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FRACTIONS, PERCENTAGES AND DECIMALS.
Introduction:
In this topic, you will use knowledge of place values to manipulate fractions, decimals and percentages. You will convert fractions to decimals, decimals to percentages and vice versa.
A fraction is a number in the form a/b where a and b are whole numbers and b is not zero.
In a fraction the top number is called the numerator(a) and the bottom number is called the denominator(b)
A fraction is in simplest form (lowest terms) when the top and bottom cannot be any smaller.
3.1 Types of fraction.
Proper Fraction:
Improper Fraction;
3.1 Exercise Set
3.2 Converting Improper Fractions to Mixed Numbers and Vice Versa.
3.2 Exercise Set
3.3 Operations on Fractions:
For fractions with plus (+) and minus ( ) signs only, nd the LCM and workout.
For fractions with combined operations, the BODMAS rule must be observed.
Activity: Work out problems from real-life situations
EXAMPLES
3.3 Exercise Set
3.3.1 Addition of Fractions with the Same Denominators
To add fractions with like or the same denominator, simply add the numerators then copy the common denominator. Always reduce your final answer to its lowest term.
EXAMPLE
3.4 Exercise Set
3.3.2 Addition of Fractions with different Denominators.
Given two unlike fractions where the denominators are NOT the same, the fractions can be solved using two methods.
LCM method Cross
Multiplication method
The following steps are followed when using the LCM method:
Steps for Adding Fractions with Unlike Denominators.
Identify the least common denominator by finding the least common multiple for the denominators.
Write equivalent fractions (making sure that each equivalent fraction contains the least common denominator(LCM))
Add the equivalent fractions that you wrote in step2. (The denominators should now be the same.)
Reduce the fraction to its lowest term
EXAMPLES
3.5 Exercise Set
1. Calculate
3.3.3 Subtraction of Fractions with Same Denominators
To subtract fractions with like or the same denominator, simply subtract the numerators then copy the common denominator. Always reduce your final answer to its lowest term.
EXAMPLE
3.3.4 Subtraction of Fractions with different Denominators.
Given two unlike fractions where the denominators are NOT the same, we follow the same steps as in addition.
EXAMPLES.
3.7 Exercise set.
3.8 Exercise Set
3.3.6 Subtraction of Mixed Fractions
3.9 Exercise set
3.3.7 Multiplication of Fractions
When multiplying fractions, the numerator and the denominator are multiplied separately.
3.10 Exercise Set
3.3.8 Multiplying Mixed Fractions
Convert the mixed fraction into an improper fraction, and then apply the multiplication rules
3.11 Exercise Set
3.3.9 Division of Fractions
Flip And Multiply.
3.13 Exercise Set
Activity: Convert Decimals to Fractions
A decimal number can be exact or inexact. An exact decimal or terminating decimal is a decimal that ends. This decimal is converted into a fraction as follows:
EXAMPLES
3.14 Exercise Set
3.15 Exercise Set
3.4.3 Multiplication and Division of decimals
To multiply or divide two decimal numbers, express the decimal numbers in fractions and then workout.
EXAMPLES
3.16 Exercise Set
3.5 Identify and Classify Decimals as Terminating, Non terminating and Recurring Decimals.
EXAMPLES
3.18 Exercise Set
3.6 Percentages.
The word 'percentage' means 'per hundred'. In this section we concentrate in converting between decimals, fractions and percentages.
Percentage is a fraction whose denominator is100
The Symbol for percentage is written as %
3.6.1 Convert Fractions and Decimals into Percentages and Vice Versa.
To change a percentage into a fraction or decimal divide by 100.Thus
3.19 Exercise Set
3. An athlete has completed 250m of a 400m race. What percentage of the distance has the athlete run?
4. In a car park, 40% of the cars are red and 720 of the cars are blue.
(a)What percentage are blue?
(b)What fraction are red?
5. A Nile Star bus has 72 seats; there are 18 empty seats on the bus.
(a)What percentage of the seats are empty?
(b)What percentage of the seats are being used?
6. Andy buys a bag of 12 apples at Arua central market; there are 4 bruised apples in the bag.
(a)What percentage of the apples are bruised?
(b)What percentage of the apples are not bruised?
3.7 Finding the Percentage Increase and Decrease
The percentage of a quantity can always be calculated in terms of percentage increase or percentage decrease. Thus this is referred to as a percentage change
EXAMPLE
3. The price of an item reduced from Shs 8,000 to Shs 6,000. Find the percentage decrease in the price of the item.
3.20 Exercise Set
1. The price of a drink increases from 4000 to 4500. What is the percentage increase?
2. The number of pupils in a school increases from 820 to 861. Calculate the percentage increase.
3. Although the lion is thought of as an African animal, there is a small population in India and elsewhere in Asia. The number of lions in India decreased from 6000 to 3900 over a 10-year period. Calculate the percentage decrease in this period.
4. The table below shows the marks obtained by some students of s.1 at Ushindi secondary school in two mathematics tests. For each one, calculate the percentage difference(change) and make a conclusion whether it is an increase or a decrease.
ACTIVITY OF INTERGRATION
Ushindi Secondary school has two sections, that is, Lower UNEB (S.1-S.4) and Upper UNEB (S.5-S.6). The Director of studies of the school needs to draw a timetable for the online lessons for both sections. The sections should start and end their morning lessons at the same time before break time, start and end their break time at the same time. The after break lessons should start at the same time. The lunchtime for both sections should start at the same time and end at the same time. The after Lunch lessons should start at the same time and end at the same time. Math must have 3 hours in a week in each class.
Support:
The time to start lessons for the two sections is 8.30am and lessons end at 4:30pm. The duration of the lesson for the Lower UNEB section is 1 hour and that of the Upper UNEB is 2 hours. Assume the following subjects to be offered.
Resources:
Knowledge of fractions, percentages, natural numbers, factors, multiples, lowest common multiples, and the subjects taught in all classes and of time.
Tasks:
Help the Director of studies by drawing the timetable for the week (Monday to Friday) for the two sections.
How many lessons does each section have up to lunchtime?
What is the total number of hours in a week for the lower section
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