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Interpreting Decimal Manipulation for 11 Plus Exams

1. Decimal Numbers

Decimal numbers are used to display the whole number and fraction together. This whole number and fractional part are separated by inserting a ‘.’, which is known as the decimal point. For example, you are going to buy some grocery items. The store manager says the total bill is £15 and 57 pence. So, to express this amount in one figure, you will express this amount as £15.57. There are many such real-life situations using decimal numbers. We use decimal numbers in our daily lives with money, weight, distance, length, etc.

Decimal Manipulation1-11+ Topicwise Article

Decimals lie between integers on the number line. They are one of the ways of representing fractions in Maths.

Decimal Manipulation2-11+ Topicwise Article

1.1 Reading Decimal Numbers

The method of reading a decimal number is to first read the whole number followed by ‘point’, then to read the digits in the fractional part separately. For example, we read 96.37 as ninety-six point three seven.

Decimal Manipulation3-11+ Topicwise Article

2. What is Decimal Manipulation?

Decimal manipulation refers to performing various mathematical operations such as addition, subtraction, multiplication, and division on decimal numbers. Decimal numbers are numbers with one or more digits to the right of the decimal point.

Here are some examples of decimal manipulation:

2.1 Addition 

To add two decimal numbers, align the decimal points and add the digits in each place value column.

For example, to add 3.14 and 2.67, we align the decimal points and add 4 + 7 in the tenths place, 1 + 6 in the hundredths place, and 3 + 2 in the ones place, giving us a total of 5.81.

2.2 Subtraction

To subtract one decimal number from another, align the decimal points and subtract the digits in each place value column.

For example, to subtract 2.67 from 3.14, we align the decimal points and subtract 7 from 4 in the tenths place, 1 from 6 in the hundredths place, and 3 from 2 in the ones place, giving us a difference of 0.47.

For example:

a) 4.031 + 5.2                                             b) 9.563 - 4.42

Decimal Manipulation4-11+ Topicwise Article

2.3 Multiplication

To multiply two decimal numbers, ignore the decimal points, multiply the numbers as if they were whole numbers, and count the total number of decimal places in both numbers.

Decimal Manipulation6-11+ Topicwise Article

For example:
a) 75 x 1.5

Decimal Manipulation7-11+ Topicwise Article

b) 3.5 x 1.5

Decimal Manipulation8-11+ Topicwise Article

For example, to multiply 3.14 by 2.67, we multiply 314 by 267, which gives us 83738, and count a total of 4 decimal places (2 in 3.14 and 2 in 2.67). We then place the decimal point in the product 2 places from the right, giving us 8.378.

2.4 Division

To divide a decimal number by another decimal number, move the decimal point of the divisor to the right until it becomes a whole number, move the decimal point of the dividend the same number of places to the right, perform the division as if it were a whole number, and then move the decimal point in the quotient back to its original position.

Decimal Manipulation8-11+ Topicwise Article

For example, to divide 3.14 by 2.67, we move the decimal point of 2.67 two places to the right, giving us 267, and move the decimal point of 3.14 two places to the right as well, giving us 314. We then perform the division 314 ÷ 267, which gives us a quotient of 1.176. We then move the decimal point in the quotient back to its original position, giving us 1.176 rounded to 3 decimal places.

For example: Divide 338.56 by 16.

Decimal Manipulation10-11+ Topicwise Article

2.5 Rounding

To round a decimal number to a certain number of decimal places, find the digit in that place and look at the digit to the right. If it is 5 or greater, round up. If it is less than 5, round down.

For example: 3.45678 rounded to 2 decimal places is 3.46.
7.84321 rounded to 1 decimal place is 7.8.

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    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

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    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
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