Weekly Maths 18/5/20 Date 18/05/20 LI: To use common factors to simplify fractions
Success criteria: • To work through presentation answering questions • Identify common factors • To recognise equivalent fractions • To use multiplication to find eqiuvalent fractions Revise Use common factors to simplify fractions
Fractions which have the same value, but represent this value using different denominators and numerators, are equivalent. We can recognise and find equivalent fractions by multiplying or dividing the numerator and denominator by the same amount. When we simplify a fraction, we use the highest common factor of the numerator and denominator to reduce the fraction to the lowest term equivalent fraction (simplest form). The highest 15 Factors of 15: 1 15 3 5 common factor is 3. A factor is 36 Factors of 36: 1 36 2 18 3 12 4 9 6 a number which divides ÷ 3 = 5 into another 15 = 5 number 36 ÷ 3 = 12 12 without a remainder Quiz Use common factors to simplify fractions
Simplify this fraction to its lowest terms.
18 72
4 2 1 3 8 8 4 9 Quiz Use common factors to simplify fractions
Which number completes this equivalent fraction sequence?
1 2 3 4 14 28 42 ?
56 52 55 54 Quiz Use common factors to simplify fractions
Which number completes this equivalent fraction pair?
27 3 99 ?
12 18 9 11
! Revise Use common multiples to express fractions in the same denomination
To compare or calculate with fractions, we often need to give them a common denominator.
We do this by looking at the denominators and finding their lowest common multiple.
We can now change the 2 3 fractions to have a
3, 6, 9, 12, 15 5, 10, 15, 20, 25 common denominator of 3 5 15 using multiplication. × 5 = 10 × 3 = 9 Remember that whatever 2 3 we do to the denominator, 3 × 5 = 15 5 × 3 = 15 we have to do to the numerator. Quiz Use common multiples to express fractions in the same denomination What is the lowest common denominator of these two fractions? Remember to look at the denominator and decide whether to multiply or divide. 5 7 12 30
48 120 60 90 Quiz Use common factors to simplify fractions
What is the lowest common denominator of these two fractions?
5 2 14 3
42 28 21 45 Quiz Use common factors to simplify fractions
Express these fractions using the lowest common denominator. 7 3 16 5 Quiz Use common multiples to express fractions in the same denomination
What is the lowest common denominator of these two fractions? 11 13 24 18
72 72 19/5/20 Date 19/05/20 LI: To compare and order fractions, including fractions > 1
Success criteria: • To work through presentation answering questionsTo compare fractions • To order fractions • To compare fractions Revise Compare and order fractions, including fractions > 1
We can order and compare fractions. When comparing fractions, we can use symbols to < > show which is the smaller or the larger fraction. is less is greater than than To compare and order… fractions with fractions with different the same fractions with mixed numbers: denominators: denominators: Simply compare Change the fractions into equivalent Change the mixed number into an the numerators. fractions with the lowest common improper fraction, by multiplying the denominator, then compare the numerators. whole number by the denominator and Remember that whatever we do to the then adding on the numerator. Then, denominator, we must do to the numerator. continue as appropriate. 5 2 5 3 Compare 1 2 and 1 1 > Compare and 7 3 9 9 9 5 9 4 As improper fractions = and The lowest common multiple is 45. 7 3 The lowest common multiple is 21. 5 25 3 27 25 27 9 27 4 28 27 28 = = < = = < 9 45 5 45 45 45 7 21 3 21 21 21 Quiz Compare and order fractions, including fractions > 1
Choose the correct symbol to compare these fractions. Multiply or divide to make the denominators the same. 5 4 8 7 What can you do to the denominator to make this easier? < > Quiz Compare and order fractions, including fractions > 1
Choose the correct symbol to compare these fractions.
7 3
Whatever you 12 7 do to the top denominator, you must do to the top value < > Compare and Order Fractions Which fraction is greater in each pair?
3 4 or 9 8 7 9 or 3 2 3 18 4 or 20 5 9 7 or 14 2 29 3 or 36 Quiz TOP TIP! Change the denominators so they can be equal
Choose the correct symbol to compare these fractions. Remember to change the denominators. 1 3 1 8 4 9
< > Quiz Compare and order fractions, including fractions > 1
Choose the correct symbol to compare these fractions.
1 3 1 2 5 3
< > Quiz Compare and order fractions, including fractions > 1
Which of these fractions is the smallest? Make the denominators the same.
13 5 9 15 6 10
! Quiz Compare and order fractions, including fractions > 1
Which of these fractions is the greatest?
