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Name:

Decimal Operations

Grade 7 Math

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Using Estimation

There are many different estimation strategies that work. Here are a just a few: 1. Front End Estimation – Use the whole numbers in front of the

decimals and follow the operation.

2. Rounding: Round numbers to the nearest whole number.

3. Compatible (Friendly) Numbers: Use numbers that are close to the

original numbers and that are easy to do mental arithmetic with.

Example Estimation

42.36 + 324.55 40 + 320 = 360

842.6 – 38.2 850 – 50 = 800

17.7 x 112.1 20 x 100 = 2000

64.99 ÷ 11.3 60 ÷ 10 = 6

Example Estimation

3.15 + 2.6 3 + 2 = 5

19.2 – 2.7 19 – 2 = 17

2.4 x 5.1 2 x 5 = 10

64.4 ÷ 8.2 64 ÷ 8 = 8

Example Estimation

5.8 + 2.7 6 + 3 = 9

182.6 – 19.5 183 – 20 = 163

6.9 x 6.8 7 x 7 = 49

700.7 ÷ 99.5 700 ÷ 100 = 7

Estimation: a reasonable guess that is close to the actual value, without calculating it exactly

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Practice:

1. Use front end estimation to estimate the answers. Show the numbers that you are using to estimate with.

a) 5.1 + 8.6 = e) 3.5 + 5.8 =

b) 130.5 – 6.3 = f) 185.6 – 2.7 =

c) 8.6 x 2.6 = g) 8.8 x 4.2 =

d) 45.68 ÷ 5.12 = h) 26.8 ÷ 2.05 =

2. Use rounding to estimate the answers. Show the numbers that you are using to estimate with.

a) 26.1 + 71.9 = e) 84.5 + 16.38 =

b) 127.78 – 12.3 = f) 58.1 – 6.37 =

c) 7.16 x 3.3 = g) 11.8 x 3.05 =

d) 48.38 ÷ 8.12 = h) 98.8 ÷ 21.5 =

3. Use compatible (friendly) numbers to estimate the answers. Show the numbers that you are using to estimate with.

a) 39.1 + 711.9 = e) 76.5 + 82.8 =

b) 957.78 – 162.3 = f) 261.4 – 22.51 =

c) 8.4 x 15.3 = g) 23.8 x 9.05 =

d) 66.2 ÷ 3.7 = h) 24.68 ÷ 4.2=

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Adding and Subtracting Decimals

Practice (Rewire both numbers and line up the decimals. No Calculators.)

24.31 + 52.83

340.8 + 24.7

34.9 + 48.1

1.357 + 7.05

When adding decimals, you must:

Line up the numbers according to place value. (The decimals should line up.)

Put in zeros as place holder if needed.

Add normally, as you would whole numbers

Carry the decimal point directly down into the answer (lined up with other

decimals)

Double Check: It’s always a good idea to use estimation to see if your answer

is reasonable.

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12.9 + 9.174

3.75 + 12.998

300.5 + 282.36

0.147 + 0.8

3.8 + 7.912

268.45 + 55.36

200.413 + 3.071

0.04 + 2.077

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Practice (Rewire both numbers and line up the decimals. No Calculators.)

74.25 – 23.14 =

689.67 – 238.5 =

536.37 – 25.25 =

536.982 – 225.543 =

When subtracting decimals, you must:

Put the number with the greater value on the top.

Line up the numbers according to place value. (The decimals should line

up.)

Put in zeros as place holder if needed.

Subtract normally, as you would whole numbers

Carry the decimal point directly down into the answer (lined up with other

decimals)

Double Check: It’s always a good idea to use estimation to see if your

answer is reasonable.

–

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39.16 – 1.24 =

4.648 – 0.263 =

260.48 – 5.37 =

605.6 – 2.06 =

8.8 – 7.912 =

237.45 – 53.37=

11.472 – 5.0201 =

89.67 – 7.8 =

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Ex. 3.12 (2 places) x 3.4 (1 place) 1248 9360 10.608 (3 places total)

Multiplying Decimals (Using standard algorithm.)

the number with the most digits goes on top

line the numbers up on the right (do not line up decimals)

multiply as normal

to determine where the decimal in the answer needs to go, you must count how many numbers there are in total after the decimals. This is the amount of numbers that should be after the decimal in the final answer.

Multiply the following decimals. Show your work.

a) 6.1 x 3

b) 5.8 x 5

c) 2.7 x 4

d) 3.6 x 8

e) 9.7 x 9 f) 7.8 x 0.6

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g) 7.72 x 4

h) 22.6 x 3 i) 5.23 x 8

j) 6.905 x 4 k) 14.82 x 4 l) 7 x 1.73

m) 8.1 x 2.5 n) 1.5 x 3.6 o) 4.97 x 1.2

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Dividend (goes on the inside)

Ex.

Divisor (goes on the outside)

Dividing Decimals 6.85 ÷ 0.5

If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places. (68.5 ÷ 5)

Divide as usual. ...

Put decimal point directly above decimal point in the dividend.

Check your answer. Divide the following decimals. Show your work.

a) 1.28 ÷ 0.4

b) 4.48 ÷ 0.7 c) 32.4 ÷ 0.6

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d) 3.31 ÷ 0.5

e) 1.68 ÷ 0.3 f) 0.306 ÷ 0.09

g) 3.368 ÷ 0.8

h) 21.64 ÷ 4 i) 3.164 ÷ 0.07

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Mental Math (Multiplying with decimals) Ex. 24.5 x 10 = 245 (move decimal one place to the right) Ex. 6.8 x 100 = 680 (move decimal two places to the right) Ex. 3.5 x 0.1 = 0.35 (move decimal one place to the left) Ex 2.76 x 0.01 = 0.0276 (move decimal two places to the left)

Multiply by 0.1 Multiply by 10 Multiply by 100

Multiply by 1000

a) 2.68

b) 2.81

c) 31.6

d) 0.28

Put It All Together. a) 4.98 x 10 = h) 2.5 x 0.1 =

b) 65.9 x 10 = i) 6.3 x 0.1 =

c) 2.97 x 1000 = j) 2.77 x 0.1 =

d) 0.098 x 100 = k) 3.46 x 0.01 =

e) 99.78 x 100 = l) 39.1 x 0.01 =

f) 0.58 x 10 = m) 0.9 x 0.1 =

g) 38.91 x 1000 = n) 0.5 x 0.01 =

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Mental Math (Dividing with decimals) Ex. 23.5 ÷ 10 = 2.35 (move decimal one place to the left) Ex. 5.1 ÷ 100 = 0.051 (move decimal two places to the left) Ex. 6.8 ÷ 0.1 = 68 (move decimal one place to the right) Ex 3.57 ÷ 0.01 = 357 (move decimal two places to the right)

Divide by 0.1 Divide by 10 Divide by 100 Divide by 1000

a) 1.12

b) 6.84

c) 12.5

d) 0.25

Put It All Together. a) 3.65 ÷ 10 = h) 2.5 ÷ 0.1 =

b) 24.5 ÷ 10 = i) 2.3 ÷ 0.1 =

c) 2.45 ÷ 1000 = j) 2.29 ÷ 0.01 =

d) 0.013 ÷ 100 = k) 3.17 ÷ 0.01 =

e) 91.47 ÷ 100 = l) 16.4 ÷ 0.01 =

f) 0.14 ÷ 10 = m) 0.7 ÷ 0.1 =

g) 36.27 ÷ 1000 = n) 0.2 ÷ 0.01 =