11 Plus Fractions Mock Test
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11 Plus Fractions Mock Test:
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Fractions are considered as representing a part of a whole quantity. Fractions are usually represented in the form of a/b where a, b are ≠ 0. The terminologies of fractions are generally used while dividing a thing into smaller parts, like sharing a pizza among friends etc.
The pizza shown in the above picture has been divided into eight pieces. When the pizza is considered a whole, then each part is given by 1/8, which is a fraction.
A fraction consists of 2 parts they are Numerator and Denominator.
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11 Plus Fractions Syllabus:
Count up and down in hundredths; recognise that hundredths arise when dividing an object
by a hundred and dividing tenths by ten.
Solve problems involving increasingly harder fractions to calculate quantities and fractions
to divide quantities, including non-unit fractions where an answer is a whole number
identify, name and write equivalent fractions of a given fraction, including tenths and
Add and subtract fractions with the same denominator
Compare and order fractions whose denominators are all multiples of the same number
Recognise mixed numbers and improper fractions and convert from one form to the other
Add and subtract fractions with the same denominator and related fractions; write
mathematical statements >1 as a mixed number (e.g. 2/5 + 4/5 = 6/5 = 11/5) 26
Multiply proper fractions and mixed numbers by whole numbers, supported by materials
Use common factors to simplify fractions; use common multiples to express fractions in the
Compare and order fractions, including fractions >1
Associate a fraction with the division to calculate decimal fraction equivalents (e.g. 0.375) for a
simple fraction (e.g. 3/8).
Add and subtract fractions with different denominators and mixed numbers, using the
concept of equivalent fractions
Multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1/4 ×
1/2 = 1/8)
Divide proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/6 ).
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Generally, fractions can be divided into three types they are
- Proper Fractions
- Improper fractions
- Mixed Fractions
The fractions in which the denominator is greater than the numerator are considered the Proper Fractions. Examples are ½, ¼, ¾, etc.
The fractions in which the denominator is greater than the numerator are considered Improper Fractions. Examples are 11/4, 5/2, 10/7 etc
The other form of representing an improper fraction is in terms of Mixed Fractions. It is a combination of a whole number and a proper fraction. Examples are 3 ½, 5 ¼, 7 ¾, etc.
Some important facts about fractions are
- The fractions with the same denominator are Like Fractions else they are said as, Unlike Fractions.
- A fraction in which numerator and denominator are equal then its value will be equal to One. Eg 2/2 = 1.
- A fraction in which the numerator = 0 then the value of the fraction will be Zero. Eg 0/100 = 0.
- A fraction in which the denominator = 0 then the fraction is said to be undefined.
Example: Jason brings a cake and cuts it into 6 equal parts and distributes among his friend, what fraction does each friend get?
Sol: No. of pieces = 6 then each one will be getting 1/6 part of the cake.
Arithmetic operations on fractions
To perform addition or subtraction, we need to check if the fractions have the same denominator or not. We will know about them in detail through some interesting and easy examples.
Consider two fractions a/b and c/b then their sum will be (a + c)/b, similarly in subtraction also, it will be (a-c)/b. Here denominators of both the fractions are equal.
Consider two fractions a/b and c/d then to find their sum or difference we must make their denominators equal. For this we must find the LCM of the denominators and based on it we must make the fractions like or we follow another method, in which the fractions are represented as (ad/bd), (bc/bd) and perform the addition or subtraction.
Example: Add 1/2 and 2/3.
Sol: First convert them into like fractions. 1/2 can be written as (1×3) / (2×3) = 3/6. Similarly, 2/3 can be written as 2/6. Now we can add both the fractions,
3/6 + 2/6 = 5/6
For multiplication it is very easy, just multiply the numerators and denominators separately. For division just reciprocate the 2nd fraction and multiply.
Multiplication of a / b & c / d = (a x b) / (c x d)
Division of a / b & c / d = (a x d) / (b x c)
Example: Multiply 1/4 and 2/3.
Sol: It is very easy just to multiply numerators and denominators separately.
1/4 x 2/3 = (1 x 2) / (4 x 3) = 2 / 12.
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