More Division

Skills PracticeCarnegie Learning 4.7

More Division

Skills PracticeCarnegie Learning 4.7

Make sure you take notes AND complete the problems in your book while I do them on the video.

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ryDecimals Decimals are like fractions in that they represent a portion of a whole number. They represent values in tenths, hundredths, thousandths, and so on.

Repeating Decimal- A repeating decimal is a decimal number that has a digit (or block of digits) that repeat over and over again without ever ending. http://www.virtualnerd.com/middle-math/number-theory-fractions/fractions-decimals/repeating-decimal-definition

Terminating Decimal– Unlike a repeating decimal, is a decimal that, when you divide the numerator by the denominator of a fraction, you end up at some point with a decimal that ends (it has a finite number of digits. http://www.virtualnerd.com/pre-algebra/rational-numbers/definitions-basics/convert-decimals-fractions/fraction-to-terminating-decimal-conversion

Voca

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ryDecimals Decimals are like fractions in that they represent a portion of a whole number. They represent values in tenths, hundredths, thousandths, and so on.

Benchmark Decimal - similar to a benchmark fraction in that it is a commonly used decimal that you use as a standard to measure other decimals. For example, 0.25, or 0.5, or 0 or 1.

Round (as in ”rounding a number”) – When you round a number, you re-write it to an easier to use form that is close to the original number, but isn’t exact. For example, 18 can be rounded to 20, or 257 can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

Voca

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ryQuotient

When you round a number, you re-write it to an easier to use form that is close to the original number, but isn’t exact. For example, 18 can be rounded to 20, or 257 can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

DivisorWhen you round a number, you re-write it to an easier to use form that is close to the original number, but isn’t exact. For example, 18 can be rounded to 20, or 257 can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

Dividend

When you round a number, you re-write it to an easier to use form that is close to the original number, but isn’t exact. For example, 18 can be rounded to 20, or 257 can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

23635 14,604

Voca

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ryQuotient

The answer in a division problem..xact. For example, 18 can be rounded to 20, or 257

can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

DivisorThe thing doing the dividing in a division problem.it \to use form that is close to the original number, but isn’t exact. For example, 18 can be rounded to 20, or 257 can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

DividendThe thing being divided up in a division problem.

/2

635 14,604

Voca

bula

ryQuotient

The answer in a division problem..xact. For example, 18 can be rounded to 20, or 257

can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

DivisorThe thing doing the dividing in a division problem.it \to use form that is close to the original number, but isn’t exact. For example, 18 can be rounded to 20, or 257 can be rounded to 250. 8/15 can b rounded to the benchmark fraction of 1/2

DividendThe thing being divided up in a division problem.

/2

23635 14,604

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ?

Long

Div

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nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

Start by changing the decimals to a fraction with 10, 100, 1000 (etc.) as a denominator.

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

24, 380 = 4600

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Multiply

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

24, 380 = 4600

5 1380 = 4600

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Multiply

Change to a mixed number

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

24, 380 = 4600

5 1380 = 4600

5 3 = 10

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Multiply

Change to a mixed number

Simplify. Stop when you have a denominator that is a power of 10 (even if it isn’t completely simplified.)

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

24, 380 = 4600

5 1380 = 4600

5 3 = 10

5.3 =

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Multiply

Change to a mixed number

Simplify. Stop when you have a denominator that is a power of 10 (even if it isn’t completely simplified.

Change your number back into a decimal.

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

24, 380 = 4600

5 1380 = 4600

5 3 = 10

5.3 =

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Multiply

Change to a mixed number

Simplify. Stop when you have a denominator that is a power of 10 (even if it isn’t completely simplified.

Change your number back into a decimal.

Do #2-6 on pages 451 & 452.

Long

Div

isio

nEven though most of you liked to change fractions to decimals to work with them, some of you are changing decimals to fractions and then solving the problem. THIS LESSON IS FOR YOU!!

1. 24.38 ÷ 4.6 = ? 2438 ÷ 46 = 100 10

2438 X 10 = 100 46

24, 380 = 4600

5 1380 = 4600

5 3 = 10

5.3 =

Start by changing the decimals to a fraction with 10, 100, 1000 (etc) as a denominator.

Change our multiplication problem into a division problem (multiply the first number by the reciprocal of the 2nd number).

Multiply

Change to a mixed number

Simplify. Stop when you have a denominator that is a power of 10 (even if it isn’t completely simplified.

Change your number back into a decimal.

Do #2-6 on pages 451 & 452.

If your number doesn’t end up with a denominator that is a power of 10, then use your superpower of turning a fraction into a decimal.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

In this case, you would multiply it by 10 (or move the decimal point one place to the right so that it is after the 5.)

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

In this case, you would multiply it by 10 (or move the decimal point one place to the right so that it is after the 5.

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

In this case, you will also multiply the dividend by 10, so that you are keeping the dividend and divisor in the same proportion.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

In this case, you will also multiply the dividend by 10, so that you are keeping the dividend and divisor in the same proportion.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

25 6 9 2

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

Your new problem looks like this:

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 69.2 ÷ 2.5 = ? 2.5 69.2

25 6 9 2

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

Your new problem looks like this:

Then, simply divide as normal.

