Converting Percentages, Decimals and Fractions, Summaries of Calculus

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Converting between Fractions, Decimals and Percentages

Lesson 4: Converting Percentages

and Decimals to Fractions

• To convert a percentage to a fraction.
• To be able to write a fraction in its simplest terms.
• To convert a decimal to a fraction. To develop an understanding of how to convert percentages and decimals to fractions.

Learning Objective

Success Criteria

Targeting Assessment Objective: A

To convert a percentage to a fraction in its simplest form, we firstly need to write it as a fraction of 100. We use 100 as our denominator because ‘per cent’ translates to ‘per 100’.

Converting Percentages to Fractions

Write 34% as a fraction in its simplest form

1. As our percentage is a whole number, we can write it as a fraction of 100:
2. However, our task is to write our answer in its simplest form. We can do this by finding the highest common factor of 34 and 100: The highest common factor of 34 and 100 is 2. 34 100 34 100

÷ 2

÷ 2

17 50 17 50

Things can be a little trickier if the percentage includes a decimal.

Converting Percentages to Fractions

Write 12.5% as a fraction in its simplest form

1. Start by writing the fraction out of 100.
2. We don’t use decimals in proper fractions so we need to ‘get rid’ of the decimal. The highest common factor of 125 and 1000 is 125. 12. 100 ÷ 125 ÷ 125 1 8 1 8

We can multiply 12.5 by 10 so we no longer have the decimal point. However, we must do the same to the denominator. × 10 × 10 125 1000

100

3. Like before, we must write our answer in its simplest form. We can do this by finding the highest common factor of 125 and 1000. 125 1000

F.D.P. Grid

Multiply by 100 Divide by 100 Divide numerator by denominator Divide numerator by denominator then multiply by 100 Place percentage over 100 (or 1000) and simplify

To convert a decimal to a fraction, we start by writing it out of 1.

Converting Decimals to Fractions

Write 0.15 as a fraction in its simplest form

1. Start by writing down the decimal as a ‘fraction’ of 1:
2. As we have two decimal places, we multiply both the numerator and the denominator by 100 (if there was just 1 digit after the decimal point, we would multiply it by 10 and if there were 3 digits, we would multiply by 1000). 0. 1 3 20

× 100

× 100

15 100

1

3. Like before, we must write our answer in its simplest form. We can do this by finding the highest common factor of 15 and 100. The highest common factor of 15 and 100 is 5. ÷ 5 ÷ 5 3 20 15 100 This is now a proper fraction.

Convert each percentage to a fraction. Write each answer in its simplest form.

Converting Decimals to Fractions

11 = 20 55 100 39 50

78 100 2 5

40 100 1 = 50 2 100 47 200

235 1000

F.D.P. Grid

Multiply by 100 Divide by 100 Divide numerator by denominator Divide numerator by denominator then multiply by 100 Place percentage over 100 (or 1000) and simplify Place fraction over 1, multiply by 10, 100 or 1000 and simplify

Pyramid Challenge

The pyramid challenge is designed to be completed in groups.

• The timer will be set; it is your challenge to complete as much of the pyramid, as a group, as possible. Accuracy and speed is key.
• Think about how you can divide the pyramid up into sections so you can complete it quicker.
• Remember: every member of your group must be doing something.

5 minutes… 5

STOP! GO!