Question

Simplify.​​​​​​​

7 2/3 + −5 1/4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 7 2/3 - 5 1/4, we first need to convert the mixed numbers into improper fractions.

7 2/3 = (7*3 + 2)/3 = 23/3

5 1/4 = (5*4 + 1)/4 = 21/4

Now, we can substitute these improper fractions into the expression:

23/3 - 21/4

To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 3 and 4 is 12.

Multiplying the first fraction by 4/4 and the second fraction by 3/3, we get:

(23/3)*(4/4) - (21/4)*(3/3)
= 92/12 - 63/12

Now, we can subtract the fractions:

(92 - 63)/12
= 29/12

The simplified expression is 29/12.

Answer 2

what is 29/12 as a mixed number?

Answer 3

[AI-generated answer — Bot GPT 3.5]

To convert the improper fraction 29/12 to a mixed number, we need to divide the numerator (29) by the denominator (12).

29 ÷ 12 = 2 remainder 5

The quotient (whole number part) is 2, and the remainder is 5. So the mixed number representation of 29/12 is 2 5/12.

Answer 4

Consider this expression:

1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify this expression, we can add up all the terms:

1/4 - 0.5 + 1/2 - 0.25 + 3/5 + 0.4

First, we need to find a common denominator for the fractions to add or subtract them. The least common denominator (LCD) in this case is 20.

Converting each fraction to have a denominator of 20:

1/4 = (1*5)/(4*5) = 5/20

1/2 = (1*10)/(2*10) = 10/20

3/5 = (3*4)/(5*4) = 12/20

Now, we substitute the fractions back into the expression:

5/20 - 0.5 + 10/20 - 0.25 + 12/20 + 0.4

Combining the like terms:

(5/20 + 10/20 + 12/20) - 0.5 - 0.25 + 0.4
= 27/20 - 0.50 - 0.25 + 0.4

To perform the subtraction and addition:

27/20 - 0.50 - 0.25 + 0.4
= 27/20 - 11/20 + 8/20
= (27 - 11 + 8)/20
= 24/20

Simplifying the fraction:

24/20 = (24/4) / (20/4) = 6/5

So, the simplified expression is 6/5.

Answer 6

Consider this expression:

1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4
You are asked to find the sum by using fractions. Which expression could you use?
Responses

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the sum of the given expression using fractions, we can use the expression:

(1/4) + (1/2) + (3/5) + (0.4)

This expression adds up all the given terms using fractions.

Answer 8

Consider this expression as a mixed fraction:

1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4

Answer 9

[AI-generated answer — Bot GPT 3.5]

To express the given expression as a mixed fraction, we need to perform the calculations and simplify the result.

(1/4) - 0.5 + (1/2) - 0.25 + (3/5) + 0.4

First, let's convert the decimal numbers to fractions:

0.5 = 5/10 = 1/2 (by dividing the numerator and denominator by 5)
0.25 = 25/100 = 1/4 (by dividing the numerator and denominator by 25)
0.4 = 4/10 = 2/5 (by dividing the numerator and denominator by 2)

Now we can substitute these fractions back into the expression:

(1/4) - (1/2) + (1/2) - (1/4) + (3/5) + (2/5)

The fractions with the same denominator can be combined:

(1/4 - 1/4) + (1/2 + 1/2) + (3/5 + 2/5)

These fractions simplify to:

0 + 1 + 5/5

Simplifying further:

1 + 5/5 = 1 + 1 = 2

So, the given expression as a mixed fraction is 2.

Answer 10

Consider this expression:

1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4
Find the sum.
Responses
A 0
B 1
C 1 1/2
D 1/2
1 2

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the sum of the given expression, let's calculate it step by step:

(1/4) - 0.5 + (1/2) - 0.25 + (3/5) + 0.4

To add or subtract fractions, we need to find a common denominator. The least common denominator (LCD) here is 20.

Converting each fraction to have a denominator of 20:

1/4 = (1*5)/(4*5) = 5/20

1/2 = (1*10)/(2*10) = 10/20

3/5 = (3*4)/(5*4) = 12/20

Now, we substitute the fractions back into the expression:

5/20 - 0.5 + 10/20 - 0.25 + 12/20 + 0.4

Combine the like terms:

(5/20 + 10/20 + 12/20) - 0.5 - 0.25 + 0.4
= 27/20 - 0.5 - 0.25 + 0.4

To perform the subtraction and addition:

27/20 - 0.5 - 0.25 + 0.4
= 27/20 - 11/20 + 8/20
= (27 - 11 + 8)/20
= 24/20

Simplifying the fraction:

24/20 = (24/4) / (20/4) = 6/5

Therefore, the sum of the given expression is 6/5. This can also be simplified as 1 1/5.

Hence, the correct response is C) 1 1/2.