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

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Ruby

09/06/2023

Maths

Subjects

Maths

Number

Approximation

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

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

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

Fraction Problems

This section demonstrates how to solve practical problems involving fractions.

Example: Rachel needs to determine how many packs of butter to buy for 80 cupcakes, where each cupcake requires 2/25 of a pack.

The solution involves multiplying the fraction by the number of cupcakes and rounding up to the nearest whole pack:

80 × 2/25 = 160/25 = 6.4 packs

Highlight: When dealing with real-world problems, remember to round up to the nearest whole unit when partial units aren't practical.

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

View

Comparing Fractions

This page explains how to compare fractions by finding a common denominator.

Example: To determine which fraction is closer to 1, 2/3 or 9/7, convert both to a common denominator of 21:

2/3 = 14/21 9/7 = 27/21

Subtracting from 1 (21/21):

21/21 - 14/21 = 7/21 21/21 - 27/21 = -6/21

Highlight: The fraction with the smaller difference from 1 (in absolute value) is closer to 1. In this case, 9/7 is closer to 1 than 2/3.

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

View

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

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

Converting Between Fractions, Decimals, and Percentages

This section explains the process of converting between fractions, decimals, and percentages.

Example: To convert 7/20 to a decimal and percentage:

Divide 7 by 20: 7 ÷ 20 = 0.35
Multiply by 100 for percentage: 0.35 × 100 = 35%

Highlight: When converting from a decimal to a fraction, place the digits after the decimal point over a power of 10 (e.g., 0.61 = 61/100).

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

View

Rounding Numbers

This page introduces the concept of rounding numbers to a specified decimal place.

Example: Rounding 13.72 to one decimal place:

Identify the last digit to keep (7)
Look at the next digit (2) as the decider
Since 2 < 5, the last digit stays the same Result: 13.7

Highlight: The digit to the right of the rounding position is called the "decider" and determines whether to round up or down.

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

View

Rounding Numbers (Continued)

This page provides another example of rounding numbers, this time to two decimal places.

Example: Rounding 7.45839 to two decimal places:

Identify the last digit to keep (5)
Look at the next digit (8) as the decider
Since 8 ≥ 5, round up Result: 7.46

Highlight: When the decider is 5 or greater, round up the last digit to be kept.

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

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:

Identify the last digit to keep (9)
Look at the next digit (8) as the decider
Since 8 ≥ 5, round up 9 to 10
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

Significant Figures

This page introduces the concept of significant figures in rounding numbers.

Definition: The first significant figure is the first non-zero digit from the left. Subsequent digits, including zeros, are counted as significant figures.

Example: In 0.002309, the significant figures are: 1st: 2 2nd: 3 3rd: 0 4th: 9

Highlight: Understanding significant figures is crucial for maintaining precision in scientific and engineering calculations.

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Subjects

Maths

Number

Approximation

Maths

•

361

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9 Jun 2023

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19 pages

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

Ruby

@ruby123456789

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

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Fraction Problems

This section demonstrates how to solve practical problems involving fractions.

Example: Rachel needs to determine how many packs of butter to buy for 80 cupcakes, where each cupcake requires 2/25 of a pack.

The solution involves multiplying the fraction by the number of cupcakes and rounding up to the nearest whole pack:

80 × 2/25 = 160/25 = 6.4 packs

Highlight: When dealing with real-world problems, remember to round up to the nearest whole unit when partial units aren't practical.

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

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Comparing Fractions

This page explains how to compare fractions by finding a common denominator.

Example: To determine which fraction is closer to 1, 2/3 or 9/7, convert both to a common denominator of 21:

2/3 = 14/21 9/7 = 27/21

Subtracting from 1 (21/21):

21/21 - 14/21 = 7/21 21/21 - 27/21 = -6/21

Highlight: The fraction with the smaller difference from 1 (in absolute value) is closer to 1. In this case, 9/7 is closer to 1 than 2/3.

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

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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.

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

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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.

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

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Join milions of students

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Converting Between Fractions, Decimals, and Percentages

This section explains the process of converting between fractions, decimals, and percentages.

Example: To convert 7/20 to a decimal and percentage:

Divide 7 by 20: 7 ÷ 20 = 0.35
Multiply by 100 for percentage: 0.35 × 100 = 35%

Highlight: When converting from a decimal to a fraction, place the digits after the decimal point over a power of 10 (e.g., 0.61 = 61/100).

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

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Rounding Numbers

This page introduces the concept of rounding numbers to a specified decimal place.

Example: Rounding 13.72 to one decimal place:

Identify the last digit to keep (7)
Look at the next digit (2) as the decider
Since 2 < 5, the last digit stays the same Result: 13.7

Highlight: The digit to the right of the rounding position is called the "decider" and determines whether to round up or down.

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

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Rounding Numbers (Continued)

This page provides another example of rounding numbers, this time to two decimal places.

Example: Rounding 7.45839 to two decimal places:

Identify the last digit to keep (5)
Look at the next digit (8) as the decider
Since 8 ≥ 5, round up Result: 7.46

Highlight: When the decider is 5 or greater, round up the last digit to be kept.

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

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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:

Identify the last digit to keep (9)
Look at the next digit (8) as the decider
Since 8 ≥ 5, round up 9 to 10
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.

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

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Significant Figures

This page introduces the concept of significant figures in rounding numbers.

Definition: The first significant figure is the first non-zero digit from the left. Subsequent digits, including zeros, are counted as significant figures.

Example: In 0.002309, the significant figures are: 1st: 2 2nd: 3 3rd: 0 4th: 9

Highlight: Understanding significant figures is crucial for maintaining precision in scientific and engineering calculations.

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

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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:

Identify the first two significant digits (50)
Look at the next digit (6) as the decider
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.

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Anna

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Basil

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David K

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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

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

Fraction Problems

Comparing Fractions

Fractions, Decimals, and Percentages

More Fractions, Decimals, and Percentages

Converting Between Fractions, Decimals, and Percentages

Rounding Numbers

Rounding Numbers (Continued)

Rounding Numbers (Special Cases)

Significant Figures

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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.

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

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

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

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

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

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Fraction Problems

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Comparing Fractions

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Fractions, Decimals, and Percentages

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More Fractions, Decimals, and Percentages

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Converting Between Fractions, Decimals, and Percentages

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Rounding Numbers

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Rounding Numbers (Continued)

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Rounding Numbers (Special Cases)

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Significant Figures

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Rounding to Significant Figures

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