Basic Numeracy Skills

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BASIC NUMERACY SKILLS – A REVISION

BODMAS
BBrackets first
OOrders (ie Powers and Square Roots, etc.)
DMDivision and Multiplication (left-to-right)
ASAddition and Subtraction (left-to-right)

Do things in Brackets First.

[pic] |  |6 × (5 + 3) |= |6 × 8 |= |48 |  | |[pic] |  |6 × (5 + 3) |= |30 + 3 |= |33 |(wrong) | |Example:

(Powers, Roots) before Multiply, Divide, Add or Subtract.
[pic] |  |5 × 22 |= |5 × 4 |= |20 |  | |[pic] |  |5 × 22 |= |102 |= |100 |(wrong) | | | | | | | | | | |Example:

Multiply or Divide before you Add or Subtract.
[pic] |  |2 + 5 × 3 |= |2 + 15 |= |17 |  | |[pic] |  |2 + 5 × 3 |= |7 × 3 |= |21 |(wrong | |Example:

Otherwise just go left to right.
[pic] |  |30 ÷ 5 × 3 |= |6 × 3 |= |18 |  | |[pic] |  |30 ÷ 5 × 3 |= |30 ÷ 15 |= |2 |(wrong) | | | | | | | | | | |Example:

EXPONENTS AND RADICALS

Any number can be expressed in the form of [pic], where x is the base and n is the exponent. A number can also be expressed in the form of [pic]. This form is called the radical, n is the index, x is the radicand.

[pic]Example:[pic]

Negative Exponents
A negative exponent means how many times to divide by the number. ([pic]) [pic]

Exercise.

Perform the following operation according to BODMAS rule

1. [pic]8. [pic]
2.[pic]9. [pic]
3.[pic] 10. [pic]
4.[pic]
5.[pic]
6.[pic]
7. [pic]

Use the order of operations to simplify the expression.
11.[pic]12.[pic]
13. [pic]14.[pic]
15.[pic]

16. [pic]
17. [pic]

Round the following to the nearest ten, nearest hundred, and nearest thousand.

16. 504817. 3972
18. 626219.9185
20. 95,790

21. Evaluate the expression (1 + z) × 2 + 12 ÷ 3 - z when z = 4.

22. In a school, [pic] of the students travel to school by car, [pic] of them walk to school and the rest travel to school by bus. a. What fraction of the students travel by bus?
b. Are there more or fewer students who travel by bus than by car? c. If 480 students travel to school by car, how many travel by bus?

Simplifying Algebraic and exponential Expressions
Eg
Simplify i. [pic]
ii. [pic]
iii. [pic]

Solving Equations

Linear Equation
Eg. Solve for x :
i. [pic]
ii. [pic]

System of Linear Equations:
Eg.Solve the following systems of equations:
[pic]

Exercise

1.Simplify :
a. [pic]
b. [pic]
c. [pic]

d. [pic]
e. [pic]
f. [pic]

2. Make [pic] the subject of [pic].

3. If [pic], what is the value of z in terms of p, q, and r?

4. For all [pic], [pic]

5. Solve for x :

a. [pic]b. [pic]

c.[pic]d. [pic]

e. [pic]f. [pic]

g. [pic]h. [pic]

i.[pic]k. [pic]

j. [pic]

6. If [pic], then g = (give your answers to 3 decimal places).

7. Solve for x and y :

a. [pic]b. [pic]

c. [pic]d. [pic]

Solving equations.
Equations from problems.

Solve each quadratic equation
1. [pic]2. [pic]
3. [pic]4. [pic]
5.[pic] 6. [pic]

7. The length of a football field is 200 feet more than the width. If the perimeter of the field is 1040 feet, what are its dimension.

8. When five times a number is decreased by 4, the result is 26. What is the number?

9. When 60% of a number is added to the number, the result is 192. What is the number?

10. One number exceeds another by 26. The sum of the numbers is 64. What are the numbers?

Percentage
1. After a 20% reduction, you purchase a television for $336. What was the television’s price before the reduction? 2. After a 30% reduction, you purchase a dictionary for $30.80. What was the dictionary’s price before the reduction? 3. If there is a 45% increase in the salary of John who is currently earning RM1500, what would be the new salary? 4. If a 12.5%...
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