Post on 03-Dec-2018
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5th Grade
Fraction Operations Part 1
2015-10-08
www.njctl.org
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· Adding Fractions with Unlike Denominators· Subtracting Fractions with Unlike Denominators
· Adding Mixed Numbers with Unlike Denominators
· Subtracting Mixed Numbers with Unlike Denominators
Table of Contents
· Finding Common Denominators· Comparing Fractional Numbers
· Fractions as a form of division
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Return toTable of Contents
Fractions as a form ofdivision
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Return toTable of Contents
Fractions as a form ofdivision[This object is a pull tab]
Teac
her N
otes
For this activity, each student will need 7 index cards, card stock, or square or rectangular scrap paper and a pair of scissors to cut.
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Imagine you have 2 sandwiches. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 2 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.
Derived from( (
Slide 5 (Answer) / 115
Imagine you have 2 sandwiches. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 2 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.
Derived from( (
[This object is a pull tab]
Ans
wer
Each person will get 1 sandwich.
2 2 = 1
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Fractions can be used to show the division operation.
2 2 = 1 can also be written as
2= 1
The fraction bar is a division bar.click
2
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Now imagine that there is only 1 sandwich. Use your paper and the scissors to show how you would share the sandwich equally between 2 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.click
Derived from( (
Slide 7 (Answer) / 115
Now imagine that there is only 1 sandwich. Use your paper and the scissors to show how you would share the sandwich equally between 2 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.click
Derived from( (
[This object is a pull tab]A
nsw
er
Each person will get 1 half of a sandwich.
1 2 = 1/2
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Now imagine that there is 1 sandwich and 3 people. Use your paper and the scissors to show how you would share the sandwich equally between 3 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.click
Person 1 Person 3Person 2
Derived from( (
Slide 8 (Answer) / 115
Now imagine that there is 1 sandwich and 3 people. Use your paper and the scissors to show how you would share the sandwich equally between 3 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.click
Person 1 Person 3Person 2
Derived from( (
[This object is a pull tab]
Ans
wer
Each person will get 1 third of a sandwich.
1 3 = 1/3
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Now lets take 3 sandwiches and share them equally with 2 people. Turn and talk about how you can share these sandwiches. Use your paper and the scissors to show how you would share them.
How many sandwiches did each person get?
Write a division sentence to show represent this.
Person 1 Person 2
click
Derived from( (
Slide 9 (Answer) / 115
Now lets take 3 sandwiches and share them equally with 2 people. Turn and talk about how you can share these sandwiches. Use your paper and the scissors to show how you would share them.
How many sandwiches did each person get?
Write a division sentence to show represent this.
Person 1 Person 2
click
Derived from( (
[This object is a pull tab]
Ans
wer
Each person can get one whole sandwich, and half of the third sandwich.
Each person will get 1 and a half sandwiches.
3 2 = 1 1/2
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Imagine you have 2 different sandwiches. There are 5 people sharing them, and each person wants a taste of each sandwich. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 5 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.
To give everyone part of each sandwich, each sandwich must be divided into fifths. Each
person can have 1/5 of each sandwich. 1/5+1/5=2/5
click
Derived from( (
Slide 10 (Answer) / 115
Imagine you have 2 different sandwiches. There are 5 people sharing them, and each person wants a taste of each sandwich. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 5 people.
How many sandwiches did each person get?
Write a division sentence to show represent this.
To give everyone part of each sandwich, each sandwich must be divided into fifths. Each
person can have 1/5 of each sandwich. 1/5+1/5=2/5
click
Derived from( (
[This object is a pull tab]
Ans
wer
Each person will get two-fifths of a sandwich.
2 5 = 2/5
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1 Which picture shows the division?
A
B
C
Derived from( (
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1 Which picture shows the division?
A
B
C
Derived from( (
[This object is a pull tab]
Ans
wer
A
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2 Which pictures show the division?
A
B
C
D
E
Derived from( (
Slide 12 (Answer) / 115
2 Which pictures show the division?
A
B
C
D
E
Derived from( (
[This object is a pull tab]
Ans
wer
A,B,C
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3 What division expression does the picture represent? Write your answer as a fraction.
Derived from( (
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3 What division expression does the picture represent? Write your answer as a fraction.
Derived from( (
[This object is a pull tab]
Ans
wer
6/4
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4 Carla was drawing a picture to show how 2 children can equally share 3 cookies. She then wrote an equation, and expressed her answer as a fraction.
Is her work correct?
If not, explain on your paper how to correct her answer.
Yes No
3 2 = 1 and 1 half = 1 1/2
Derived from( (
Slide 14 (Answer) / 115
4 Carla was drawing a picture to show how 2 children can equally share 3 cookies. She then wrote an equation, and expressed her answer as a fraction.
Is her work correct?
If not, explain on your paper how to correct her answer.
Yes No
3 2 = 1 and 1 half = 1 1/2
Derived from( (
[This object is a pull tab]
Ans
wer Yes
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5 Hillary was solving the same problem, but she did it differently.
