Adding & Subtracting Fractions & Mixed Numbers: Word Problems Quiz

Albert has managed to trim some of his cat’s claws. On the left paw, he trimmed 15 of its claws, and on the right paw, he trimmed 25.

What fraction of the cat’s two paws was he able to trim in total?

3/5

Step 1: Interpret the problem.
The problem wants us to do:

1/5+2/5

Step 2: Add the fractions.
Since the denominators are the same, we can directly add the numerators of these fractions. Just retain the denominator.

1/5+2/5=1+2/5=3/5

Albert was able to trim3/5of his cat’s two paws. 

Baron is cooking two dishes. Dish A needs 3 1/3tablespoons of liquid seasoning, while Dish B only needs 1/4 tablespoon of the same liquid seasoning.

Calculate the total amount of liquid seasoning required to cook these two dishes.

3 7/12 tablespoons

Step 1: Interpret the problem.
The problem wants us to do:

3 1/3+1/4

One way to solve this is to add the whole numbers separately and then add the fractions separately as well. However, we can only do that right away if the denominators are the same.

So first, we should find their LCM.

 

Step 2: Find the LCM to make equivalent mixed numbers and fractions.
List some multiples of the denominators:

Multiples of 3: 3, 6, 9, 12, …
Multiples of 4: 4, 8, 12, …

In this pair of numbers, the LCM is 12 (as emphasized).

3 1/3=3 1×4 4×4=3 4/12

1/4= 1×3 4×3=3/12

 

Step 3: Establish the mixed number.

Sum of Whole Numbers: 3+0=3

Sum of Fractions: 4/12+3/12=7/12

The sum of whole numbers and fractions =3+7/12

To write this as a mixed number, simply drop the + sign: 3 7/12

 

Step 4: Simplify the resulting mixed number if possible.
7 is a prime number and is not a factor of 12, so the mixed number is already in its simplest form.

Therefore, the total amount of liquid seasoning required is 3 7/12 tablespoons.

Cole drank 812 glasses of water yesterday, while Diana drank 538 glasses.

Determine the total amount of water they drank yesterday.

13 7/8 glasses

Step 1: Interpret the problem.
The problem wants us to do: 8 1/2+5 3/ 8

One way to solve this is to add the whole numbers separately and then add the fractions separately as well. However, we can only do that right away if the denominators are the same.

So first, we should find their LCM. 

Step 2: Find the LCM to make equivalent mixed numbers.
List some multiples of the denominators:

Multiples of 2: 2, 4, 6, 8, …
Multiples of 8: 8, 16, 24, …

In this pair of numbers, the LCM is 8 (as emphasized).

8 1/2=8 1×4 2×4=8 4/ 8

5 3/8stays the same as the denominator is already 8. 

Step 3: Establish the mixed number.

Sum of Whole Numbers: 8+5=13

Sum of Fractions: 4/8+3/8=7/8

The sum of whole numbers and fractions =13+7/8

To write this as a mixed number, simply drop the + sign: 13 7/8

Step 4: Simplify the resulting mixed number if possible.
7 is a prime number and is not a factor of 8, so the mixed number is already in its simplest form.

Therefore, Cole and Diana drank a total of 13 7/8 glasses of water yesterday. 

Enid was able to summarize a math lesson into a 56 of a page of paper. George copied Enid’s work, however, because his handwriting is larger, it filled up 145pages of paper.

Calculate the mixed number that describes the total number of pages of paper they used.

2 19/30 pages

Step 1: Interpret the problem.
The problem wants us to do: 5/6+1 4/5

One way to solve this is to add the whole numbers separately and then add the fractions separately as well. However, we can only do that right away if the denominators are the same.

So first, we should find their LCM.

 Step 2: Find the LCM to make equivalent mixed numbers and fractions.
List some multiples of the denominators:

Multiples of 6: 6, 12, 18, 24, 30, …
Multiples of 5: 5, 10, 15, 20, 25, 30, …

In this pair of numbers, the LCM is 30 (as emphasized).

5/6=5×5 6×5=25/30

1 4/5=4×6 5×6=24/30

 Step 3: Establish the mixed number. Perform regrouping if necessary.

Sum of Whole Numbers: 0+1=1

Sum of Fractions: 25/30+24/30=49/30

Now that the sum of fractions is an improper fraction, we can express this as yet another mixed number.

49/30=30/30+19/30=1+19/30

Establish the mixed number =1+(1+19/30)=2+19/30

To write this as a mixed number, simply drop the + sign: 2 19/30

Step 4: Simplify the resulting mixed number if possible.
19 is a prime number and is not a factor of 30, so the mixed number is already in its simplest form.

The total amount of paper they used is 2 19/30.