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 32.164 ÷ 7.04 = ? 7.04 3 2 . 1 6 4

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

Your new problem looks like this:

Then, simply divide as normal.Let’s try

another one!!

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 32.164 ÷ 7.04 = ? 7.04 3 2 . 1 6 4

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

Your new problem looks like this:

Then, simply divide as normal.Let’s try

another one!!

Long

Div

isio

nDividing by a decimal number really isn’t very different from dividing by a number without a decimal. Some of you already know this technique, but it’s important to know WHY it works. (really, this will help you with algebra later).

1. 32.164 ÷ 7.04 = ? 7.04 3 2 . 1 6 4

Look at your divisor to decide what you would need to multiply it by to make it a whole number.

You need to multiply your dividend by that same number.

Your new problem looks like this:

Then, simply divide as normal.

Do problems 7-12 on pages 452 and 453.

Long

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isio

n

1. 5 0 . 3 2 ÷ 6 . 8 = 7 . 4

You will need to do some estimating..

Somehow, you need to come up with a division problem that is less than 10.

Where does that decimal point go???

Long

Div

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n

1. 5 0 . 3 2 ÷ 6 . 8 = 7 . 4

You will need to do some estimating..

Somehow, you need to come up with a division problem that is less than 10.

For example, 50/10 is 5(sorta 10).

Where does that decimal point go???

Long

Div

isio

n

1. 5 0 . 3 2 ÷ 6 . 8 = 7 . 4

You will need to do some estimating..

Somehow, you need to come up with a division problem that is less than but near 10.

Where does that decimal point go???

Try another way: What about 500 / 68? Would that work?

Long

Div

isio

n

1. 5 0 . 3 2 ÷ 6 . 8 = 7 . 4

You will need to do some estimating..

Somehow, you need to come up with a division problem that is less than but near 10.

For example, 50/10 is 5(sorta 10).

Where does that decimal point go???

Try another way: What about 500 / 68? Would that work?

In that case, it would be 503.2 ÷ 68 = 7.4

Long

Div

isio

n

1. 5 0 . 3 2 ÷ 6 . 8 = 7 . 4

You will need to do some estimating..

Somehow, you need to come up with a division problem that is less than but near 10.

For example, 500/100 is 5(sorta 10).

Where does that decimal point go???

Try another way: What about 500 / 68? Would that work?

In that case, it would be 503.2 ÷ 68 = 7.4

Can you think of one more way?

Long

Div

isio

n

1. 5 0 . 3 2 ÷ 6 . 8 = 7 . 4

You will need to do some estimating..

Somehow, you need to come up with a division problem that is less than but near 10.

For example, 500/100 is 5(sorta 10).

Where does that decimal point go???

Try another way: What about 500 / 68? Would that work?

In that case, it would be 503.2 ÷ 68 = 7.4

Can you think of one more way? Do problems 13-18 on page 453.

Long

Div

isio

nHave you ever put numbers in your calculator, gotten an answer, and thought, “oh wow—that can’t be right?”

1. 3.7 ÷ 0.7 = ?

ROUND your numbers to the nearest WHOLE number.

Long

Div

isio

nHave you ever put numbers in your calculator, gotten an answer, and thought, “oh wow—that can’t be right?”

1. 3.7 ÷ 0.7 = ?

4 ÷ 1 =

ROUND your numbers to the nearest WHOLE number.

Long

Div

isio

nHave you ever put numbers in your calculator, gotten an answer, and thought, “oh wow—that can’t be right?”

1. 3.7 ÷ 0.7 = ?

4 ÷ 1 = 4

ROUND your numbers to the nearest WHOLE number.

Divide your rounded numbers.

Long

Div

isio

nHave you ever put numbers in your calculator, gotten an answer, and thought, “oh wow—that can’t be right?”

19. 3.8 ÷ 0.7 = ?

4 ÷ 1 = 4

20. 49.7 ÷ 25.3 = ?

50 ÷ 25 =

ROUND your numbers to the nearest WHOLE number.

Long

Div

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nHave you ever put numbers in your calculator, gotten an answer, and thought, “oh wow—that can’t be right?”

19. 3.8 ÷ 0.7 = ?

4 ÷ 1 = 4

20. 49.7 ÷ 25.3 = ?

50 ÷ 25 = 2

ROUND your numbers to the nearest WHOLE number.

Divide your rounded numbers.

Do #19-24 on page 453

Long

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nHave you ever put numbers in your calculator, gotten an answer, and thought, “oh wow—that can’t be right?”

19. 3.8 ÷ 0.7 = ?

4 ÷ 1 = 4

20. 49.7 ÷ 25.3 = ?

50 ÷ 25 = 2

ROUND your numbers to the nearest WHOLE number.

Divide your rounded numbers.

Do #19-24 on page 453 - 455 (19-24 is estimates only)

For 25 thru 30, you ALSO need to do the actual division.

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