1/2 x 4/3 = (1 x 4) / (2 x 3) = 4/6

Step 3: Multiply the division result by the product from step 2
Now, we have 4/6 + 5/6 x 8/7. We can perform multiplication first:

5/6 x 8/7 = (5 x 8) / (6 x 7) = 40/42

Step 4: Add the fractions
Finally, we can add 4/6 and 40/42:

4/6 + 40/42 = (4 x 7) / (6 x 7) + 40/42 = 28/42 + 40/42 = 68/42

Step 5: Simplify the fraction (if possible)
To simplify 68/42, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

68 ÷ 2 / 42 ÷ 2 = 34/21

Therefore, the simplified form of the expression 1/2 x 4/3 + 5/6 / 7/8 is 34/21.