2 3 1 5 12 3 20/5/20 Date 20/05/20 LI: To add subtract fractions with different denominators and mixed numbers
Success criteria: • To work through presentation answering questions • To add and subtract fractions • To compare fractions Revise Add and subtract fractions with different denominators and mixed numbers When we add and subtract fractions with different denominators, we need to give them a common denominator. We use the lowest common multiple as the common denominator to create equivalent fractions which we can then add and subtract.
If one of the fractions is a multiple of the If the fractions aren’t multiples of each other, other, use multiplication to change the use multiplication to change them both to smaller denominator to the same denominator the lowest common denominator. as the other fraction. 5 2 8 3 + = - = 9 3 9 4 5 2×3 6 8×4 32 3×9 27 + = = = 9 3×3 9 9×4 36 4×9 36 5 6 11 2 32 27 5 + = = 1 - = 9 9 9 9 36 36 36 Revise Add and subtract fractions with different denominators and mixed numbers If the fractions involve adding or subtracting mixed numbers, there are two methods that can be used.
Add the whole numbers and the fractions Convert the mixed numbers to improper separately. fractions.
To changed mixed number fractions, multiply the denominator with the whole number then add that to 3 1 the numerator. 2 + 3 = 5 4 5 1 2 - 1 = 2 + 3 = 5 6 5 17 6 85 36 49 3 1 12 5 17 - = - = + = + = 6 5 30 30 30 5 4 20 20 20 17 17 49 19 5 + = 5 = 1 20 20 30 30 Quiz Add and subtract fractions with different denominators and mixed numbers
What is the answer to this fraction addition?
4 2 9 + 5
6 6 38 14 45 45 Quiz Add and subtract fractions with different denominators and mixed numbers
What is the answer to this fraction addition?
5 4 8 + 7
9 10 1 1 11 1 56 56 56 Add and Subtract Fractions with Different Denominators
For each pair of fractions, find the ‘lowest common denominator’ and complete the calculation: 1 1 + = 2 3
4 2 + = 5 9
2 4 + = 3 5
3 7 + = 6 9 Quiz Add and subtract fractions with different denominators and mixed numbers
What is the answer to this fraction subtraction?
8 3 9 - 4
5 5 24 36 5 36 21/5/20 Date 21/05/20 LI: To multiply and divide fractions
Success criteria: • To work through presentation answering questions • To multiply fractions • To divide fractions Revise Multiply simple pairs of proper fractions, writing the answer in its simplest form
When we multiply fractions by whole numbers or other fractions, we can think of the multiplication sign as the word ‘of’. 1 1 × 15 = 5 is the same as of 15 = 5 3 3
Multiplying a proper fraction by a Multiplying pairs of proper Cancelling out whole number fractions 5 5 2 × 4 × Sometimes, there is no need to 9 6 3 calculate at all. If the numerator Whole numbers can be written as Calculate the answer by and denominator of the different fractions with a denominator of 1. multiplying the numerators and fractions are the same, they cancel 4 So 4 = then multiplying the 1 each other out. denominators. 4 3 5 2 10 × = The calculation is now written, × = 5 4 5 4 6 3 18 9 × 1 The numerator on the first fraction Sometimes, an answer will need cancels out the denominator on the To calculate the answer, multiply simplifying by finding the highest second fraction, leaving us with the numerators and then multiply common factor. the numerator 3 and the the denominators. The highest common factor of 10 denominator 5, which is the 5 4 20 20 2 answer to the calculation in its 9 × 1 = 9 9 = 2 9 and 18 is 2. 10 5 simplest form. 18 = 9 4 3 3 5 × 4 = 5 Quiz Multiply simple pairs of proper fractions, writing the answer in its simplest form
What is the answer to this fraction multiplication? When multiplying fractions, you multiply the numbers diagonally
3 × 1 5 8
3 4 6 40 40 40 Quiz Multiply simple pairs of proper fractions, writing the answer in its simplest form
What is the answer to this fraction multiplication?
8 5 9 × 6
45 20 20 54 27 54 Quiz Multiply simple pairs of proper fractions, writing the answer in its simplest form
What is the answer to this fraction multiplication?
3 2 8 × 3
8 2 1 24 6 4 Revise Divide proper fractions by whole numbers
Multiplication and division are inverse operations of each other. 1 1 1 ÷ 5 × ÷ 7 × ÷ 10 × is the same as 5 is the same as 7 is the same as 10 When we divide a proper fraction by a whole number, we actually use multiplication.
