Basic Numeracy Skills
BASIC NUMERACY SKILLS – A REVISION
BODMAS
B Brackets first
O Orders (ie Powers and Square Roots, etc.)
DM Division and Multiplication (left-to-right)
AS Addition 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. 5048 17. 3972
18. 6262 19.9185
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
BODMAS
B Brackets first
O Orders (ie Powers and Square Roots, etc.)
DM Division and Multiplication (left-to-right)
AS Addition 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. 5048 17. 3972
18. 6262 19.9185
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