Fractions

Mixed numbers and improper fractions

1. 2 and 1 over 2 is an example of a mixed number. 2. This is when whole numbers and fractions are written together. 3. The same fraction can also be shown as an improper fraction, 5 over 2. 4. This is worth the same amount as the mixed number, but does not separate between whole numbers and parts. 5. Improper fractions have numerators which are bigger than the denominators. 6. Improper fractions are sometimes called top-heavy fractions.

Unitary method - fractions of amounts

1. A unitary method simply means finding out what one of something is worth first. 2. Example 3. Find 3 over 4 of 16. - First work out 1 over 4 of 16, then multiply the answer by 3 to get 3 over 4. - 1 over 4 of 16 is the same as 16 \ 4 which is 4. - If 1 over 4 of 16 = 4, then 3 over 4 of 16 must be three times this amount, so 3 over 4 of 16 = 12 ( 4 x 3 = 12).

Converting fractions to decimals and then ordering

1. Another method for ordering fractions is to convert fractions to decimals. 2. always write the final answer as the fractions appeared in the question.

Working out equivalent fractions

1. Equivalent fractions are made by multiplying or dividing the denominator and numerator of the fraction by the same number. 2. For example, to find fractions that are equivalent to 1 over 3, multiply the numerator and denominator by the same number, or the multiplier 3. Multiplying or dividing both parts of a fraction by the same number will always create equivalent fractions. 4. There are an infinite amount of equivalent fractions that can be found because there is an infinite amount of numbers to multiply by.

Multiplying fractions - fractions of amounts

1. Example 2. Find 2 over 5 of 40. - Multiply 2 over 5 by 40. - 2 over 5 x 40 = 2 over 5 x 40 over 1 (40 can be written as 40 over 1) = 80 over 5 = 16

Ordering fractions using common denominators

1. Fractions can be compared by finding equivalent fractions with the same denominator. 2. Common denominators are made using common multiples of the two numbers, for example 24 is the lowest common multiple of 8 and 12 ( 8 x 3= 24 and 12 x 2 = 24). 3. There are many other common multiples of 8 and 12 but 24 is the lowest. 4. always write the final answer as the fractions appeared in the question.

Using fractions

1. Fractions show parts of whole numbers, for example, the fraction 1 over 4 shows a number that is 1 part out of 4, or a quarter. 2. Fractions are one way of showing numbers that are parts of a whole. 3. Other ways are decimals and percentages. 4. You can also convert between fractions, decimals and percentages. 5. Like whole numbers and decimals, fractions can be either positive or negative. For example, 3 and 1 over 5 or - 1 over 4.

Adding and subtracting fractions

1. Fractions with the same denominators can be added (or subtracted) by adding (or subtracting) the numerators. 2. For instance, 2 over 9 + 3 over 9 = 5 over 9 or 6 over 11 - 4 over 11 = 2 over 11. 3. If two fractions do not have the same denominator, then find a common denominator by making equivalent fractions.

Fractions of amounts

1. There are many methods to find fractions of amounts, including: - multiplying fractions - a unitary method

Ordering fractions

1. There are many methods used to order fractions, including: - using common denominators - converting fractions to decimals and then ordering

Converting improper fractions to mixed numbers

1. To convert an improper fraction to a mixed number, work out how many whole numbers there are by dividing the numerator by the denominator. 2. Make the remainder the new numerator and leave the denominator as it was.

Dividing fractions

1. To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. 2. This means simply that the divide sign is swapped for a multiply sign, and the second fraction is flipped upside down. 3. If the question contains mixed numbers then the answer should be converted to a mixed number

Multiplying fractions

1. To multiply two fractions together, multiply the numerators together and multiply the denominators together. 2. If the fractions to be multiplied contain mixed numbers, first convert them to improper fractions and then multiply the numerators together and multiply the denominators together. 3. If the question contains mixed numbers then the answer should be converted to a mixed number

Converting mixed numbers to improper fractions

1. To turn mixed numbers into improper fractions, look at the denominator of the fraction first. 2. This will be the denominator of the improper fraction. 3. To convert any mixed number to an improper fraction: - multiply the whole number by the denominator - add on the numerator

Fraction arithmetic on a calculator

1. Using a calculator can help to complete fraction arithmetic but it is important to know how your calculator completes the calculations. 2. Many modern calculators work by pressing a fraction button first and then typing the question onto the screen using the directional pad. 3. Other calculators work by pressing the numerators first, then the fraction button and then the denominators to type in the fraction. 4. Consult the instructions that accompany the calculator.

Equivalent fractions

1. are fractions that are worth exactly the same even though they are written differently. 2. 1 over 4 is worth the same as 2 over 8 because 2 over 8 will simplify to 1 over 4 by dividing by a common factor of 2.

reciprocal

1. the reciprocal of a number is 1 divided by that number. 2. the reciprocal of a fraction is the fraction turned upside down, eg the reciprocal of 3 over 4 is 4 over 3.