It has been noted that a few illustrations/diagrams have been partially cut off as a result of the teacher video being embedded. We have reproduced these diagrams in this document (3 pages) for you to read alongside the course video if you so wish.

FRACTIONS

Fractions are parts of a WHOLE and written as [X/Y] where the top number is the part (numerator) and the bottom number is the number of parts it's divided by (denominator) e.g. think about a pizza.

There are different types:

Proper – top number is small than the bottom.

Improper – top number is bigger than the bottom.

Mixed number – whole number and then a proper fraction next to it.

Well go over the following at a high level using the 2 fractions (the video will show you how it's done):

[6/12] and [2/8]

• Simplifying – look at factors.
• Converting to same denominator – look at multiples.
• Adding – same denominator, keep denominator and add top numbers.
• Subtracting – same denominator, keep denominator and minus the top numbers.
• Multiplying – multiply across both top and bottom.
• Dividing – swap the denominator and numerator around for one of the fractions and then multiply.
• Comparing – same denominator and compare the top numbers.

PERCENTAGES AND DECIMALS

Decimals and percentages are the same as FRACTIONS but they're expressed in different ways.

Percentages are expressed as fractions out of 100. Think about the % as a 1 and 2 zeros.

What percentages are: 1/100, 2/100, 10/100, 20/100, 17/100, 83/100

Let's look at decimals now… if it's a fraction, why do we need this? It's just a different form of expression. What is the most commonly seen decimal?

• How do you convert fractions to decimal? Divide the top number by the bottom number. E.g. 10/20
• To convert a decimal to a fraction, use the place value of numbers in the decimal. Remember decimals go up by 10ths.

COMMON PERCENTAGES, FRACTIONS AND DECIMALS

DECIMAL MOVEMENT

• The short cuts for multiplication

  • If additional zeros added on
  • If nothing else changes, decimal point on answer moves right by the number of zeros that were added.
  • g. 10 x 1.1 = 11  100 x 1.1 = 110 (point moved one unit right due to extra zero, every time it moves right it will add a zero unless there is already a number there e.g. 10 x 0.123 = 1.23  100 x 0.123 = 12.3 )
  • If zeros taken off
  • If nothing else changes, decimal point on answer moves left by the number of zeros that were added.
  • g. 100 x 1.1 = 110  10 x 1.1 = 11 (point moved one unit left due to zero taken away)

• The short cuts for division (demonstration PQ1)

  • Move decimal to the left if the 'number being divided' is reduced and/or if the 'number dividing by' increases and Move decimal to the right if the 'number being divided' is increased and/or if the 'number dividing by' decreases

• Tips and Tricks

  • A seemingly whole number is really a number with a decimal point at the end with zeros
  • g. 145 = 145.000000 = 145.000 = 145.0
  • This is the reason why if moving a decimal point to the right/left and there is no existing number, we add a zero to it because there are already existing 'zero' numbers

Let's now go through some illustrated examples below.

If 20 ÷ 2.50 = 80, then 20 ÷ 250 = ?

(A) 800 (B) 8 (C) 0.8 (D) 0.08

Paloma made 2000ml of lemonade by mixing 750ml of lemon juice with 250ml of syrup with the remainder being water. What fraction of the lemonade was just water?

(A) 3/4 (B) 4/4 (C) 3/8 (D) 4/8

Q 31 - Solve for x

[(x-7)/6] + [1/2] = [8/6]

A X = 12 B X = 1/3 C X = 1 1/3 D X = 5/6 E 8

Q19 - Questions 19 to 21 refer to the following information:

This multiplication table shows that, for example 50 x 0.5 = 25

Using the number pattern shown in the table

0.5 x 0.5= ?

A 2.5 B 25 C 0.25 D 250

Q 20 - From the information given in the table.

0.025 ÷ 0.5 = ?

A 0.5 B 2.5 C 250 D 0.05

Q 21 - From the information given in the table

500 x 0.5 = ?

A 250 B 25 C 25 D 500

If 0.4 x 0.6 = 0.24, what is 40 x 0.06 = ?

(A) 0.0024 (B) 0.024 (C) 2.4 (D) 24

Key Rules to remember:

• Fractions, Decimals and Percentages are the same thing expressed differently.
• Know how to add, subtract, multiply, divide and convert.
• Follow the short cuts with decimal points.

Now it's time to do your assignment.

1. Download the assignment question here.
2. Print it out or if you want to do it electronically, save it.
3. Complete the questions to it.
4. Then check the solutions on the video below or download the ANSWER KEY here.