UK K12 GCSE/A-Level: Year 4 KS2 Mathematics - Fractions, to Decimals Equivalence

Learning Objectives

By the end of this topic, students will be able to:

• Understand the concept of equivalence between fractions and decimals.
• Convert simple fractions to decimals and vice versa.
• Identify equivalent fractions and decimals.
• Apply the concept of equivalence to solve problems.

Core Concepts

Fractions and decimals are two ways to represent the same value. A fraction is a part of a whole, while a decimal is a way to show a part of a whole using a point. For example, the fraction 1/2 and the decimal 0.5 are equivalent because they both represent one half of a whole.

Equivalent Fractions

Equivalent fractions are fractions that have the same value, but with different numerators and denominators. For example, 1/2 and 2/4 are equivalent fractions because they both represent one half of a whole.

Converting Fractions to Decimals

To convert a fraction to a decimal, we divide the numerator by the denominator. For example, to convert 1/2 to a decimal, we divide 1 by 2, which gives us 0.5.

Converting Decimals to Fractions

To convert a decimal to a fraction, we can use the place value of the decimal to determine the numerator and denominator. For example, the decimal 0.5 can be converted to the fraction 1/2.

Worked Examples

Example 1

Convert the fraction 3/4 to a decimal.

To convert 3/4 to a decimal, we divide 3 by 4, which gives us 0.75.

Example 2

Convert the decimal 0.25 to a fraction.

To convert 0.25 to a fraction, we can use the place value of the decimal. Since 0.25 has one digit after the decimal point, we can write it as 25/100. We can simplify this fraction by dividing both the numerator and denominator by 25, which gives us 1/4.

Example 3

Identify equivalent fractions for 1/2.

Equivalent fractions for 1/2 are 2/4, 3/6, and 4/8.

Common Misconceptions

• Students may think that equivalent fractions have the same numerator and denominator, but this is not always true.
• Students may struggle to convert fractions to decimals, especially if the denominator is not a multiple of 10.
• Students may not understand that equivalent fractions have the same value, but different representations.

Exam Tips

• Make sure to read the question carefully and understand what is being asked.
• Use a calculator to convert fractions to decimals, but make sure to show your working.
• Identify equivalent fractions by finding common factors between the numerator and denominator.
• Use the place value of the decimal to convert it to a fraction.

MCQs with Explanations

MCQ 1 [F]

What is the decimal equivalent of the fraction 1/2? A) 0.25 B) 0.5 C) 0.75 D) 1.0

Correct answer: B) 0.5 Why the distractors fail: A) 0.25 is the decimal equivalent of 1/4, not 1/2. C) 0.75 is the decimal equivalent of 3/4, not 1/2. D) 1.0 is the decimal equivalent of 1/1, not 1/2.

MCQ 2 [H]

Identify equivalent fractions for 2/4. A) 1/2 B) 3/6 C) 4/8 D) 5/10

Correct answer: A) 1/2 Why the distractors fail: B) 3/6 is equivalent to 1/2, but it is not the only equivalent fraction. C) 4/8 is equivalent to 1/2, but it is not the only equivalent fraction. D) 5/10 is not equivalent to 2/4.

MCQ 3 [F]

What is the fraction equivalent of the decimal 0.5? A) 1/2 B) 2/4 C) 3/6 D) 4/8

Correct answer: A) 1/2 Why the distractors fail: B) 2/4 is equivalent to 1/2, but it is not the only equivalent fraction. C) 3/6 is equivalent to 1/2, but it is not the only equivalent fraction. D) 4/8 is equivalent to 1/2, but it is not the only equivalent fraction.

MCQ 4 [H]

Identify the equivalent fraction for 3/6. A) 1/2 B) 2/4 C) 4/8 D) 6/12

Correct answer: A) 1/2 Why the distractors fail: B) 2/4 is equivalent to 1/2, but it is not the only equivalent fraction. C) 4/8 is equivalent to 1/2, but it is not the only equivalent fraction. D) 6/12 is equivalent to 1/2, but it is not the only equivalent fraction.

MCQ 5 [F]

What is the decimal equivalent of the fraction 1/4? A) 0.25 B) 0.5 C) 0.75 D) 1.0

Correct answer: A) 0.25 Why the distractors fail: B) 0.5 is the decimal equivalent of 1/2, not 1/4. C) 0.75 is the decimal equivalent of 3/4, not 1/4. D) 1.0 is the decimal equivalent of 1/1, not 1/4.

Short-answer Questions

1. Convert the fraction 2/4 to a decimal.
2. Identify equivalent fractions for 3/6.
3. Convert the decimal 0.25 to a fraction.
4. Identify the equivalent fraction for 4/8.
5. What is the decimal equivalent of the fraction 1/4?