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Easy Fractions, Rounding & Converting Maths Guide for KS2 and Year 7

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Easy Fractions, Rounding & Converting Maths Guide for KS2 and Year 7
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Ruby

@ruby123456789

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Fractions, decimals, percentages, and rounding numbers are fundamental concepts in mathematics. This guide covers various aspects of these topics, including converting between different representations, solving fraction problems, and applying rounding rules. It also explores powers, roots, and standard form notation.

  • Fractions can be expressed as parts of a whole or used in calculations
  • Decimals and percentages are alternative ways to represent fractional values
  • Rounding numbers involves adjusting values to a specified level of precision
  • Powers and roots are used to represent repeated multiplication and its inverse
  • Standard form is a way to express very large or small numbers concisely

09/06/2023

324

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Fractions, Decimals, and Percentages

This page provides a comprehensive table showing the relationships between fractions, decimals, and percentages.

Example:

  • 1/2 = 0.5 = 50%
  • 1/4 = 0.25 = 25%
  • 3/4 = 0.75 = 75%

Highlight: Understanding these equivalences is crucial for converting fractions, decimals, and percentages in various mathematical contexts.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Square Roots

This page introduces the concept of square roots as the inverse operation of squaring.

Definition: The square root of a number is a value that, when multiplied by itself, gives the number.

Example: √49 = 7 because 7 × 7 = 49

Highlight: The square root symbol (√) is used to denote this operation.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Rounding Numbers (Special Cases)

This section covers a special case in rounding where rounding up a 9 is necessary.

Example: Rounding 45.698 to two decimal places:

  1. Identify the last digit to keep (9)
  2. Look at the next digit (8) as the decider
  3. Since 8 ≥ 5, round up 9 to 10
  4. Replace 9 with 0 and add 1 to the digit on the left Result: 45.70

Highlight: When rounding up a 9, it becomes 0, and you must add 1 to the next digit to the left.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Rules for Powers

This section covers the rules for working with powers in mathematical operations.

Highlight: Key rules for powers include:

  1. When multiplying powers with the same base, add the exponents.
  2. When dividing powers with the same base, subtract the exponents.
  3. When raising a power to another power, multiply the exponents.

Example: (x^3)^2 = x^(3×2) = x^6

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Rounding to Significant Figures

This section demonstrates how to round numbers to a specified number of significant figures.

Example: Rounding 506.07 to two significant figures:

  1. Identify the first two significant digits (50)
  2. Look at the next digit (6) as the decider
  3. Since 6 ≥ 5, round up Result: 510

Highlight: When rounding to significant figures, you may need to add zeros to maintain the correct magnitude of the number.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Cube Roots

This section extends the concept of roots to cube roots.

Definition: The cube root of a number is a value that, when multiplied by itself twice, gives the number.

Example: ∛27 = 3 because 3 × 3 × 3 = 27

Highlight: Cube roots can be calculated using a scientific calculator or by recognizing perfect cubes.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

More Fractions, Decimals, and Percentages

This page continues with additional examples of fraction, decimal, and percentage equivalences.

Example:

  • 1/10 = 0.1 = 10%
  • 1/5 = 0.2 = 20%
  • 3/8 = 0.375 = 37.5%

Highlight: Recognizing these patterns helps in quickly converting between different representations of the same value.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Estimation

This section introduces estimation techniques for calculations and square roots.

Example: Estimating 42.6 × 12.1: Round 42.6 to 40 and 12.1 to 10 40 × 10 = 400

Example: Estimating √6242 ÷ 57: √6242 ≈ √6000 = √(60 × 100) ≈ 10 × √6 ≈ 10 × 2.4 = 24 57 ≈ 60 24 ÷ 60 = 0.4

Highlight: Estimation is useful for quick mental calculations and checking the reasonableness of exact answers.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Rounding to Nearest Whole Number, 10, 100, etc.

This page explains how to round numbers to the nearest whole number, 10, 100, or other powers of 10.

Example: Rounding 6751 to the nearest hundred:

  1. Identify the hundreds digit (7)
  2. Look at the tens digit (5) as the decider
  3. Since 5 ≥ 5, round up Result: 6800

Highlight: When rounding to powers of 10, focus on the digit in the relevant place value and use the next digit to the right as the decider.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

View

Converting from Standard Form

This final page demonstrates how to convert a number from standard form to ordinary notation.

Example: Converting 4.95 × 10^-3 to an ordinary number: Move the decimal point 3 places to the left (because the exponent is negative) Result: 0.00495

Highlight: When converting from standard form, the exponent indicates how many places and in which direction to move the decimal point.

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Knowunity is the #1 education app in five European countries

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I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

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The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

/

Maths

/

Number

/

Approximation

Easy Fractions, Rounding & Converting Maths Guide for KS2 and Year 7

user profile picture

Ruby

@ruby123456789

·

12 Followers

Follow

Fractions, decimals, percentages, and rounding numbers are fundamental concepts in mathematics. This guide covers various aspects of these topics, including converting between different representations, solving fraction problems, and applying rounding rules. It also explores powers, roots, and standard form notation.