5 3 5 ÷ 6 = ÷ 10 = 9 8 ÷ 4 = 6
5 1 3 1 5 1 × = × = 9 6 8 × 4 = 6 10
5 × 1 5 3 × 1 3 5 × 1 5 1 = = = = 9 × 6 54 8 × 4 32 6 × 10 60 12 Quiz Divide proper fractions by whole numbers
What is the answer to this fraction division?
2 5 ÷ 7
14 2 14 5 35 35
! Quiz Divide proper fractions by whole numbers
What is the answer to this fraction division?
3 8 ÷6
18 18 1 6 48 16 Quiz Divide proper fractions by whole numbers
What is the answer to this fraction division?
5 9 ÷12
5 60 60 108 9 108 You can also divide proper fractions with each 2 3 other. ÷ 3 7 To calculate this sum, you need to change the division symbol to a multiplication X. After this, you will flip the fraction on the right 3 7 side upside down, so it reads . 7 3 2 7 14 Now you will do x = If you want to 3 3 9 5 simplify this, it will = 1 9 3 3 ÷ 5 4 8 3 4 5 ÷ ÷ 7 5 9 6
2 8 7 2 1 7 ÷ ÷ ÷ 4 7 9 6 4 5 Revise Calculate fractions of an amount
To calculate fractions of an amount, there are different methods to choose from.
Using fractions of an Multiplying the unit Subtracting from the amount to find the fraction total amount whole 5 6 5 of 981 = of 371 = of ? = 335 9 7 8 Divide the amount by the Divide the amount by the Divide the amount by the denominator to find the unit denominator to find the unit numerator to find the unit fraction. fraction. fraction. 1 1 1 of 981 = 981 ÷ 9 = 109 of 371 = 371 ÷ 7 = 53 335 ÷ 5 = 67 so = 67 9 7 8 Multiply the unit fraction amount Subtract this unit fraction from Multiply the unit fraction amount by the numerator. the total amount. by the denominator to find the whole. 5 6 of 981 = 109 × 5 = 545 of 371 = 371 − 53 = 318 9 7 67 × 8 = 536 4/5 of 20
20 divided by 5 = 4 4 x 4 = 16 16 = 4/5 of 20
¾ of 48
48 divided by 4 = 12 3 x 12 = 36 36= ¾ of 48 Quiz Calculate fractions of an amount
What is the answer to this fraction calculation? Divide 486 by 9 then times the answer by 4.
4 of 486 9
216 54 270 Quiz Calculate fractions of an amount
What is the answer to this fraction calculation?
7 of 8 616
77 539 462 22/5/20 Date 22/05/20 LI: To order and compare numbers with up to three decimal places and convert decimals into fractions
Success criteria: • To work through presentation answering questions • To compare decimals • To convert decimals into fractions Quiz Order and compare numbers with up to three decimal places
Choose the correct symbol to compare these decimal numbers.
0.436 0.416
< > Quiz Order and compare numbers with up to three decimal places
Choose the correct symbol to compare these decimal numbers.
0.013 0.103
< > Quiz Order and compare numbers with up to three decimal places
Choose the correct symbol to compare these decimal numbers.
1024.663 1024.673
< > Revise Recall and use equivalences between simple fractions, decimals and percentages
Fractions, decimals and percentages are all different ways of expressing a proportion. A percentage is a proportion out of one hundred. The sign % stands for 'per cent' which means 'out of 100’. Here are some fraction, percentage and decimal equivalents that we can learn as facts: Fraction Percentage Decimal 1 50% 0.5 2 1 25% 0.25 4 3 75% 0.75 4 1 20% 0.2 5 1 10% 0.1 10 Revise Recall and use equivalences between simple fractions, decimals and percentages
For trickier equivalents, we can use the rules in this diagram to help us:
Percentage to 3 Fraction to Fraction 5 Write the percentage as a Fraction Decimal fraction with a Divide the numerator denominator of 100 and by the denominator. then simplify. 3 = 3 ÷ 5 = 0.6 60 6 3 5 = = 100 10 5
60% 0.6 Percentage Decimal to Percentage Multiply the decimal by 100 and add the % sign. Decimal 0.6 x 100 = 60% Quiz Recall and use equivalences between simple fractions, decimals and percentages
Convert this decimal into a percentage.
0.467
467% 46% 46.7% Quiz Recall and use equivalences between simple fractions, decimals and percentages
Convert this decimal into a fraction. The answers has been simplified
0.35
7 7 7 5 20 100 Convert the following decimals into fractions and percentages
0.37 0.72 0.96 0.56 0.43 0.03 0.84