Year 7 - Task 2 Revision

A fraction represents a part of a whole.
It's written as two numbers separated by a slash or line, like this: 3/4.

-Numerator (top number): Shows how many parts we have.

-Denominator (bottom number): Shows how many equal parts the whole is divided into.

For example, 3/4 means we have 3 parts out of 4 equal parts.

Fractions

Proper, Improper and Mixed Fractions

We see three kinds of fractions, most common is our proper fraction where the numerator is smaller than the denominator, representing a portion of a whole. If we see an improper fraction, where the numerator is larger than the denominator, its best to convert this to a mixed numeral to show the how many whole numbers and remaining parts it has.

We compare fractions using the equals, less than, and greater than symbols. The aim is to express the difference in size, even when the fractions have different denominators.

Compare

Equivalent fractions are fractions that represent the same portion but have been divided into different quantities. An example is a 1/2 is the same or equal to 50/100.

​​Equivalent

Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1.
We achieve this by dividing them by their HCF.

Simplify

We can add and subtract fractions that have the same denominator, we keep the denominator and complete the operation across the numerators.
If they have different denominators, we first have to multiply each fraction by the opposite denominator to create two new equivalent fractions that have equal denominators, then we can complete the operation as normal.

Adding and Subtracting

Multiplying

Dividing

Multiplying fractions requires two steps:
1. multiply the two numerators
2.multiply the two denominators

This creates a new fraction and we then simplify this by dividing it by its highest common factors.

Dividing fractions uses three steps:
1. KEEP the first fraction
2.CHANGE the divide to a multiply
3.FLIP the second fraction

Once we have done this, we complete the multiplication like normal and simplify our answer.

Converting between mixed and improper fractions means changing how a number looks, but not its value. A mixed number has a whole number and a fraction (like 2½), while an improper fraction has a larger numerator than its denominator (like 5/2).

​

​Converting Improper and Mixed Fractions

By Eliza Lans

​This is when we show the multiplication of the base.
The base is multiplied by itself the number of times as determined by the power.

Index Notation

​Index notation is a way to show repeated multiplication using a superscript called an index, power or exponent. We also use this to show a number as a product of its prime factors.

​​Expanded Form

Numerical form is just the normal way we write numbers using digits and place value, like 2401.

​​Numerical Form

Factors are numbers that are multiplied together to get another number. We use factor pairs to list all the factors of composite numbers.
eg.
Factors of 12 = 1x12, 2x6, 3x4

​​Factors

Multiples of a number are the results of multiplying that number by whole numbers. They form a sequence that keeps increasing.

eg.
The multiples of 6 are 6, 12, 18, 24...

​​Multipes

​Primes are numbers greater than 1 that only have two factors, 1 and themselves.

eg.
Factors of 7 = 1 & 7

​​Primes

These are little tricks that help you know if a number can be divided evenly (with no remainder) by another number.
Think back to the lesson I made you write them all out!

The square root of a number is the number that, when multiplied by itself, gives the original number.

➤ Example: The square root of 49 is 7, because 7 × 7 = 49.
Which makes 49 a square number.

​​Square numbers and square roots

The cube root of a number is the number that, when multiplied by itself three times, gives the original number.

➤ Example: The cube root of 27 is 3, because 3 × 3 × 3 = 27
Which makes 27 a cube number.

​​Cube numbers and cube roots