Year 7 - Task 2 Revision

Fractions Revision

By Eliza Lans

A fraction represents a part of a whole.
It's written as two numbers separated by a slash or line, like this: 3/4.

-Numerator (top number): Shows how many parts we have.

-Denominator (bottom number): Shows how many equal parts the whole is divided into.

For example, 3/4 means we have 3 parts out of 4 equal parts.

Fractions

Proper, Improper and Mixed Fractions

We see three kinds of fractions, most common is our proper fraction where the numerator is smaller than the denominator, representing a portion of a whole. If we see an improper fraction, where the numerator is larger than the denominator, its best to convert this to a mixed numeral to show the how many whole numbers and remaining parts it has.

Labelling

Label these three types of fraction and their parts:

Drag labels to their correct position on the image

numerator

mixed fraction

denominator

improper
fraction

proper fraction

fraction

whole number

We compare fractions using the equals, less than, and greater than symbols. The aim is to express the difference in size, even when the fractions have different denominators.

Compare

Equivalent fractions are fractions that represent the same portion but have been divided into different quantities. An example is a 1/2 is the same or equal to 50/100.

​​Equivalent

Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1.
We achieve this by dividing them by their HCF.

Simplify

Reorder

Compare: Put these fractions in order from smallest to largest (ascending):

• $$\frac{2}{12}$$

• $$\frac{2}{8}$$

• $$\frac{3}{6}$$

• $$\frac{2}{3}$$

• $$\frac{4}{2}$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Match

Equivalence: Match the following fractions with their equivalent:

• $$\frac{15}{9}$$

• $$\frac{12}{72}$$

• $$\frac{3}{4}$$

• $$\frac{20}{100}$$

• $$\frac{5}{3}$$

• $$\frac{1}{6}$$

• $$\frac{6}{8}$$

• $$\frac{1}{5}$$

Labelling

Simplify: Reduce these fractions to their smallest form:

Drag labels to their correct position on the image

2

8

7

14

2

5

3

3

13

1

​

We can add and subtract fractions that have the same denominator, we keep the denominator and complete the operation across the numerators.
If they have different denominators, we first have to multiply each fraction by the opposite denominator to create two new equivalent fractions that have equal denominators, then we can complete the operation as normal.

Adding and Subtracting

Multiple Select

Adding: What is the answer to $$\frac{2}{6}+\frac{1}{6}=$$

• $$\frac{3}{12}$$

• $$\frac{3}{6}$$

• $$\frac{1}{2}$$

• $$\frac{2}{6}$$

Multiple Choice

Subtracting: What is the answer to $$\frac{8}{8}-\frac{5}{8}=$$

• $$\frac{5}{16}$$

• $$\frac{3}{4}$$

• $$\frac{1}{2}$$

• $$\frac{5}{8}$$

Multiple Select

Adding (different denominators): What is the answer to $$\frac{3}{5}+\frac{1}{2}=\frac{ }{10}+\frac{5}{ }=\frac{ }{ }$$

• $$\frac{11}{10}$$

• $$\frac{8}{7}$$

• $$1\frac{1}{10}$$

• $$\frac{4}{7}$$

Multiple Select

Subtracting (different denominators): What is the answer to $$\frac{2}{4}-\frac{1}{6}=\frac{ }{24}-\frac{ }{24}=\frac{ }{24}$$

• $$\frac{12}{24}$$

• $$\frac{8}{24}$$

• $$\frac{4}{24}$$

• $$\frac{1}{3}$$

Multiplying

Dividing

Multiplying fractions requires two steps:
1. multiply the two numerators
2.multiply the two denominators

This creates a new fraction and we then simplify this by dividing it by its highest common factors.

Dividing fractions uses three steps:
1. KEEP the first fraction
2.CHANGE the divide to a multiply
3.FLIP the second fraction

Once we have done this, we complete the multiplication like normal and simplify our answer.

Labelling

Multiplying: Put the correct fraction next to the problem:

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Labelling

Dividing: Put the correct steps and answer next to each problem:

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Converting between mixed and improper fractions means changing how a number looks, but not its value. A mixed number has a whole number and a fraction (like 2½), while an improper fraction has a larger numerator than its denominator (like 5/2).

