Please help with these maths questions

1) From a ribbon of lenghth 2 2/7m, I used 4/7m to wrap a box and 1 5/7m to tie a bow. How many metres of ribbon did I used?

2) Sammy's water tank contained 7 2/5 L of water in the morning. By the end of the day, there was 1 4/5 left. How many Litres of water was used?

3) Yesterday, James swam for 2 2/3h and studied for 1 2/3h. Today, he studied 3 1/3h and did not swim. How many more hours did he study today than yesterday?

Thank you

we will be happy to check your work for you.

My answers for the above questions are

1) 0

2) 5 3/5

3) 1 2/3

1) To find the total amount of ribbon used, you need to add the length used to wrap the box and the length used to tie the bow.

Given:
Length of ribbon = 2 2/7m
Length used to wrap the box = 4/7m
Length used to tie a bow = 1 5/7m

To add the lengths, you need to make sure the denominators are the same.

First, convert the mixed numbers to improper fractions:
2 2/7 = (7 * 2 + 2) / 7 = 16/7
1 5/7 = (7 * 1 + 5) / 7 = 12/7

Now, add the lengths used:
Total length used = (4/7) + (12/7) = 16/7 + 12/7 = 28/7

Since the denominator is 7, you can simplify the fraction:
28/7 = 4

Therefore, you used 4 meters of ribbon in total.

2) To find the amount of water used, you need to subtract the amount of water left from the initial amount.

Given:
Initial amount of water = 7 2/5 L
Amount of water left = 1 4/5 L

To subtract the amounts, you need to make sure the denominators are the same.

Convert the mixed numbers to improper fractions:
7 2/5 = (5 * 7 + 2) / 5 = 37/5
1 4/5 = (5 * 1 + 4) / 5 = 9/5

Now, subtract the amounts:
Water used = (37/5) - (9/5) = 37/5 - 9/5 = 28/5

Since the denominator is 5, you can simplify the fraction:
28/5 = 5 3/5

Therefore, 5 3/5 L of water was used.

3) To find the difference in hours James studied today compared to yesterday, you need to subtract the time he studied yesterday from the time he studied today.

Given:
Time James swam yesterday = 2 2/3h
Time James studied yesterday = 1 2/3h
Time James studied today = 3 1/3h

To subtract the times, you need to make sure the denominators are the same.

Convert the mixed numbers to improper fractions:
2 2/3 = (3 * 2 + 2) / 3 = 8/3
1 2/3 = (3 * 1 + 2) / 3 = 5/3
3 1/3 = (3 * 3 + 1) / 3 = 10/3

Now, subtract the times:
Difference in study time = (10/3) - (5/3) = 10/3 - 5/3 = 5/3

Since the denominator is 3, you can't simplify the fraction further.

Therefore, James studied 5/3 hours more today than yesterday.