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confidential 1 Adding & Subtracting Fractions ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES.

Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

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Page 1: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 1Adding & Subtracting Fractions

ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS

AND DIFFERENCES.

Page 2: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 2Adding & Subtracting Fractions

REVIEW

• Write each fraction in simplest form a) 3 = 1 18 6 b) 21 = ¾ 28 c) 6 = 3 38 19

Page 3: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 3Adding & Subtracting Fractions

Review

• Write each improper fractions as a mixed number

• 11 = 1 1 15 = 1 2

10 10 9 3

Find the LCD of 1 and 4 3 9 LCD = 9

Page 4: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 4Adding & Subtracting Fractions

ROUNDING FRACTIONS AND MIXED NUMBERS

Page 5: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 5Adding & Subtracting Fractions

ROUNDING FRACTIONS AND MIXED NUMBERS

• To round to the nearest half, we can use certain guidelines:

i) ROUND UP : If the numerator is almost as large as the denominator, round the number up to the next whole number.

Example: 7 rounds to 1 8 7 is almost as

large as 8.

Page 6: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 6Adding & Subtracting Fractions

Rounding fractions

ii) ROUND TO ½ : If the numerator is about half of the denominator, round the fraction to ½.

Example : 2 3 rounds to 2 ½ 8

3 is about half of 8

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ROUNDING FRACTIONS

iii) ROUND DOWN : If the numerator is much smaller than the denominator, round the number down to the whole number.

Example: 1/8 rounds to 0.

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confidential 8Adding & Subtracting Fractions

Examples- Round to the nearest half

• Round 3 1 to the nearest half. 6 The numerator of 1 is much smaller than 6

the denominator. So 3 1 rounds to 3. 6

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confidential 9Adding & Subtracting Fractions

Example – 2

• Round 1 5 to the nearest half. 8 The numerator 5 is about half of the

denominator 8. So, 1 5 = 1 ½ 8

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confidential 10Adding & Subtracting Fractions

Example – 3

• Round 8 8 to the nearest half. 9

since the numerator of the fractional part is almost equal to the denominator.

So 8 8 rounds to 9. 9

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confidential 11Adding & Subtracting Fractions

Your Turn

• Round each number to the nearest half• 8 1 = 8 12

2 9 = 3

10

5 = ½ 12

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confidential 12Adding & Subtracting Fractions

Use rounding to solve a problem

• If you need 1 ¼ kilograms of flour needed to make sweets, should you buy 1 ½ kilograms or 1 kilogram?

Answer : Since 1 kilogram is less than 1¼ kilograms, we should round up and

buy 1 ½ kilograms.

Page 13: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 13Adding & Subtracting Fractions

Page 14: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

confidential 14Adding & Subtracting Fractions

ESTIMATING SUMS AND DFFERENCES

Page 15: Adding & Subtracting Fractions confidential1 ROUNDING FRACTIONS & MIXED NUMBERS- ESTIMATING SUMS AND DIFFERENCES

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REVIEW

• Estimate using rounding:a) 2.3 + 7.9 + 4.1 = 2 + 8 + 4 = 14b) 9.3 – 4.758 = 9 – 5 = 4c) 12.006 + 5. 21 – 4.23 = 12 + 5 – 4

= 13

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Estimating Sums and Differences

• We can estimate sums and differences of fractions by rounding each fraction to the nearest half. Then add or subtract.

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Estimate Sums

☼ Estimate 5 + 11 8 12

5 rounds to ½ 8

11 Rounds to 1

12

5 + 11 = ½ + 1 = 1 ½

8 12

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Estimate Differences

Estimate 7 - 1

13 6

7 Rounds to ½

13

1 Rounds to 0

6

7 - 1 = ½ - 0 = ½

13 6

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Your Turn

• Estimate:1. 2 + 7 = ½ +1 = 1 ½ 5 82. 6 + 4 = ½ + ½ = 1 13 9 3. 9 - 4 = 1 – ½ = ½ 10 94. 6 - 3 = ½ - ½ = 0 9 7

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Mixed Number Sum And Differences

• We can estimate sums and differences of mixed numbers by rounding each number to the nearest whole number.

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Example – Mixed Number Sum

• Estimate 4 5 + 2 1

6 5

4 5 rounds to 5. 2 1 rounds to 2

6 5

Estimate 5 – 2 = 7

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confidential 22Adding & Subtracting Fractions

Example – Mixed Difference

• Estimate 2 5 - 2

8 5

2 5 - 2 = 2 ½ - ½ = 2 8 5

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Your turn

• Estimate• 3 1 + 1 5 = 3 + 2 = 5 8 6 2 7 - 1 8 = 3 – 2 = 1 8 9

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Let’s have fun

• http://www.thekidzpage.com/freekidsgames/xword/fairytalepuzzle.html

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Round up to solve a problem

• The width of a room is 9 ¼ feet and length of a room is 12 ½ feet. About how much border the room will have?

• Width = 10 feet Length = 13Border is about 10 + 10 + 13 + 13 =

46

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Your turn

• Estimate the perimeter of rectangle if length is 13 9 inches an breadth is 2 ¼ in

11Length = 14 and Breadth = 2Perimeter = 14 + 14 + 2+ 2 = 32

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Practice Problems

• Round each number to the nearest half

1. 2 4/5 = 3 2. 4 4/9 = 4 ½ 3. 6 11/12 = 7 4. 3 2/3 = 3 ½ 5. 6 1/7 = 6

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Practice Problems

• James walked 6 5 miles. To the nearest 8

half male, how many miles did she walk.

To the nearest half, he walked about 6 ½ miles.

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Practice Problems

• Estimatea. 9/10 – ½ = 1 – ½ = ½ b. 3/8 – 1/9 = ½ - 0 = ½c. 1 9/10 – 1 1/8 = 2 – 1 = 1d. 4 1/3 + 1 1/9 = 4 + 1 = 5e. 6 ¼ + 2 5/6 + 3 3/8 = 6 + 3 + 3 =

12

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Review

• To round to the nearest half:• If the numerator s almost as large as the

denominator, round the number to the nearest half

If the numerator is about half of the denominator, round the fraction to ½.

If the numerator is much smaller than the denominator, round the number down to the whole number.

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