Fraction notation

Whole The sum of all the parts. The whole equals 1 (unless otherwise stated).

Fraction A number of equal parts

Numerator The top part of a fraction. This counts how many parts we have.

Denominator The bottom part of a fraction. This counts the total number of parts in a whole.

Proper Fraction Numerator ≤ Denominator, e.g.

Adding Equal Parts Fractions with equal denominators can be added directly. E.g.

Improper Fraction Numerator > Denominator, e.g.

Integer A whole number

An integer written next to a fraction, for example: In mixed numbers the integer and Mixed Number fractional part are added together, so the total value is 1 +

Add & Subtract Fractions

Two fractions that have the same value, or count the same quantity, but use different Equivalent Fractions numerators and denominators. E.g.

Equivalent Fractions To find equivalent fractions, multiply the numerator and denominator by any integer.

Simplify a Fraction Divide the numerator and denominator by its highest common factor.

Unit Fraction A fraction where the numerator is 1, e.g.

Compare Unit Fractions The unit fraction with the largest denominator is the smallest.

Compare Fractions Make a common denominator first. The fraction with the largest denominator is bigger.

Add Fractions Make a common denominator using equivalent fractions. Then add numerators.

Common Choose the lowest common multiple of both denominators. Denominator (The first number in both times tables)

Subtract Fractions Make a common denominator. Then subtract numerators.

The negative of a fraction is the same as making either the numerator OR the Negative Fractions denominator negative (but not both).

www.MathsPad.co.uk Multiply & Divide fractions

The Whole is 1 means of 1 of Means multiply. Is the same as lots of Means multiply. 3 lots of is the same as

The whole is now 12. We must split the whole into 4 equal parts, and select 1.

It is the same as

This means . It is the same as and

Two methods depending on whether the whole (the integer) can be split evenly by the Fraction × Integer denominator of the fraction:

Method 1:

This means split the whole (12) into 4 equal parts, and select 3. i.e. 12 ÷ 4 × 3 = 9

Method 2: If the whole (4) cannot be evenly split by the denominator (5), multiply the

numerator and the integer. The denominator remains the same.

Multiply Fractions Multiply numerators and denominators directly. If common factors, cancel first.

Reciprocals Any pair of numbers that multiply to make 1

Reciprocal of a fraction Turn the fraction upside down. E.g. the reciprocal of is

Reciprocal of an Integer Is 1 divided by the integer. E.g. The reciprocal of 18 is

Dividing by a Fraction Instead, multiply by the reciprocal of the fraction.

Dividing by an Integer Instead, multiply the reciprocal of the integer.

Fractions & decimals

Fraction To Divide the numerator by the denominator using short division Decimal

The numerator goes inside the division symbol. Add a decimal point and zeroes to the numerator. Ask, how many times does the denominator go into the numerator? Short Division If none, carry the numerator over to the next decimal place. Write 0 at the top. If some, write the number are the top and carry the remainder over to the next decimal place.

Count the number of decimal places. Write the decimal number as your numerator and Decimal To the denominator will be 10, 100, 1000 etc depending on the number of decimal places Fraction in the question. E.g. 0.4587 = (4 decimal places = 4 zeroes)

www.MathsPad.co.uk Fractions, Decimals & Percentages

Percentage A fraction out of 100. Instead of the denominator, we write %

23% This means

Decimal To Multiply by 100 (e.g. 0.05 = 5%) Percentage

Percentage To Divide by 100. (e.g. 23% = 0.23) Decimal

Fraction To Find an equivalent fraction out of 100. The numerator is the percentage. Percentage Or, Divide the numerator by the denominator and multiply by 100.

Percentage To Write the percentage as the numerator. The denominator is 100. E.g. (23% = ) Fraction

Fracon Decimal Percentage Fracon Decimal Percentage

0.5 50%

0.1 10% 0.01 1%

0.2 20% 0.05 5%

0.25 25% 0.125 12.5%

1 100%

Percentages

Find the total number of people/objects. The total is usually the number that something Write as a % is ‘out of’ or a ‘percentage of’. Write a fraction with this total as the denominator. The numerator is the quantity required. Now convert to a percentage.

Calculate 10% Divide by 10

Calculate 1% Divide by 100

Calculate 85% Multiply by 85, divide by 100.

Calculate Multiply by 115, divide by 100. Alternatively, multiply by 115/100 = 1.15 115%

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