Decomposing Fractions
Decompose 3/5
ex: 2/5 + 1/5
Add 4/8 + 2/8
6/8
1 3/8 + 1 2/8 =
2 5/8
8 6/8 - 3 3/8
5 3/8
Lena walked 2 1/4 miles in the morning and 1 2/4 miles in the afternoon.
How many miles did she walk altogether?
2 1/4 + 1 2/4 = 3 3/4 miles
Decompose 8/9
ex: 4/9 + 4/9
Subtract
7/9 - 2/9
5/9
3 1/6 + 5 4/6 =
8 5/6
6 2/3 - 5 1/3 =
1 1/3
A rope was 5 3/8 feet long. Sam cut off 2 1/8 feet.
How much rope is left?
5 3/8 − 2 1/8 = 3 2/8 = 3 1/4 feet
(Subtract fractions, then simplify.)
Decompose 1 2/3
ex 3/3 + 2/3
add 14/28 + 3/28
17/28
4 5/10 + 6 9/10 =
11 4/10
9 2/4 - 6 3/4 =
2 3/4
Mr. Chen used 3 3/6 cups of flour in the morning and 2 4/6 cups later.
How many cups of flour did he use in total?
3 3/6 + 2 4/6 = 5 7/6 = 6 1/6 cups
(Regroup because 7/6 > 1.)
Decompose 6/12 in two ways
ex 3/12 + 3/12 and 5/12 +1/12
Subtract and Simplify
9/10-3/10
6/10 simplifies to 3/5
3 1/2 + 2 1/2
6
6 3/4
A board was 7 2/5 feet long. A carpenter cut off 3 4/5 feet.
How long is the board now?
7 2/5 − 3 4/5
Borrow 1 whole:
7 2/5 → 6 7/5
6 7/5 − 3 4/5 = 3 3/5 feet
Decompose 1 2/5 in two ways
ex 1 + 2/5 and 1 + 1/5 + 1/5
Add and simplify
3/6+3/6
6/6 simplifies to 1
7 7/9 + 3 5/9=
11 3/9 or 11 1/3
7 - 3 1/3
3 2/3
Maria biked 4 3/10 miles on Saturday and 2 5/10 miles on Sunday.
Her weekly goal was 6 8/10 miles.
Did she reach her goal? If so, how many miles over did she go? If not, how many more miles does she need?
First add:
4 3/10 + 2 5/10 = 6 8/10 miles
Compare to goal:
6 8/10 − 6 8/10 = 0
👉 She reached her goal exactly.