Fractions, Decimals & Percentages

ByMark Fothergill

&Alan Carroll

What are Fractions?

Fractions are proportions of Numbers. They are expressed as one proportion of another number.

Definition:

A number written with the bottom part (the Denominator) telling you how many parts the whole is divided into, and the top part (the Numerator) telling how many you have.

Maths in Fractions

Multiplying – easy

Multiply Top and Bottom Separately.

Dividing – easy

Turn the Second Fraction Upside Down and Multiply.

Maths in Fractions

Cancelling Down – easy

Divide the Top and Bottom by the same number until they will not divide any more.

Addition/Subtraction – tricky

i) Get the Bottom Lines the same (get a “common denominator”).

ii) Add or Subtract the Top Lines only!

Maths in FractionsFinding Fractions of Numbers – easy

1. Multiply the Initial Number by the Numerator of the Fraction.

2. Divide by the Denominator

Or,

1. Divide the Initial Number by the Denominator of the Fractions.

2. Multiply by the Numerator

Uses across the Curriculum

1. Algebra

2. Statistics – Pie Charts

Misconceptions

1. Mixing Addition/Subtraction with Multiplication.

2. Children find it difficult to put fractions into real life scenarios so can believe they are nothing to do with reality.

What are Decimals?A Decimal is similar to a Fraction in the way that it is not just a whole number. A Decimal can include tenths, hundredths or thousands of a whole number.

Maths in DecimalsAdding/Subtracting Decimals – easy

1. Line up the Decimals at the Decimal Point.

2. Add or Subtract like a ‘normal’ Calculation.

Multiplying by 10 – the basis for all Decimal Multiplication – easy

1. Move the Decimal point ONE place to the left.

…………….BUT WHY?

Maths in Decimals

Multiplying/Dividing Decimals - easy

1. Multiply the numbers as if they had no Decimal Point.

2. Find their place value and put the Decimal Point where it should be.

Uses across the Curriculum

1. Money

2. Time

3. Science

Misconceptions1. Multiplying Decimals by 10 – “Just put a 0 on the end”

2. 0.999’ is the same as 1. (higher achievers only)

2. In time 2.50 is not the same as Half Past Two

What are Percentages?Derived from Per – Cent (from 100)

A means of expressing a number as a fraction of 100.

(i.e. a portion expressed in hundredths)

An easy way to show comparisons of different numbers or fractions.

Maths in PercentagesConverting Decimals to Percentages – easy

Multiply the Decimal by 100.

Converting Fractions to Percentages – easy

1. Divide the Numerator by the Denominator (Converting to a Decimal)

2. Multiply by 100.

Or,

1. Multiply the Numerator by 100.

2. Divide by the Denominator.

Maths in PercentagesFinding Percentages Greater than 100% - easy

1. Find 1% by dividing by 100.

2. Multiply by the desired new percentage. (e.g. x125 for 125%)

Reverse Percentage Calculations – easy

1. Divide through by the Percentage number.

2. Multiply by 100 to get back to 100%.

Uses across the Curriculum1. Statistics.

2. Comparisons in Humanities.

Misconceptions1. Realising that Fractions and percentages are in fact equivalent and not a whole different set of numbers.

2. Mixing up certain fractions with percentages.

3. Increasing by a percentage then decreasing results in a change in the number.

Concept of Equivalence

Any Fraction, Decimal or Percentage can be expressed in any of the other two forms.

GameRules

1. Pick 2 Cards.

2. Decide whether they are Equivalent.

3. If you think they’re equivalent call “KEEP IT”

4. If you think they’re not equivalent call “BIN IT”

5. For each set of equivalent cards your team will score 1 point.

6. If a card is turned whose equivalent partners have already been ‘kept’ by a team, then it is possible for either team to call “STEAL IT”. This will gain your team 1 additional point.

7. The Team with the highest number of points will win the game.