O Level – Elementary Mathematics

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Laws of Arithmetic

1. Commutative law

a+b=b+a
ab = ba

2. Associative law
a+(b+c)=(a+b)+c
a(bc) = (ab)c

3. Distributive law
a(b + c)= ab + ac
a(b — c) = ab — ac

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2015 Schedule Elementary Math

S3 1.5 hrs WED 5.30pm – 7pm
S3 2 hrs FRI 3pm – 5pm
S4 1.5 hrs WED 7pm – 8.30pm
S4 2 hrs SUN 6pm – 8pm

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Fractions

1. Proper fractions: The numerator is smaller than the denominator. A proper fraction is part of a whole, so it is smaller than 1.

e.g. 3/5 and 5/7.

2. Improper fractions: The numerator is greater than or equal to the denominator. The fraction is greater than or equal to 1.

e.g. 5/3 7/7 and 13/5.

3. Mixed numbers: Numbers that contain a whole number part and a proper fraction part.

e.g. 1 1/3 and 6 2/5.

4. Equivalent fractions: Fractions having the same value but are in different form. When the numerator and denominator of a fraction are multiplied or divided by the same non¬zero number, we get an equivalent fraction.

e.g. 1/3 = 2/6 = 5/15

5. A fraction is in its lowest terms or simplest form when its numerator and denominator has no more common factor other than 1.

e.g. 1/5 is reduced to lowest terms but 2/10 not.

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Addition and Subtraction of Fractions

1. Add/subtract the whole numbers first.

2. Find the lowest common multiple (LCM) of the fractions and convert them into fractions with the same denominators before adding/subtracting the fractions.

Example 1
3/5 + 1/4
= 12/20 + 5/20 (LCM is 20)
= 17/20

Example 2
-3 1/2 – (-2 2/3)
= -3 1/2 + 2 2/3
= -1 -1/2 + 2/3 (LCM 6)
= -1 -3/6 + 4/6
= -1 + 1/6
= -5/6

Multiplication of Fractions

1. Convert all mixed numbers to improper fractions first.

2. Simplify the fractions first by ‘cancelling’, to see if anything will divide into any of the top numbers and also the bottom numbers.

3. Multiply the numerators, then the denominators together

Evaluate

a) 8/9 x 3/4

b) -1 2/5 x 2/3

c) 2 1/2 x 3 1/5

Ans

(a) 2/3 (b) – 14/15 (c) 8

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Multiplication of Fractions

1. Convert all mixed numbers to improper fractions first.

2. Simplify the fractions first by ‘cancelling’, to see if anything will divide into any of the top numbers and also the bottom numbers.

3. Multiply the numerators, then the denominators together.

Example

2 2/3 * 1 1/5
= 8/3 * 6/5
= 48/15
= 3 3/15

For Exam based questions with full worked solution. Please contact Mr Ong @98639633 or Angie @96790479

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Division of Fractions

1. Convert all mixed numbers to improper fractions first.

2. To divide two fractions, turn the second one upside down and then multiply

Example

3 1/3 divide 5/6
= 10/3 * 6/5
= 4

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Secondary 3 Year End Exams and Secondary 4 Prelim Preparatory Classes

for Elementary Math

Open for Registration Now!

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Question

(a) A shopkeeper bought a digital camera for $200. He then sold it at a profit of 35%.
What was the selling price?

(b) Mr Smith was able to buy the digital camera sold in (a), at a discount. If he paid y dollars for the camera, find, in terms of y, the percentage discount.

Solution

a) Selling price = (153/100) X 200 = $270

b) Percentage discount
= ((270 -y)/270) x 100%
= (2700 – 10y)/27 %

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Solve the pair of simultaneous equations
6x + 5y = 6
2 y – 3x = 15

Worked Solution

6x + 5y = 6 …… (1)
2 y -3x = 15 ⇒ 4 y – 6x = 30 …… (2)
(1) + (2): 9 y = 36
y = 4
Then (1): 6x + 5(4)= 6
6x = -14
x = -7/3

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