🌱 Sprout · Printable packMATHEMATICS · YEAR 6

Fractions, decimals and percentages

Name Date
🎯 What you'll learn - tick each one off!
📖 Learn

One Amount, Three Forms

A fraction, a decimal and a percentage can all describe exactly the same amount, just written in a different way. Knowing how to swap between the three forms is one of the most useful skills in maths, from reading a sale sign in a shop to understanding a test result or a weather forecast.

To change a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). To change a decimal to a percentage, multiply by 100, since "percentage" simply means "out of 100". To go the other way, from a percentage back to a fraction, write the percentage over 100 and simplify if you can. Fraction, decimal and percentage are just three different ways of writing the exact same amount.

3/4 as a decimal: 3 ÷ 4 = 0.75

0.75 as a percentage: 0.75 × 100 = 75%

So 3/4 = 0.75 = 75%

"Percent" means "per hundred", so 100% is a whole one, 50% is one half and 1% is one hundredth.
fractiondecimalpercentageequivalent
✏️ Activity 1

Complete the Conversion Table

Complete the missing fraction, decimal or percentage in each row of the table. Use what you learnt about converting between the three forms.

RowFractionDecimalPercentage
11/2
20.25
310%
43/5
50.75
620%
📖 Learn

Finding Percentages of Amounts

Finding a percentage of an amount means working out that fraction of a quantity, such as money, a length or a group of people. You use this in real life to work out a sale discount, a tip, or how many students in a class chose a particular answer. The easiest way to start is by finding 10% of the amount, because 10% is always the amount divided by 10, which is the same as moving the decimal point one place to the left.

Once you know 10%, you can build up to almost any percentage. For 20%, double the 10% amount. For 5%, halve the 10% amount. For 1%, divide the whole amount by 100. For 50%, simply halve the whole amount. Once you have these "friendly" percentages worked out, add or multiply them together to find trickier percentages, like 30% or 45%.

Find 30% of $40.

Step 1: find 10% of $40 by dividing by 10. 10% of $40 = $4.

Step 2: 30% is 3 lots of 10%, so multiply. 3 × $4 = $12.

So 30% of $40 = $12.

Check your answer makes sense: since 30% is less than half, the answer should be less than half of $40, which is $20. $12 is less than $20, so it checks out.
percentage of an amount10% methodmultiply
✏️ Activity 2

Shade the Hundredths Grids

Shade each hundredths grid to match the percentage given. Each grid has 100 small squares, so every square is worth 1%.

  1. Shade 8%.
  2. Shade 30%.
  3. Shade 45%.
  4. Shade 55%.
✏️ Activity 3

Order and Compare

Look carefully at each question below. You may convert the numbers to a common form on scrap paper before you answer.

Write these six numbers in order from smallest to largest: 3/10, 45%, 0.6, 1/4, 80%, 0.05

Decide if each statement is true or false.

  1. 0.5 is the same as 50%.
  2. 3/4 is greater than 60%.
  3. 0.2 is less than 1/8.
  4. 90% is the same as 9/10.

Which of these numbers is the largest?

  1. 1/3
  2. 30%
  3. 0.35
  4. 3/8
✏️ Activity 4

Percentages in Everyday Problems

Solve each problem. Show your working in the space given, and write full sentence answers for the word problems.

  1. Find 40% of $65.
  2. Find 15% of $80.
  3. A $120 jacket is reduced by 25% in a sale. How much money is saved, and what is the new sale price?
  4. Chloe scored 34 out of 40 on a maths test. What percentage did she get?
  5. Find 65% of $200 using two different strategies, for example the 10% method and halving. Show both methods.

🔑 Answer sheet

For the parent or supervisor: set this page aside before handing over the worksheet.

Activity 1

  1. Row 1: 1/2 = 0.5 = 50%
  2. Row 2: 1/4 = 0.25 = 25%
  3. Row 3: 1/10 = 0.1 = 10%
  4. Row 4: 3/5 = 0.6 = 60%
  5. Row 5: 3/4 = 0.75 = 75%
  6. Row 6: 1/5 = 0.2 = 20%

Activity 2

  1. 8 squares shaded (8%).
  2. 30 squares shaded (30%).
  3. 45 squares shaded (45%).
  4. 55 squares shaded (55%).

Activity 3

  1. Smallest to largest: 0.05, 1/4, 3/10, 45%, 0.6, 80% (as decimals: 0.05, 0.25, 0.3, 0.45, 0.6, 0.8)
  2. True: 0.5 = 50%.
  3. True: 3/4 = 75%, which is greater than 60%.
  4. False: 0.2 = 20%, which is greater than 1/8 (12.5%), not less than it.
  5. True: 90% = 9/10.
  6. D) 3/8: 3/8 = 0.375, which is greater than 1/3 (about 0.33), 30% (0.3) and 0.35.

Activity 4

  1. $26 (10% of $65 = $6.50, so 40% = 4 × $6.50 = $26).
  2. $12 (10% of $80 = $8, 5% = $4, so 15% = $8 + $4 = $12).
  3. $30 is saved and the new price is $90 (25% of $120 = $30; $120 - $30 = $90).
  4. 85% (34/40 = 0.85 = 85%).
  5. Model answer: 65% of $200 = $130. Accept any correct method that reaches $130, for example 50% + 10% + 5% = $100 + $20 + $10 = $130, or 10% ($20) × 6.5 = $130.

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