109r. Equivalent Fractions and Simplifying Fractions

Learning Intentions

• To understand what equivalent fractions are
• To understand that fractions have a numerical value, and two distinct fractions, like and , can have the same numerical value
• Simplify fractions

Pre-requisite Summary

• Know that a fraction represents part of a whole or part of a collection
• Understand that the numerator tells how many parts are being considered
• Understand that the denominator tells how many equal parts the whole is divided into
• Be able to Recognise basic fractions such as and
• Recall multiplication facts and division facts
• Know that factors are numbers that divide exactly into another number

Worked Examples

Worked Example 1

State whether each pair of fractions is equivalent:

a) and

b) and

c) and

Worked Example 2

Solve an equivalent fraction for each:

a)

b)

c)

Worked Example 3

Simplify each fraction:

a)

b)

c)

Worked Example 4

Simplify each fraction fully:

a)

b)

c)

Worked Example 5

Use equivalent fractions to compare:

a) and

b) and

c) and

Worked Example 6

Write each fraction in simplest form:

a)

b)

c)

Problems

Problem 1

State whether each pair of fractions is equivalent:

a) and

b) and

c) and

Problem 2

Find an equivalent fraction for each:

a)

b)

c)

Problem 3

Simplify each fraction:

a)

b)

c)

Problem 4

Simplify each fraction fully:

a)

b)

c)

Problem 5

Use equivalent fractions to compare:

a) and

b) and

c) and

Problem 6

Write each fraction in simplest form:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

State whether each pair of fractions is equivalent:

a) and

b) and

c) and

d) and

Exercise 2.

Find an equivalent fraction for each:

a)

b)

c)

d)

Exercise 3.

Complete each statement with an equivalent fraction:

a)

b)

c)

d)

Exercise 4.

Simplify each fraction:

a)

b)

c)

d)

Exercise 5.

Simplify each fraction fully:

a)

b)

c)

d)

Exercise 6.

Write each fraction in simplest form:

a)

b)

c)

d)

Exercise 7.

Use equivalent fractions to decide whether each statement is true or false:

a)

b)

c)

d)

Exercise 8.

Fill in the missing number:

a)

b)

c)

d)

Reasoning

Exercise 9.

Explain why and have the same numerical value.

Exercise 10.

A student says that and are different because the numbers in the numerator and denominator are different. Explain the mistake.

Exercise 11.

Noah says that to simplify a fraction, you can subtract the same number from the numerator and denominator. Is he correct? Explain.

Exercise 12.

Explain why and are equivalent.

Exercise 13.

A student simplifies to and says the fraction is fully simplified. Describe the error.

Problem-solving

Exercise 14.

A recipe uses of a cup of milk. Another recipe uses of a cup of milk. Do they use the same amount? Explain.

Exercise 15.

A class shaded of a shape. Write this fraction in simplest form.

Exercise 16.

A student writes two fractions, and . Show whether they represent the same amount.

Exercise 17.

A packet is full. Write this in simplest form and explain what it means.

Exercise 18.

Liam says that is equivalent to . Show how to Check whether he is correct.

Exercise 19.

Write three different fractions that are all equivalent to .

Potential Misunderstandings

• Students may think fractions are only equivalent if the numerator and denominator are exactly the same
• Students may focus on the appearance of the numbers rather than the numerical value of the fraction
• Students may think equivalent fractions must have the same denominator
• Students may forget that to make an equivalent fraction, the numerator and denominator must both be multiplied or divided by the same non-zero number
• Students may try to add or subtract the same number to the numerator and denominator to make equivalent fractions
• Students may simplify only one part of the fraction instead of both parts
• Students may stop simplifying before the fraction is in simplest form
• Students may confuse simplifying a fraction with changing its value
• Students may not recognise that a simplified fraction and the original fraction represent the same amount

Next: 110r. Operations with Fractions and Mixed Numerals