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# Math mind map

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by

Tweet## martin bendico

on 25 January 2013#### Transcript of Math mind map

8 12 There are two ways to estimate front-end estimation and benchmarking. For front end estimation just take the first number and use them to do the question. For benchmarks you round to the number it already is if it is 4 or less if it is 5 or more you round one number up. Math Mind Map Chapter 3 3.1: Fractions to Decimals By: Martin Bendico, Cameron Laveck, and Jacob Skitsko Numbers can be written in both fraction and decimal form .For example 4 can be written as 4 and also 4.0

1

1

10 means 1 divided by 10 or 1 tenth

remember that 1 is 0.1 in decimal form, to convert a decimal into a fraction try to make the denominator 10, 100, or 1000 first ( adjust the numerator accordingly) for example if the number is 2 you would multiply both the numerator and the denominator by 2, to get 4 10 These are examples of fractions in decimal form and decimals in fraction form. 6 5 18 18 10 100 100 10000 0.6 0.05 0.18 0.018 fraction decimal Decimals such as 0.7 and 0.63 are called terminating decimals; they have a definite number of decimal places.

A decimal such as 0.3333333 and so on are known as repeating decimals; they go on infinitely (the numbers under the dash are what repeat). The proper way to write this example of repeating decimals would be 0.3 Remember how to use benchmarks 0,1 and 1 to order and compare fractions for example, 1 you would round to 0 because it is closer to 0 then 1 or 1. But 6 would be rounded to 1 because it is closer to it then 1 or 0. 9 Would be rounded to 1 because it is closer to 1 then 1 or 0, because the numerator and denominator are close in value. 2 10 2 10 2 10 2 Use benchmarks to order the fractions. One way to order them is on a number line. Another way to order fractions is to give them a common denominator. By multiplying the numerators and denominators by the same number to get a denominator that all the fractions that you're trying to order can have for example; 3 9 5 x3 x3 15 Patterns occasionally occur when turning fractions to decimals and vice versa ; for example whatever the numerator is when it's over the denominator of 9 it will be a repeating decimal of the numerator. As an example, 7 over 9 would be 0.7. If we don't need an exact answer we can just estimate. We can also estimate to see if our answer that we got is reasonable. Adding and subtracting decimals is otherwise the same as normal addition or subtraction. Any fraction greater than 1 could be written as a mixed number.

The benchmarks 0,1could be use to compare the

fraction parts of mixed numbers. to order these on to a number line you would have to turn them all into the same type of fraction.For this question we are going to turn all of them into mixed number fractions 2 16 6 10 20 If the quotient is not a terminating decimal then use paper and pencil. For example; Divide 39.2/0.9. First estimate, 39.2 is close to 40 and 0.9 is close to 1 so the answer will be close to 40,divide like you would the whole numbers; 392/9. After that add on however many decimal places there were, in this example there's 2 decimal points so we move 2 decimal points in from the left. 3 7 3 1 1 2 14 9 1 6 12 , , , , 3 14 1 1 2 6 12 , , can stay the same 14 9 14 3 would be 1 5 9 3.6 Order of Operations with Decimals 3.7 Relating Fractions, Decimals, and Percents in mixed number form. would be 4 2 3 in mixed number form. Percent means per one hundred

36% is 36 and 0.36 100 Do you remember what BEDMAS stands for?

It's the order you do Order of Operations in, Brackets, Exponents, Division/Multiplication and Addition/Subtraction

you just go left to right, same with Addition/Subtraction.

For example, for 12.376 : (4.75 + 1.2) + 2.45 x 0.2 - 1.84

you would do the brackets( ) first, then division; it's closest to the left; followed by multiplication; it's farther to the right; the addition and subtraction from right to left. If you get 0.73 then you did it right. We can use number lines to show how percents relate to fractions, and decimals. For example; 0.5 50% 50 100 8 100 100% 100 1 0 0% 100 0 Simply, this is the same as normal Order of Operations if you already know how to multiply, divide, subtract, and add with decimals; which we already reviewed. Decimals, and fractions can be written as percents also, for example; 0.26 =26 =26% 100 3.8 Solving Percent Problems 96 =0.96= 96% 100 To write a fraction as a percent find an equivalent fraction with a denominator of 100 if the number is 2 digit, 10 if it's 1 digit 1000 if it's 3; and so on. Hello! My name is Andrew Wiles, and to day I will be teaching you all about fractions and decimals, with percents of course! Now, let us waste no further time, our first subject will be "Fractions to Percents". 6 5 18 18 1.Write each fraction as a decimal.

