Working with Fractions Fractions are an essential part of mathematics that students encounter in the 11-plus exams. This section covers various aspects of fract...
Fractions are an essential part of mathematics that students encounter in the 11-plus exams. This section covers various aspects of fractions, including understanding equivalent fractions, simplifying fractions, comparing and ordering them, and performing operations such as addition, subtraction, multiplication, and division.
Equivalent fractions are different fractions that represent the same value. For example, 1/2 is equivalent to 2/4 and 3/6. To find equivalent fractions, you can multiply or divide the numerator and the denominator by the same number.
Problem: Find two equivalent fractions for 3/4.
Solution:
Thus, 6/8 and 9/12 are equivalent to 3/4.
Simplifying fractions involves reducing them to their lowest terms. This is done by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by this number.
Problem: Simplify the fraction 8/12.
Solution:
The simplified fraction is 2/3.
To compare fractions, they must have a common denominator. If they do not, find the least common denominator (LCD) and convert the fractions before comparing. You can also convert fractions to decimal form for easier comparison.
Problem: Compare 1/3 and 1/4.
Solution:
When adding or subtracting fractions with different denominators, first find a common denominator. Then adjust the numerators accordingly before performing the operation.
Problem: Add 1/4 and 1/6.
Solution:
The sum is 5/12.
To multiply fractions, multiply the numerators together and the denominators together. To divide fractions, multiply by the reciprocal of the second fraction.
Problem: Multiply 2/3 by 3/4.
Solution:
The product is 1/2.
Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator and adding the numerator. Conversely, to convert an improper fraction to a mixed number, divide the numerator by the denominator.
Problem: Convert 2 1/3 to an improper fraction.
Solution:
To find a fraction of an amount, multiply the amount by the numerator and then divide by the denominator.
Problem: Find 2/5 of 20.
Solution:
Thus, 2/5 of 20 is 8.
Understanding fractions is crucial for success in the 11-plus mathematics exam. Mastery of these concepts will not only aid in exam preparation but also in future mathematical endeavors.