025. Adding Fractions and Mixed Numerals

Learning Intentions

• To understand that adding fractions requires a common denominator
• add two fractions by considering their lowest common denominator
• add two mixed numerals

Pre-requisite Summary

• Understand that the denominator tells the number of equal parts in the whole
• Understand that fractions can only be combined directly when the parts are the same size
• Be able to Solve equivalent fractions
• Be able to find the lowest common multiple of two denominators
• Be able to convert between improper fractions and mixed numerals
• Be able to Simplify fractions where appropriate

Worked Examples

Worked Example 1

a) Explain why can be added directly.

b) Find .

c) Explain why cannot be added directly.

Worked Example 2

Add by Use the lowest common denominator:

a)

b)

Worked Example 3

Add by using the lowest common denominator:

a)

b)

Worked Example 4

Add two mixed numerals:

a)

b)

Worked Example 5

Add two mixed numerals:

a)

b)

Worked Example 6

a) Add .

b) Write the answer in simplest form.

c) Explain whether converting to improper fractions first would also work.

Problems

Problem 1

a) Explain why can be added directly.

b) Find .

c) Explain why cannot be added directly.

Problem 2

Add by using the lowest common denominator:

a)

b)

Problem 3

Add by using the lowest common denominator:

a)

b)

Problem 4

Add two mixed numerals:

a)

b)

Problem 5

Add two mixed numerals:

a)

b)

Problem 6

a) Add .

b) Write the answer in simplest form.

c) Explain whether converting to improper fractions first would also work.

Exercises

Understanding and Fluency

Exercise 1.

Add fractions with the same denominator:

a)

b)

c)

Exercise 2.

State the lowest common denominator and then add:

a)

b)

c)

Exercise 3.

Add by using the lowest common denominator:

a)

b)

c)

Exercise 4.

Add by using the lowest common denominator:

a)

b)

c)

Exercise 5.

Add two mixed numerals:

a)

b)

c)

Exercise 6.

Add two mixed numerals:

a)

b)

c)

Exercise 7.

Add and simplify where needed:

a)

b)

c)

Exercise 8.

Add and write the answer in simplest form:

a)

b)

c)

Reasoning

Exercise 9.

Explain why fractions must have a common denominator before they can be added.

Exercise 10.

A student says . Explain the mistake.

Exercise 11.

Explain why the denominator usually stays the same after adding fractions with a common denominator.

Exercise 12.

A student finds . Explain why this is incorrect.

Problem-solving

Exercise 13.

Mia walked km in the morning and km in the afternoon. How far did she walk altogether?

Exercise 14.

A recipe uses cup of milk and cup of cream. How much liquid is used altogether?

Exercise 15.

A rope is m long and another rope is m long. What is their total length?

Exercise 16.

A tank is filled by L from one jug and L from another jug. How much water is added altogether?

Exercise 17.

A student completed of a task on Monday and on Tuesday. What fraction of the task was completed altogether?

Exercise 18.

A ribbon piece of m is joined to a piece of m. What is the total length?

Potential Misunderstandings

• Students may think numerators and denominators can both be added directly
• Students may not Recognise that denominators represent the size of the parts
• Students may Choose a common denominator that is not a common multiple
• Students may find a common denominator but forget to rename the numerators
• Students may Use a common denominator correctly but fail to simplify the final answer
• Students may add the whole-number parts and fractional parts of mixed numerals without first finding a common denominator for the fractions
• Students may convert mixed numerals to improper fractions incorrectly
• Students may forget to regroup when the fractional part of a mixed numeral sum is greater than

Next: 026. Subtracting Fractions and Mixed Numerals