026. Subtracting Fractions and Mixed Numerals

Learning Intentions

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

Pre-requisite Summary

• Understand that the denominator tells the size of the equal parts
• Understand that fractions can only be subtracted 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
• Understand regrouping when subtracting whole numbers and mixed numerals

Worked Examples

Worked Example 1

a) Explain why can be subtracted directly.

b) Find .

c) Explain why cannot be subtracted directly.

Worked Example 2

Subtract by Use the lowest common denominator:

a)

b)

Worked Example 3

Subtract by using the lowest common denominator:

a)

b)

Worked Example 4

Subtract two mixed numerals:

a)

b)

Worked Example 5

Subtract two mixed numerals:

a)

b)

Worked Example 6

a) Subtract .

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 subtracted directly.

b) Find .

c) Explain why cannot be subtracted directly.

Problem 2

Subtract by using the lowest common denominator:

a)

b)

Problem 3

Subtract by using the lowest common denominator:

a)

b)

Problem 4

Subtract two mixed numerals:

a)

b)

Problem 5

Subtract two mixed numerals:

a)

b)

Problem 6

a) Subtract .

b) Write the answer in simplest form.

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

Exercises

Understanding and Fluency

Exercise 1.

Subtract fractions with the same denominator:

a)

b)

c)

Exercise 2.

State the lowest common denominator and then subtract:

a)

b)

c)

Exercise 3.

Subtract by using the lowest common denominator:

a)

b)

c)

Exercise 4.

Subtract by using the lowest common denominator:

a)

b)

c)

Exercise 5.

Subtract two mixed numerals:

a)

b)

c)

Exercise 6.

Subtract two mixed numerals:

a)

b)

c)

Exercise 7.

Subtract and simplify where needed:

a)

b)

c)

Exercise 8.

Subtract 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 subtracted.

Exercise 10.

A student says . Explain the mistake.

Exercise 11.

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

Exercise 12.

A student finds . Explain why this is incorrect.

Problem-solving

Exercise 13.

Mia used m of ribbon from a piece that was m long. How much ribbon is left?

Exercise 14.

A tank contained L of water. L was poured out. How much water remains?

Exercise 15.

A rope is m long. A piece of m is cut off. What length remains?

Exercise 16.

A container held kg of rice. kg was used. How much rice remains?

Exercise 17.

A student completed of a task and still had left to revise. How much more had been completed than remained?

Exercise 18.

A ribbon piece of m is shortened by m. What is the new length?

Potential Misunderstandings

• Students may think numerators and denominators can both be subtracted 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 subtract the denominator after converting to equivalent fractions
• Students may Use a common denominator correctly but fail to simplify the final answer
• Students may subtract 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 being subtracted is larger than the fractional part in the starting mixed numeral

Next: 027. Multiplying Fractions, Mixed Numerals and Whole Numbers