The 1st problem: 2 2/5 + 1/15
How your friend did the work:
2 2/5 + 1/15
2 12/15 + 1/15
2 13/15***I think it's 2 7/15 am I right?
The 2nd problem: 9 1/2 - 5 7/12
How your friend did the work:
9 1/2 - 5 7/12
9 6/12 - 5 7/12
8 18/12 - 5 7/12
3 11/12***I got the same thing am I right?
The 3rd problem: -4 7/8 x 2/3
How your friend did the problem:
-4 7/8 x 2/3
-4 14/24
-4 7/12***I got -3 1/4 am I right?
The 4th problem: -3 1/5 ÷ -2/3
-3 1/5 ÷ -2/3
-16/5 x -3/2
-8/5 x -3/1
-24/5
-4 4/5***I got the same thing am I right?
Thank you for the help!!
You're ok until the last one
-8/5 x -3/1 = +24/5
You lost the minus sign.
For the first problem, you mentioned that your friend did the following steps:
2 2/5 + 1/15
2 12/15 + 1/15
2 13/15
You are asking if the answer is 2 7/15. To verify this, let's break it down.
To add fractions, we need to have a common denominator. The common denominator for 5 and 15 is 15. Let's convert the mixed number 2 2/5 to an improper fraction:
2 2/5 = (5 * 2 + 2) / 5 = 12/5
Now, let's rewrite the addition using the common denominator of 15:
12/5 + 1/15
To add the fractions, we need the same denominator, which is 15. So, we multiply the numerator and denominator of the first fraction by 3:
(12/5) * (3/3) + (1/15) = 36/15 + 1/15
Now that the two fractions have the same denominator, we can add the numerators:
36/15 + 1/15 = 37/15
Therefore, the answer is indeed 2 13/15, not 2 7/15. Your friend's calculation is correct.
Now let's move on to the second problem:
9 1/2 - 5 7/12
Your friend did the following steps:
9 1/2 - 5 7/12
9 6/12 - 5 7/12
8 18/12 - 5 7/12
3 11/12
You are asking if the answer is 3 11/12. To verify this, let's break it down.
To subtract fractions, we need to have a common denominator. The common denominator for 2 and 12 is 12. Let's convert the mixed number 9 1/2 to an improper fraction:
9 1/2 = (2 * 9 + 1) / 2 = 19/2
Now, let's rewrite the subtraction using the common denominator of 12:
19/2 - 5 7/12
To subtract mixed numbers, we can convert the second mixed number to an improper fraction as well:
5 7/12 = (12 * 5 + 7) / 12 = 67/12
Now that both numbers are in improper fraction form, we can proceed with the subtraction:
19/2 - 67/12
To subtract the fractions, we need the same denominator, which is 12. So, we need to multiply the numerator and denominator of the first fraction by 6:
(19/2) * (6/6) - (67/12) = 114/12 - 67/12
Now that the two fractions have the same denominator, we can subtract the numerators:
114/12 - 67/12 = 47/12
Since 47/12 cannot be simplified any further, we leave it as an improper fraction. Therefore, the answer is indeed 3 11/12. Your friend's calculation is correct.
Now let's move on to the third problem:
-4 7/8 x 2/3
Your friend did the following steps:
-4 7/8 x 2/3
-4 14/24
-4 7/12
You are asking if the answer is -3 1/4. To verify this, let's break it down.
To multiply fractions, we can multiply the numerators and multiply the denominators. However, when dealing with mixed numbers, it's better to convert them to improper fractions first.
-4 7/8 = (-4 * 8 + 7) / 8 = -39/8
Now, let's rewrite the multiplication using the improper fraction:
-39/8 x 2/3
To multiply the fractions, we can multiply the numerators and denominators:
(-39/8) * (2/3) = (-39 * 2) / (8 * 3) = -78 / 24
Since -78/24 can be simplified, let's divide both the numerator and denominator by their greatest common divisor, which is 6:
-78/24 = (-78/6) / (24/6) = -13/4
Therefore, the answer is indeed -13/4 or -3 1/4. Your friend's calculation is correct.
Finally, let's move on to the fourth problem:
-3 1/5 ÷ -2/3
Your calculation:
-3 1/5 ÷ -2/3
-16/5 x -3/2
-8/5 x -3/1
-24/5
-4 4/5
You are asking if the answer is -4 4/5. To verify this, let's break it down.
To divide fractions, we can multiply by the reciprocal of the divisor.
-3 1/5 ÷ -2/3
The reciprocal of -2/3 is -3/2. Let's rewrite the division using the reciprocal:
(-3 1/5) * (-3/2)
To multiply the fractions, we can multiply the numerators and denominators:
(-16/5) * (-3/2) = (16 * 3) / (5 * 2) = 48/10
Since 48/10 can be simplified, let's divide both the numerator and denominator by their greatest common divisor, which is 2:
48/10 = (48/2) / (10/2) = 24/5
Therefore, the answer is indeed 24/5 or 4 4/5. Your calculation is correct.
In conclusion, your friend's calculations were correct for all four problems. Great work!