Is her work correct?
If not, explain on your paper how to correct her answer.
Yes No
3 2 = six thirds = 6/3 = 2
Derived from( (
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5 Hillary was solving the same problem, but she did it differently.
Is her work correct?
If not, explain on your paper how to correct her answer.
Yes No
3 2 = six thirds = 6/3 = 2
Derived from( (
[This object is a pull tab]
Her drawing and her division expression is correct, but she divided 3 cookies in half and so she had 6 halves, not thirds.
Each child would get 3 halves which equals 1 and 1/2.
three halves = 1 1/2
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This fraction line represents division.
It can be read as:
27 over 527 out of 527 divided by 5
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Return toTable of Contents
FindingCommon
Denominators
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How many halves make a whole circle?
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How many fourths make half of this circle?
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How many sixths make 1/3 of this circle?
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How many eighths can fit in 1/4 of this circle?
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How many different combinations can you make to fill the circle?Keep track of what pieces you use. (You may need to rotate your pieces.)
1/8
1/4
1/21/3
1/61/7
1/5
Slide 30 / 115Fix the Sticks
You can use the set of Skip Counting Sticks to find common denominators for two fractions with unlike denominators. If you don't have a set of sticks, you can create them by listing the multiples of the denominator.
For the fractions and , line up the sticks this way for the denominator of each fraction:
Find the smallest number in the "denominator" sticks that is common in both fractions.
It's 12. The least common denominator of and is 12.
3 4
4 8 12 16 20 24 28 32 36
6 1218 24 30 36 42 48 54
...
...
1 6
3 4 1 6
3 4
1 6
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A quick way to find LCDs...
List multiples of the larger denominator, and stop when you find a common multiple for the smaller denominator.
Ex: and
Multiples of 5: 5, 10, 15
Ex: and
Multiples of 9: 9, 18, 27, 36
2 5
1 3
3 4
2 9
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11 Find the LCD of this pair of fractions.
2 4
1 6
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12 Find the LCD of this pair of fractions.
3 5
5 6
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13 Find the LCD of this pair of fractions.
2 9
1 3
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14 Find the LCD of this pair of fractions.
3 4
3 7
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15 Find the LCD of this pair of fractions.
5 6
3 8
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Return toTable of Contents
Comparing Fractional Numbers
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Comparing Fractional Numbers
Common DenominatorsWhen you have two fractions with common denominators, all you have to do is compare the numerators.
Unlike DenominatorsTo compare fractions with unlike denominators, you have to rewrite both fractions with a common denominator. Then, compare the numerators.
> 8 9
7 9
2 3 7 10
2 3
2030
=
7 10
2130
=< 2
3 7 10
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Compare the fractions
1. 4 2 7 5
4 7
2035
=
2 5
1435
=
4 2 7 5
>
2. 11 1317 17
11 1317 17
<
3. 4 3 5 4
4 5
1620
=
3 4
1520
=
4 3 5 4
>
click
click
click
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16 True or false?
4 7
2 3
>
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17 True or false?
5 6
5 8
>
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18 Compare the two fractions.
A >
8 11
3 4
B <
C =
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19 Compare the two fractions.
A >
3 12
1 4
B <
C =
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20 Compare the two fractions.
A >
4 9
5 8
B <
C =
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21 Ali has completed of his essay, and
Veronica has completed of her essay.
A Ali has completed more (>) than Veronica.
B Ali has completed less (<) than Veronica.
CAli and Veronica have completed the same amount (=).
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22 Sasha has eaten of her lunch, and
Cloe has eaten of her lunch.
A Sahsa has eaten more (>) than Cloe.
B Sasha has eaten less (<) than Cloe.
CSasha and Cloe have eaten the same amount (=).
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23 Liam knows of this weeks vocabulary
words, and Joshua knows of the words.
A Liam knows more (>) words than Joshua.
B Liam knows less (<) words than Joshua.
CLiam and Joshua knowthe same amount (=) of words.
Slide 49 / 115Internet links for more practice
Finding fractions on a number line link
Comparing Fractions Model
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Adding Fractions with Unlike
Denominators
Return to Table of Contents
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Adding Fractions with Unlike Denominators
To add fractions with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Then, add the fractions. (Using the LCD is often the fastest method, as it requires the least amount of simplification.)
Make sure your answer is in simplest form.
4 9 5 8
+
4 9
5 8
+ 32724572
+
7772
= 1 5 72
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+ +
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Try these!Click the boxes to see work and answers.Be sure to simplify all answers.
2 5 1 4
+
8 20 5 20
+
1320
3 7 2 8
+
24561456
+
3856
= 1928
= 1 2740
4 5 7 8
+
32403540
+
6740
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Adding Fractions with Unlike Denominators link
Internet Link for Practice
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24 2 5 1 3
+
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25 3 10 2 5
+
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26 5 8 3 5
+
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27
3 4
7 9
+
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28 5 7
1 3
+
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29 Two friends get their hair cut. Natasha
gets of a foot cut off, and Briar gets
of a foot cut off. What is the total length
of hair the two friends get cut off?