  • Fractions can be expressed as parts of a whole or used in calculations
  • Decimals and percentages are alternative ways to represent fractional values
  • Rounding numbers involves adjusting values to a specified level of precision
  • Powers and roots are used to represent repeated multiplication and its inverse
  • Standard form is a way to express very large or small numbers concisely

09/06/2023

324

 

11/10

 

Maths

10

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Fractions, Decimals, and Percentages

This page provides a comprehensive table showing the relationships between fractions, decimals, and percentages.

Example:

  • 1/2 = 0.5 = 50%
  • 1/4 = 0.25 = 25%
  • 3/4 = 0.75 = 75%

Highlight: Understanding these equivalences is crucial for converting fractions, decimals, and percentages in various mathematical contexts.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Square Roots

This page introduces the concept of square roots as the inverse operation of squaring.

Definition: The square root of a number is a value that, when multiplied by itself, gives the number.

Example: √49 = 7 because 7 × 7 = 49

Highlight: The square root symbol (√) is used to denote this operation.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Rounding Numbers (Special Cases)

This section covers a special case in rounding where rounding up a 9 is necessary.

Example: Rounding 45.698 to two decimal places:

  1. Identify the last digit to keep (9)
  2. Look at the next digit (8) as the decider
  3. Since 8 ≥ 5, round up 9 to 10
  4. Replace 9 with 0 and add 1 to the digit on the left Result: 45.70

Highlight: When rounding up a 9, it becomes 0, and you must add 1 to the next digit to the left.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Rules for Powers

This section covers the rules for working with powers in mathematical operations.

Highlight: Key rules for powers include:

  1. When multiplying powers with the same base, add the exponents.
  2. When dividing powers with the same base, subtract the exponents.
  3. When raising a power to another power, multiply the exponents.

Example: (x^3)^2 = x^(3×2) = x^6

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Rounding to Significant Figures

This section demonstrates how to round numbers to a specified number of significant figures.

Example: Rounding 506.07 to two significant figures:

  1. Identify the first two significant digits (50)
  2. Look at the next digit (6) as the decider
  3. Since 6 ≥ 5, round up Result: 510

Highlight: When rounding to significant figures, you may need to add zeros to maintain the correct magnitude of the number.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Cube Roots

This section extends the concept of roots to cube roots.

Definition: The cube root of a number is a value that, when multiplied by itself twice, gives the number.

Example: ∛27 = 3 because 3 × 3 × 3 = 27

Highlight: Cube roots can be calculated using a scientific calculator or by recognizing perfect cubes.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

More Fractions, Decimals, and Percentages

This page continues with additional examples of fraction, decimal, and percentage equivalences.

Example:

  • 1/10 = 0.1 = 10%
  • 1/5 = 0.2 = 20%
  • 3/8 = 0.375 = 37.5%

Highlight: Recognizing these patterns helps in quickly converting between different representations of the same value.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Estimation

This section introduces estimation techniques for calculations and square roots.

Example: Estimating 42.6 × 12.1: Round 42.6 to 40 and 12.1 to 10 40 × 10 = 400

Example: Estimating √6242 ÷ 57: √6242 ≈ √6000 = √(60 × 100) ≈ 10 × √6 ≈ 10 × 2.4 = 24 57 ≈ 60 24 ÷ 60 = 0.4

Highlight: Estimation is useful for quick mental calculations and checking the reasonableness of exact answers.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Rounding to Nearest Whole Number, 10, 100, etc.

This page explains how to round numbers to the nearest whole number, 10, 100, or other powers of 10.

Example: Rounding 6751 to the nearest hundred:

  1. Identify the hundreds digit (7)
  2. Look at the tens digit (5) as the decider
  3. Since 5 ≥ 5, round up Result: 6800

Highlight: When rounding to powers of 10, focus on the digit in the relevant place value and use the next digit to the right as the decider.

fractions without a calculation Expressing as a fraction eig. wunte 180 as a fraction of 80 winke the first number over the 180=9 80 4 secon

Converting from Standard Form

This final page demonstrates how to convert a number from standard form to ordinary notation.

Example: Converting 4.95 × 10^-3 to an ordinary number: Move the decimal point 3 places to the left (because the exponent is negative) Result: 0.00495

Highlight: When converting from standard form, the exponent indicates how many places and in which direction to move the decimal point.

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Know error intervals thumbnail

Chemistry - Quantitative Chemistry summary AQA

Here is a summary of the Quantitative Chemistry Topic from AQA chemistry paper 1.

168

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Know Quantitative Chemistry summary AQA thumbnail

Maths - Upper and Lower Bounds

contains: - how to find bounds - smallest and highest possible answer - difference between discrete and continuous data

20

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Know Upper and Lower Bounds thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.