​

​Converting Improper and Mixed Fractions

Match

Converting: Match the following improper fraction with their mixed fraction counterpart and visa versa

• $$4\frac{1}{6}$$

• $$\frac{10}{3}$$

• $$2\frac{1}{4}$$

• $$\frac{15}{3}$$

• $$1\frac{3}{8}$$

• $$\frac{25}{6}$$

• $$3\frac{1}{3}$$

• $$\frac{9}{4}$$

• $$5$$

• $$\frac{11}{8}$$

Indices Revision

By Eliza Lans

​This is when we show the multiplication of the base.
The base is multiplied by itself the number of times as determined by the power.

Index Notation

​Index notation is a way to show repeated multiplication using a superscript called an index, power or exponent. We also use this to show a number as a product of its prime factors.

​​Expanded Form

Numerical form is just the normal way we write numbers using digits and place value, like 2401.

​​Numerical Form

Labelling

Terminology: Label the image with the below terms:

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Numerical Form

Expanded Form

Index Form

Base

Power/Index/Exponent

Match

Conversion: Match the Index, Expanded or Numerical form with their counterpart:

• $$9^2$$

• $$12\ \times12\times12$$

• $$125$$

• $$6^5$$

• $$4\times4\times4$$

• $$18$$

• $$12^3$$

• $$5^3$$

• $$6\times6\times6\times6\times6$$

• $$64$$

Factors are numbers that are multiplied together to get another number. We use factor pairs to list all the factors of composite numbers.
eg.
Factors of 12 = 1x12, 2x6, 3x4

​​Factors

Multiples of a number are the results of multiplying that number by whole numbers. They form a sequence that keeps increasing.

eg.
The multiples of 6 are 6, 12, 18, 24...

​​Multipes

​Primes are numbers greater than 1 that only have two factors, 1 and themselves.

eg.
Factors of 7 = 1 & 7

​​Primes

Fill in the Blank

Multiples: List the first five multiples of 7

Fill in the Blank

Multiples: List the first five multiples of 12

Labelling

Factors: break 60 down into its factors using this factor tree

Drag labels to their correct position on the image

15

3

5

2

Labelling

Factors: break the numbers down into their factors and write them as a product of their prime factors

Drag labels to their correct position on the image

6

11

2 x 3 x 5

11 x 2 x 3

15

2

3

5

3

2

Dropdown

Primes: Fill in the missing prime numbers in ascending order:

2,​

Select answer

, 5, 7, ​

Select answer

, 13, ​ ​

Select answer

, 19, ​

Select answer

Hotspot

Primes: There are 5 primes and 4 composite numbers in this picture, click on all of the PRIMES:

These are little tricks that help you know if a number can be divided evenly (with no remainder) by another number.
Think back to the lesson I made you write them all out!

Divisibility

Multiple Choice

Divisibility: What number can 436 be divide by?

• 9

• 10

• 5

• 8

Multiple Choice

Divisibility: What number can 365 be divide by?

• 10

• 5

• 2

• None

Multiple Choice

Divisibility: What number can 275 be divide by?

• 12

• 2

• 4

• 11

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

➤ Example: The square root of 49 is 7, because 7 × 7 = 49.
Which makes 49 a square number.

​​Square numbers and square roots

The cube root of a number is the number that, when multiplied by itself three times, gives the original number.

➤ Example: The cube root of 27 is 3, because 3 × 3 × 3 = 27
Which makes 27 a cube number.

​​Cube numbers and cube roots

Hotspot

Square numbers: Click on all the square numbers
*Hint* the first number is 1 because 1 x 1 = 1

Multiple Choice

Square roots: Use the chart to find what the $$\sqrt[]{144}$$ is?

• 9

• 11

• 12

• 6

Multiple Choice

Square roots: Use the chart to find what the $$\sqrt[]{81}$$ is?

• 9

• 11

• 12

• 6

Multiple Choice

Square roots: Use the chart to find what the $$\sqrt[]{25}$$ is?

• 9

• 5

• 10

• 6

Fill in the Blank

Cube Number: What cube number would this make $$4^{3\ }=4\times4\times4\ =$$ ?

Multiple Choice

Cube roots: Use the chart to find what the $$\sqrt[3]{27}$$ is?

• 3

• 5

• 4

• 7

Multiple Choice

Cube roots: Use the chart to find what the $$\sqrt[3]{512}$$ is?

• 3

• 5

• 4

• 8

Multiple Choice

HARD: Evaluate (solve) $$\sqrt[]{25}\ +2^3$$

• 11

• 32

• 100

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