Registration open for 2025 classes...
A fraction can be written in lowest term or simplified form by dividing both numerator and denominator with the same number.
To add/subtract fractions, they must have equal denominator.
If the denominators are not equal, make them equal before adding or subtracting.
To multiply, divide fractions, they need not have equal denominator.
To divide fractions, invert the dividing fraction then multiply.
To add/subtract mixed numbers, first add/subtract whole numbers, then add/subtract fractional parts.
To multiply/divide mixed numbers, it is better to convert them to improper fractions, them multiply/divide.
Fractions can be converted to equivalent decimals.
1/2 = 5/10 = 0.5
1/4 = 25/100 = 0.25
1/5 = 2/10 = 0.2
1/10 = 0.1
Fractions can be converted to equivalent percentages.
1/2 = 1/2 x 100% = 50%
1/4 = 1/4 x 100% = 25%
1/5 = 1/5 x 100% = 20%
1/10 = 1/10 x 100% = 10%
QUESTION 1 - REMAINDER CONCEPT
Julaiha spent 7/10 of her pocket money on Food and 1/3 of the remainder on a Drink.
If she has $2 now, how much was her pocket money?
Food = 7/10
Remainder = 1 - (7/10) = 3/10
Drink = (1/3) x (3/10) = 1/10
Balance = (3/10) - (1/10) = 2/10
2 units --> $2
Pocket Money, 10 Units --> $10
QUESTION 2 - PART WHOLE CONCEPT
Ahamed spent 1/2 of his money on 2 books and 3 pens.
The cost of a book is three times the cost of a pen.
He bought some more pens with 1/3 of his remaining money.
Find the total number of pens he bought.
cost of 1 book --> cost of 3 pens
cost of 2 books --> cost of 6 pens
(1/2) of money --> 2 books + 3 pens
(1/2) of money --> 6 pens + 3 pens
(1/2) of money --> 9 pens
Remaining money --> 1- (1/2) = (1/2) of money --> 9 pens
(1/3) of remaining money --> (1/3) x 9 pens = 3 pens
So Ahamed bought = 6 + 3 = 9 pens in Total.
QUESTION 3 - EQUAL FRACTION CONCEPT
There are 50 students in a School Hall.
6/10 of the boys and 4/5 of the girls left the Hall.
Now the number of girls in the hall is 1/3 the number of boys.
How many students in the hall now?
How many students left the hall?
FRACTION OF STUDENTS LEFT THE HALL
boys --> 6/10
girls --> 4/5
FRACTION OF STUDENTS REMAINING IN THE HALL
boys --> 1 - (6/10) = 4/10
girls --> 1 - (4/5) = 1/5
NOW IN THE HALL
Number of girls = (1/3) x Number of boys
Number of boys = 3 x number of girls
(4/10) B <---> 3 x (1/5) G
(4/10) B <---> (3/5) G
Make the numerator the same, (12/30) B <---> (12/20) G
So, boys --> 30 units and girls --> 20 units
Total = 30 units + 20 units
50 units --> 500 students
1 unit --> 10 students
boys --> 30 units = 300
(4/10) x 300 = 120 boys in the Hall now
girls --> 20 units = 200
(1/5) x 200 = 40 girls in the Hall now
So 120 + 40 = 160 students in the Hall now.
500 - 160 = 340 students left the Hall.
QUESTION 4 - SINGLE UNCHANGED CONCEPT
4/5 of the students in a class are boys. After 35 boys left the class, 1/3 of the students in the class now are boys. How many girls are there in the class?
Number of Girls in unchanged. We shall apply BCA (BEFORE --> CHANGE --> AFTER) concept
BEFORE
Boys --> 4 unit
Girls --> 1 unit
CHANGE
35 Boys left the hall
AFTER
Boys --> 1 part
Girls --> 2 parts
Let us change all to x.
Number of Girls in unchanged, so it has to be equal in BEFORE and AFTER.
BEFORE
Boys --> 8x
Girls --> 2x
CHANGE
35 Boys left the hall
AFTER
Boys --> 1x
Girls --> 2x
8x - 1x = 7x --> 35
1x --> 5
Girls = 2x --> 10