a) 5 b) 4 c) 8

2.Write each decimal as a fraction. a) 0.6 b) 0.16 c) 0.41

3.Write each fraction as a decimal then explain the pattern you see, answer d) e) and f) with the pattern ( convert d), e) and f) to fractions ).

a) 999 b) 999 c) 999

d) 0.004 e) 0.018 f) 0.205 1 54 115 5 10 Example Questions 3.2 Comparing and Ordering fractions and Decimals 3.3 Adding and Subtracting Decimals 3.4 Multiplying Decimals 3.5 Dividing Decimals The way to order these fractions and mixed numbers from least to greatest would be

3, 6, 14, 1 , 14 2 9 If you remember how to multiply 2 whole numbers using base ten blocks this next part will be simple, this

shows 20 x 16 = 100

+ 100 + 60 + 60 + 320.

In this way we can

also multiply

decimals. Instead of

the big cube

showing 100, it will

represent 1. The rod

shows 0.1 and the

small cube shows

0.01. 1 3 However there is another way of multiplying decimals.

For this example I will explain it by showing you how to use this tool. For this we would multiply the 1 by the 2, the 1 by the

0.5, the 2 by the

0.6 and lastly

the 0.5 by the 0.6.

You would

then put the

answers to

these questions

in the crossing box's of those numbers. Then finally add all of these up for you final answer. 1 0.6 2

0.5 Example Questions 1.Order each set of numbers from least to greatest: a) 1,1-, -,- b) 2-,3,-,-

2. a) Use any method to order these numbers from greatest to least, explain the method.

b) Use a different method-verify you answer in a)

-, 1, 3-, , 2

3.Identify the number that isn't in the correct order: show where it should go and explain.

a) -, 6-, 6.25, 6- b) 1-, 1-, -, 1.2, - Example Questions 1. Use front-end estimation to estimate the sum/difference. a) 2.876 - 0.975 b) 9.7 - 1.36

c) 71.382 + 6.357 d) 125.12 + 37.84

2. Find 2 numbers with the difference of 151.297.

3. Use each of the digits from 0-7 to make this true, find as many answers as you can.

[ ].[ ][ ][ ] + [ ].[ ][ ][ ] = 5.788 Example Questions 1. Multiply: a) 2.6 x 1.5 b) 2.3 x 0.4 c) 0.8 x 0.7

2. The fuel consumption rates on Josie's car is Highway: 23.3km/L and City: 21.2km/L. The car holds 40.2L of fuel.

a) How far could Josie drive on a full tank on the highway before she ran out?

b) How far could she drive on a full tank in the city? What assumptions did you make?

3. a) Multiply 18 x 12 b) Use only your answer and estimation to find the following:

i) 1.8 x 12 ii) 18 x 0.12 iii) 0.18 x 12 iv) 0.18 x 0.12 Let's say a 1L jug of juice costs $7.99, and is on sale for 15%. To find out how much you save, calculate 15% of $7.99 : 15% = = 0.15. So 15% of $7.99 = 0.15 x $7.99.

We would round the answer to

the nearest cent, so instead of

being $1.1985 it's $1.20. To

calculate the price we're paying

, or the sales price we find out

how much percent we aren't

saving on, so in this case 85%, then we repeat the process with the new numbers to find the sales price, not just how much we're saving. 15

100 We can show how much we're saving on a number line: Now we can estimate to check if our answer is accurate, 15% is nearly 20% which is and $7.99 is nearly $10. So we say of 10 (2) is about 15% of $7.99, which is close to 10. 2 is close to our answer so we can say it's reasonable. 0 $1.20 $7.99

(15%) (100%) 1

5 1

5 Example Questions 1. Calculate: a) 10% of 30 b) 18% of 36 c) 67% of 112

2. The regular price of a computer game is $60, Find the sale price before taxes: a) 25% off b) 30% off c) 40% off

3. The GST tax is currently 5%, find the GST and the cost of the item of both a) and b). a) bike: $129 b) DVD: $24.99 Example Questions 1. Write each percent as a decimal and a fraction

a) 2% b) 9% c) 28% d) 94%

2. Fred had on a test, Jane had 82% on a test. Who did better and how do you know?

3.Suppose each pattern is continued on a hundred chart and the numbers in the pattern are red. For each pattern, what percent of the numbers are red? a) 4, 8, 12, 16, 20...

b)1, 3, 5, 7... c) 2, 4, 8, 16... d) 1, 3, 7, 17... 8

10 Example Questions 1. Evaluate: a) 4.6 + 5.1 - 3.2

b) 46.4 - 10.8 x 3 c) 85.6 - 0.4 x 7

2. Evaluate, then explain why the answers are different.

a) 9.8 - 3.2 - 0.4 + 2.6 b) (9.8 - 3.2) - (0.4 + 2.6)

