Mathematics Basic Operations and Concepts

Basic Operations

• Addition is combining two or more numbers to find their sum.
• Subtraction is finding the difference between two numbers.
• Multiplication is repeated addition of a number by itself.
• Division is splitting a number into equal parts.

Factors

• Factors are numbers that divide exactly into another number without leaving a remainder.
• Example: The factors of 12 are 1, 2, 3, 4, 6 and 12.

Lowest Common Multiple

• Lowest Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers.
• Example: The LCM of 4 and 6 is 12.

Highest Common Factor

• Highest Common Factor (HCF) is the largest number that is a factor of two or more numbers.
• Example: The HCF of 12 and 18 is 6.

Ordering Fractions

• Fractions can be ordered from smallest to largest by comparing their numerators and denominators.
• Example: To order 1/2, 1/4 and 3/4, first compare the denominators. 1/4 and 3/4 have the same denominator, so we compare their numerators. Hence, the order is 1/4, 1/2, 3/4.

Comparing Fractions

• Fractions can be compared by finding a common denominator or using cross-multiplication.
• Example: To compare 2/3 and 3/4, we can find a common denominator of 12: 2/3 = 8/12 and 3/4 = 9/12. Hence, 3/4 is greater than 2/3 because 9/12 is greater than 8/12.

Mean

• Mean is the average of a set of numbers.
• To find the mean, we add up all the numbers in the set and then divide by the number of numbers in the set.
• Example: If the scores are 5, 7, 8, and 10, the mean is (5 + 7 + 8 + 10) / 4 = 7.5.

Finding the Missing Number

• If we know the mean and three out of four scores, we can calculate the missing score.
• Example: If the mean is 7.5, and the scores are 5, 7, and 8, the missing score is (7.5 x 4) - 5 - 7 - 8 = 10.

Finding the Number of Scores

• If we know the total score and the mean, we can calculate the number of scores.
• Example: If the total score is 30 and the mean is 6, the number of scores is 30 / 6 = 5.