Sums and Differences of Mixed Numbers

Introduction:

In this chapter, we will learn about rounding a mixed number to the nearest whole number, adding and subtracting mixed numbers.

Let us understand mixed numbers,

A mixed number is a combination of a whole number and a proper fraction represented together.  It generally represents a number between any two whole numbers.

Example 1:

Parts of a mixed number:

A mixed number is formed by combining three parts. They are,

1. A whole number
2. A numerator
3. A denominator

Using number line for rounding of the fractions

Example 1:

After the class pizza party, there were 1×5/6 cheese pizzas and 2×5/6 vegetarian pizzas left over. How many pizzas were left over in total after the party?

Solution:

Use a number line to round fractions and mixed numbers to the nearest whole number.

So, 1×5/6  + 2×5/6  = 2 + 3, or 5

5 pizzas were left over after the class party.

Addition by rounding the fractions

Example 1:

After the class pizza party, there were 1×5/6 cheese pizzas and 2×5/6 vegetarian pizzas left over. How many pizzas were left over in total after the party?

Solution:

Use a number line to round fractions and mixed numbers to the nearest whole number.

Round each fraction as per the benchmark.

1×5/6 is close to 2.

2×5/6 is close to 3.

So, 1×5/6   2×5/6 is about 2 + 3 = 5.

Example 2:

James has five cups of strawberries. He wants to use 1×3/4   cups of strawberries for a fruit salad and 3×1/2  cups for jam. Does James have enough strawberries to make both recipes? Solve this problem any way you choose.

Solution:

Round each fraction as per the benchmark.

1×3/4 is close to 2.

So, 1×3/4 + 3×1/2 is about 2 + 3×1/2 = 5×1/2.

The total cups of strawberries required to make both fruit salad and jam are 5×1/2.

Hence, James does not have enough strawberries to make both recipes.

Subtraction by rounding the fractions

Example 1:

Ron used 2×2/5 liters of paint from a tin of 5×7/8 liter. To color the walls of his room, what fraction of paint is still left in the tin?

Solution:

Round each fraction as per the benchmark.

5×7/8 is close to 6.

2×2/5 is close to 2.

So, 5×7/8 – 2×2/5 is about 6 – 2 = 4.

Exercise:

• Round the mixed numbers to their nearest whole numbers.

a. 2×3/4                 b. 1×5/7                 c. 2×3/10

•  Use the number line to round the mixed numbers to the nearest whole numbers.

a. 11×4/6               b. 11×2/8  

• Use the number line to round the mixed numbers to the nearest whole numbers.

a. 11×8/12             b. 11×4/10

• Estimate the sum.

a. 2×2/3 + 6×7/12                   b. 12×1/3 + 2×1/4

• Estimate the difference.

            a. 2×1/8 – 5/7                        b. 10×5/6 – 2×3/8      

• Estimate the sum.

            a. 2×1/3 + 3×3/4 + 6×1/9                       b. 12×1/3 + 2×2/3     

• Estimate the difference.

            a. 9×11/12 – 4×3/8 – 1×7/10                      b. 4×3/4 – 2×2/3

       

• A man pours 2×2/8 gallons of paint from a bucket into a tray. After he finishes pouring, there are 1×1/4 gallons of paint left in his bucket. How much paint did the man pour into the tray?
• Michelle ran for 1×1/5  h and then walked for 2×1/4 h. For how long did she travel?
• Ronald and Stephen race to see who can collect the most tennis balls on the ground. Ronald has collected 5×1/3 sets. Stephen has collected 4×3/4 sets. Who has collected more sets? How much more?

Concept map:

What have we learned:

• Understand parts of a mixed number.
• Use number line and round the fraction.
• Add and subtract by rounding the fractions