3. Use at least 4 of the numbers from 0.1-0.9 and any operation or brackets to make each whole number from 1-5. : : : We can also divide with base 10 blocks! Since multiplication and division are related this is possible. However this particular strategy doesn't work with repeating decimals. That's where the previous strategy comes in. Example Questions 1. Divide: a) 0.8 - 0.1 b) 1.2 - 0.3 c) 2.7 - 0.6

2. Use front-end estimation to check your answers and round them to the nearest tenth, divide. a) 8.36 - 2.4 b) 1.98 - 1.3

c) 27.82 - 3.9 d) 130.4 - 5.4

3. Alicia worked 37.5 h and earned $346.88. How much money did she earn per hour and why is the answer different if you use a calculator? : : : : : : : 7

6 15

12 2

9 10

4 1

3 9

2 17

5 1

4 2

20 29

5 2

10 3

8 3

2 7

16 3

4 Answer Key 3.1

1. a) 0.5 b) 0.4 c) 0.8

2. a) 6 b) 16 c) 41

3. a) 0.001 b) 0.054 c) 0.115

d) 4 e)18 f)205

3.2 1.

a)1, 7, 15, 1 b)2 ,2 ,3,4

2. 1,2,17, 3

3.29,6 , 6 b)1 ,1 1.2,3,3

0.5

3.3

1.a)1905b)8.6c)7775d)162.96

2.151.297-253.891

3.2.894+2.894

3.4

1.a)3.9b)2.116c)0.56

b)i)21.6ii)2.16iii)2.16iv)0.o216

3.5

1.a)3b)0.5c)0.598

2.a)273b)210c)1575

3.64.5b)12.495

1.a)52.4b)-14c)1498

2.a)8b)2.8

3.52.4

3.7

1.a)o.2b).9c0o.24d)o.94

2.jane

3.25%

3.8

1.a)163.636b)90.909c)20

2.a)2580b)499.8c)859.4

3.213 10 10 10 10 100 100 999 999 999 12 9 2 1 3 2 4 1 4 5 1 4 5 2 10 2 20 7 10 3 8 2 4 Example Questions 1. Find the sale price before the taxes of each item. a) coat: 55% off $90 b) shoes: 45% off $40

c) sweater: 30% off %50

2. The GST tax is at 5%, for each item find the GST and price including GST. a) bike: $129

b) $24.99 c) skateboard: $42.97

3. There are 641 First Nations bands in Canada, about 30% of these are in B.C. About how many bands are in B.C.

Full transcript1

1

10 means 1 divided by 10 or 1 tenth

remember that 1 is 0.1 in decimal form, to convert a decimal into a fraction try to make the denominator 10, 100, or 1000 first ( adjust the numerator accordingly) for example if the number is 2 you would multiply both the numerator and the denominator by 2, to get 4 10 These are examples of fractions in decimal form and decimals in fraction form. 6 5 18 18 10 100 100 10000 0.6 0.05 0.18 0.018 fraction decimal Decimals such as 0.7 and 0.63 are called terminating decimals; they have a definite number of decimal places.

A decimal such as 0.3333333 and so on are known as repeating decimals; they go on infinitely (the numbers under the dash are what repeat). The proper way to write this example of repeating decimals would be 0.3 Remember how to use benchmarks 0,1 and 1 to order and compare fractions for example, 1 you would round to 0 because it is closer to 0 then 1 or 1. But 6 would be rounded to 1 because it is closer to it then 1 or 0. 9 Would be rounded to 1 because it is closer to 1 then 1 or 0, because the numerator and denominator are close in value. 2 10 2 10 2 10 2 Use benchmarks to order the fractions. One way to order them is on a number line. Another way to order fractions is to give them a common denominator. By multiplying the numerators and denominators by the same number to get a denominator that all the fractions that you're trying to order can have for example; 3 9 5 x3 x3 15 Patterns occasionally occur when turning fractions to decimals and vice versa ; for example whatever the numerator is when it's over the denominator of 9 it will be a repeating decimal of the numerator. As an example, 7 over 9 would be 0.7. If we don't need an exact answer we can just estimate. We can also estimate to see if our answer that we got is reasonable. Adding and subtracting decimals is otherwise the same as normal addition or subtraction. Any fraction greater than 1 could be written as a mixed number.

