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FDP conversions
Moving fluently between fractions, decimals and percentages using a conversion grid.
Half a pizza, 0.5 of a pizza and 50% of a pizza are the same amount. Fractions, decimals and percentages are three ways of writing the same thing. In this lesson you will learn how to:
- see all three on a hundred square
- change a decimal into a percentage, and back again
- change a fraction into a decimal and a percentage, and back again
- fill in a conversion grid, and learn the facts by heart
- write one amount as a percentage of another, like a test score
- put fractions, decimals and percentages in order
1. Three ways to write the same amount
35 of the 100 squares are shaded. That is 35 hundredths: the fraction has 100 on the bottom, the decimal has 5 in the hundredths column, and the percentage is 35 out of 100.
Paint it, then read it three ways
- Tap a square: every square up to it is painted, a column at a time.
- Watch the fraction, the decimal and the percentage change as you paint.
2. Decimals and percentages
0.35 as a percentage
× 100 moves every digit two places to the left. 0.35 × 100 = 35, so 0.35 = 35%.
7% as a decimal
÷ 100 moves every digit two places to the right. Zeros fill the empty places: 7% = 0.07.
Slide the digits: × 100 or ÷ 100
- Step 1: pick × 100 or ÷ 100 and watch the digits slide. Step 2: read the answer.
- Two with no slips moves you up a level. Level 2 brings tricky zeros; level 3 brings numbers bigger than 1 and thousandths.
3. Fractions to decimals and percentages, and back
Example: 320 as a decimal and a percentage
20 × 5 = 100, so multiply the top by 5 too: 3 × 5 = 15, so it is 15 hundredths: 0.15, which is 15%.
When the bottom cannot make 100: divide
No whole number times 8 makes 100. So work out 3 ÷ 8 with short division (Lesson 2.3):
38 = 0.375, which is 37.5%.
Back to a fraction: 45%
45% is 45 out of 100. Then simplify (Lesson 3.1): 45 and 100 can both be divided by 5.
45% = 0.45 = 920 in its simplest form.
Make it out of 100
- Pick the button that turns the bottom number into 100, then read the percentage.
- Level 3 brings eighths (divide instead). Level 4 goes backwards: simplify until you cannot go further.
4. The conversion grid
Build new rows from the ones you know
15 = 20%, so 35 is 3 lots of 20% = 60% = 0.6.
18 = 12.5%, so 38 = 3 × 12.5% = 37.5%.
More than one whole
1 whole is 100%. So 114 = 100% + 25% = 125% = 1.25.
One to know: 13 = 0.333… (the 3s go on for ever), which is about 33%.
Fill the grid
- Tap an empty box with a ?, then pick what goes in it.
- A whole grid with no slips moves you up a level. Level 2 brings twentieths and twenty-fifths; level 3 brings eighths and amounts bigger than 1.
5. Make a set
Nine cards hide three sets. Each set is one amount written as a fraction, a decimal and a percentage. Tap three cards that are equal to make a set. Watch out for look-alikes such as 0.4 and 4%.
6. One amount as a percentage of another
Example: Ava scores 18 out of 25 in a spelling test. What percentage is that?
- Write it as a fraction:18 out of 25 = 1825
- What makes 25 into 100?25 × 4 = 100
- Do the same to the top:18 × 4 = 72
Simplify first: 12 out of 40
No whole number times 40 makes 100. Simplify first: 1240 = 310 (divide both by 4). Then 310 = 30100 = 30%.
7. Conversion workshop
Work it out step by step. Level 1 is out of 10, 50 and 100; level 2 is out of 20 and 25; level 3 simplifies first; level 4 turns percentages into fractions; level 5 brings bigger totals and percentage rises.
8. Putting them in order
Example: put 38, 0.4 and 35% in order, smallest first
As percentages they are 37.5%, 40% and 35%. So the order is 35%, 38, 0.4.
Line them up
Your order, smallest first:
- Tap the cards from smallest to largest.
- Stuck? Work out the percentages on rough paper, or tap Show as percentages.
9. Practice: pick your level
Start with Foundation if you are in Year 4 or just starting. Move up when you are getting most of them right.
The mistakes that cost marks
- Moving the digits only one place. Writing 0.5 as 5%. × 100 moves the digits two places: 0.5 = 50%.
- Losing the zero. Writing 7% as 0.7. 7 ÷ 100 = 0.07 (0.7 would be 70%).
- Writing the top and bottom side by side. Writing 34 as 0.34, or 15 as 15%. make the bottom 100: 34 = 75% and 15 = 20%.
- Not simplifying. Leaving 45% as 45100 when the question asks for the simplest form. divide the top and bottom by 5: 920.
- Forgetting to make it out of 100. Saying 18 out of 25 is 18%. 25 × 4 = 100, so 18 × 4 = 72: it is 72%.
- Comparing without changing the form. Saying 0.45 is bigger than 0.5 because 45 is bigger than 5. 0.45 = 45% and 0.5 = 50%, so 0.5 is bigger.
Quick checklist
Tick each one when you can do it without help.
All ticked. Brilliant work! You have finished Lesson 3.9 and the whole of Module 3.
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