The benchmarks 0,1could be use to compare the

fraction parts of mixed numbers. to order these on to a number line you would have to turn them all into the same type of fraction.For this question we are going to turn all of them into mixed number fractions 2 16 6 10 20 If the quotient is not a terminating decimal then use paper and pencil. For example; Divide 39.2/0.9. First estimate, 39.2 is close to 40 and 0.9 is close to 1 so the answer will be close to 40,divide like you would the whole numbers; 392/9. After that add on however many decimal places there were, in this example there's 2 decimal points so we move 2 decimal points in from the left. 3 7 3 1 1 2 14 9 1 6 12 , , , , 3 14 1 1 2 6 12 , , can stay the same 14 9 14 3 would be 1 5 9 3.6 Order of Operations with Decimals 3.7 Relating Fractions, Decimals, and Percents in mixed number form. would be 4 2 3 in mixed number form. Percent means per one hundred

36% is 36 and 0.36 100 Do you remember what BEDMAS stands for?

It's the order you do Order of Operations in, Brackets, Exponents, Division/Multiplication and Addition/Subtraction

you just go left to right, same with Addition/Subtraction.

For example, for 12.376 : (4.75 + 1.2) + 2.45 x 0.2 - 1.84

you would do the brackets( ) first, then division; it's closest to the left; followed by multiplication; it's farther to the right; the addition and subtraction from right to left. If you get 0.73 then you did it right. We can use number lines to show how percents relate to fractions, and decimals. For example; 0.5 50% 50 100 8 100 100% 100 1 0 0% 100 0 Simply, this is the same as normal Order of Operations if you already know how to multiply, divide, subtract, and add with decimals; which we already reviewed. Decimals, and fractions can be written as percents also, for example; 0.26 =26 =26% 100 3.8 Solving Percent Problems 96 =0.96= 96% 100 To write a fraction as a percent find an equivalent fraction with a denominator of 100 if the number is 2 digit, 10 if it's 1 digit 1000 if it's 3; and so on. Hello! My name is Andrew Wiles, and to day I will be teaching you all about fractions and decimals, with percents of course! Now, let us waste no further time, our first subject will be "Fractions to Percents". 6 5 18 18 1.Write each fraction as a decimal.

a) 5 b) 4 c) 8

2.Write each decimal as a fraction. a) 0.6 b) 0.16 c) 0.41

3.Write each fraction as a decimal then explain the pattern you see, answer d) e) and f) with the pattern ( convert d), e) and f) to fractions ).

a) 999 b) 999 c) 999

d) 0.004 e) 0.018 f) 0.205 1 54 115 5 10 Example Questions 3.2 Comparing and Ordering fractions and Decimals 3.3 Adding and Subtracting Decimals 3.4 Multiplying Decimals 3.5 Dividing Decimals The way to order these fractions and mixed numbers from least to greatest would be

3, 6, 14, 1 , 14 2 9 If you remember how to multiply 2 whole numbers using base ten blocks this next part will be simple, this

shows 20 x 16 = 100

+ 100 + 60 + 60 + 320.

In this way we can

also multiply

decimals. Instead of

the big cube

showing 100, it will

represent 1. The rod

shows 0.1 and the

small cube shows

0.01. 1 3 However there is another way of multiplying decimals.

For this example I will explain it by showing you how to use this tool. For this we would multiply the 1 by the 2, the 1 by the

0.5, the 2 by the

0.6 and lastly

the 0.5 by the 0.6.

You would

then put the

answers to

these questions

in the crossing box's of those numbers. Then finally add all of these up for you final answer. 1 0.6 2

0.5 Example Questions 1.Order each set of numbers from least to greatest: a) 1,1-, -,- b) 2-,3,-,-

2. a) Use any method to order these numbers from greatest to least, explain the method.

b) Use a different method-verify you answer in a)

-, 1, 3-, , 2

3.Identify the number that isn't in the correct order: show where it should go and explain.

a) -, 6-, 6.25, 6- b) 1-, 1-, -, 1.2, - Example Questions 1. Use front-end estimation to estimate the sum/difference. a) 2.876 - 0.975 b) 9.7 - 1.36

c) 71.382 + 6.357 d) 125.12 + 37.84

2. Find 2 numbers with the difference of 151.297.

3. Use each of the digits from 0-7 to make this true, find as many answers as you can.

[ ].[ ][ ][ ] + [ ].[ ][ ][ ] = 5.788 Example Questions 1. Multiply: a) 2.6 x 1.5 b) 2.3 x 0.4 c) 0.8 x 0.7

2. The fuel consumption rates on Josie's car is Highway: 23.3km/L and City: 21.2km/L. The car holds 40.2L of fuel.

a) How far could Josie drive on a full tank on the highway before she ran out?

b) How far could she drive on a full tank in the city? What assumptions did you make?

3. a) Multiply 18 x 12 b) Use only your answer and estimation to find the following:

i) 1.8 x 12 ii) 18 x 0.12 iii) 0.18 x 12 iv) 0.18 x 0.12 Let's say a 1L jug of juice costs $7.99, and is on sale for 15%. To find out how much you save, calculate 15% of $7.99 : 15% = = 0.15. So 15% of $7.99 = 0.15 x $7.99.

We would round the answer to

the nearest cent, so instead of

being $1.1985 it's $1.20. To

calculate the price we're paying

, or the sales price we find out

how much percent we aren't

saving on, so in this case 85%, then we repeat the process with the new numbers to find the sales price, not just how much we're saving. 15

100 We can show how much we're saving on a number line: Now we can estimate to check if our answer is accurate, 15% is nearly 20% which is and $7.99 is nearly $10. So we say of 10 (2) is about 15% of $7.99, which is close to 10. 2 is close to our answer so we can say it's reasonable. 0 $1.20 $7.99

(15%) (100%) 1

5 1

5 Example Questions 1. Calculate: a) 10% of 30 b) 18% of 36 c) 67% of 112

2. The regular price of a computer game is $60, Find the sale price before taxes: a) 25% off b) 30% off c) 40% off

3. The GST tax is currently 5%, find the GST and the cost of the item of both a) and b). a) bike: $129 b) DVD: $24.99 Example Questions 1. Write each percent as a decimal and a fraction

a) 2% b) 9% c) 28% d) 94%

2. Fred had on a test, Jane had 82% on a test. Who did better and how do you know?

3.Suppose each pattern is continued on a hundred chart and the numbers in the pattern are red. For each pattern, what percent of the numbers are red? a) 4, 8, 12, 16, 20...

b)1, 3, 5, 7... c) 2, 4, 8, 16... d) 1, 3, 7, 17... 8

10 Example Questions 1. Evaluate: a) 4.6 + 5.1 - 3.2

b) 46.4 - 10.8 x 3 c) 85.6 - 0.4 x 7

2. Evaluate, then explain why the answers are different.

a) 9.8 - 3.2 - 0.4 + 2.6 b) (9.8 - 3.2) - (0.4 + 2.6)

3. Use at least 4 of the numbers from 0.1-0.9 and any operation or brackets to make each whole number from 1-5. : : : We can also divide with base 10 blocks! Since multiplication and division are related this is possible. However this particular strategy doesn't work with repeating decimals. That's where the previous strategy comes in. Example Questions 1. Divide: a) 0.8 - 0.1 b) 1.2 - 0.3 c) 2.7 - 0.6

2. Use front-end estimation to check your answers and round them to the nearest tenth, divide. a) 8.36 - 2.4 b) 1.98 - 1.3

c) 27.82 - 3.9 d) 130.4 - 5.4

3. Alicia worked 37.5 h and earned $346.88. How much money did she earn per hour and why is the answer different if you use a calculator? : : : : : : : 7

6 15

12 2

9 10

4 1

3 9

2 17

5 1

4 2

20 29

5 2

10 3

8 3

2 7

16 3

4 Answer Key 3.1

1. a) 0.5 b) 0.4 c) 0.8

2. a) 6 b) 16 c) 41

3. a) 0.001 b) 0.054 c) 0.115

d) 4 e)18 f)205

3.2 1.

a)1, 7, 15, 1 b)2 ,2 ,3,4

2. 1,2,17, 3

3.29,6 , 6 b)1 ,1 1.2,3,3

0.5

3.3

1.a)1905b)8.6c)7775d)162.96

2.151.297-253.891

3.2.894+2.894

3.4

1.a)3.9b)2.116c)0.56

b)i)21.6ii)2.16iii)2.16iv)0.o216

3.5

1.a)3b)0.5c)0.598

2.a)273b)210c)1575

3.64.5b)12.495

1.a)52.4b)-14c)1498

2.a)8b)2.8

3.52.4

3.7

1.a)o.2b).9c0o.24d)o.94

2.jane

3.25%

3.8

1.a)163.636b)90.909c)20

2.a)2580b)499.8c)859.4

3.213 10 10 10 10 100 100 999 999 999 12 9 2 1 3 2 4 1 4 5 1 4 5 2 10 2 20 7 10 3 8 2 4 Example Questions 1. Find the sale price before the taxes of each item. a) coat: 55% off $90 b) shoes: 45% off $40

c) sweater: 30% off %50

2. The GST tax is at 5%, for each item find the GST and price including GST. a) bike: $129

b) $24.99 c) skateboard: $42.97

3. There are 641 First Nations bands in Canada, about 30% of these are in B.C. About how many bands are in B.C.