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30 On Monday Bobby completes of his
science project. On Thursday he
completes of the project. What fraction
of the project is completed after these
two days of work?
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31 Yolanda used of her new beads to
make a necklace. She then used of the
beads to make a bracelet. What fraction
of her beads has she used so far?
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Subtracting Fractions
with Unlike Denominators
Return to Table of Contents
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Subtracting Fractions withUnlike Denominators
To subtract fractions with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Then, subtract the fractions. (Using the LCD is often the fastest method, as it requires the least amount of simplification.)
Make sure your answer is in simplest form.
4 9
3 8
4 9 3 8
32722772 5 72
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2 5 1 4
8 20 5 20
3 20
Try these!Click the boxes to see work and answers.Be sure to simplify all answers.
3 7 2 8
24561456
1056
= 5 28
4 5 3 8
32401540
1740
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32 4 5 1 7
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33 2 3 1 6
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34 6 7 3 5
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35 3 4
5 9
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36
3 5
1 6
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37 It is of a mile to Alyssa's best
friend's house. So far she has walked
of a mile to her friend's house. How
much farther does she have to walk?
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38 A recipe for pancakes calls for of a cup of
milk. Deven only has of a cup of milk. How
much more milk does Deven need?
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39 Use the chart to solve the problem. How much less rain fell on Wednesday than on Thursday?
Rainfall in inches
Wednesday
Thursday
Friday
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AMAZING FRACTIONS Quick Review
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A few reminders...
1. If the problem is written in a horizontal format, rewrite the fractions in a vertical format.
2. Check for a common denominator. Rewrite with a common denominator if necessary.
3. Double check the sign to see if you are doing addition or subtraction.
4. Make sure you write your answer in simplest form.
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40 4 5
3 5
+
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41 4 9
2 9
+
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42 6 8
4 8
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43 6 7
4 5
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44 2 3
1 5
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45 3 4
2 3
+
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46 Rebecca painted of a mural. Justina
painted of it. How much of the mural
did the girls paint?
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47 Mr. Phillips class completed of their
project for the science program on
Monday. On Tuesday, they completed
another of it. How much more did they
complete on Tuesday than on Monday?
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48 On Saturday of the plants in Ms.
Drake's flower bed had flowers on them.
On Sunday another of them had
flowers on them. What fraction of her
plants have flowers on them now?
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AddingMixed Numbers
with Unlike Denominators
Return to Table of Contents
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Adding Mixed Numberswith Unlike Denominators
To add mixed numbers with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator . Add the fractions. Then, add the whole numbers. Make sure your answer is in simplest form.
2 1 6
+ 1 2 5
2 5 30
+ 1 1230
3 1730
5 7 9
+ 2 2 3
5 7 9
+ 2 6 9
7 13 9
= 8 4 9
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1212
+ 1 12
= 1312
=x 49 1 3
8 3 4
+
x 4
x 3x 3
=
9 4 12
8 9 12
+
17 1312
= 18 1 12
1st-Find
Common Denominator(click here)
3rd-RenameFraction
(click here)
2nd-Add
Fractions(click here)
Steps to add and simplify.
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10 1 5
Try this...
9 1 2
+ 7 10
click
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6 1 6
Try this...
3 5 12
+ 3 42
click
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49
A
5 3 4
+ 2 7 12
=
7 1612
B 8 4 12
C
7 5 8
D
8 1 3
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50
A
2 3 8
+ 5 5 12
=
7 1924
7 8 20
B
7 8 12
C
8 7 12
D
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51
5 2 10
5 5 12
A
3 1 4
+ 2 1 6
=
B
5 1 2
C
6 5 12
D
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52
14 3730
A
9 2 5
+ 5 5 6
=
B 14 7 11
14 3740
C
15 7 30
D
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531 2
3+ 2 1
2=
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54 Find the sum.
5 2 10
+ 7 4 10
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55 A recipe for sugar cookies needs
cups of flour. A recipe for oatmeal
cookies needs cups of flour. How
much flour altogether are needed to make
the two recipes?
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56 Jasmin made a necklace that is
inches long. Diandra made one that is
inches long. What is the total length of
the two necklaces?
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57 A recipe calls for cups of peanuts
and cups of walnuts. How many cups
of nuts in all are needed for the recipe?
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SubtractingMixed Numbers
with Unlike Denominators
Return to Table of Contents
Slide 100 / 115Subtracting Mixed Numbers
with Unlike Denominators
To subtract mixed numbers with unlike denominators, the fractions as equivalent fractions with a common denominator . Subtract the fractions. Then, subtract the whole numbers. Make sure your answer is in simplest form.
2 1 5
1 1 6
2 6 30
1 5 30
1 1 30
5 7 9
2 1 3
5 7 9
2 3 9
3 4 9
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In this problem, you can not subtract two thirds from one third, because the first numerator is smaller than the second. When this happens, you need to borrow from the whole number.
How many thirds are in 1 whole?
How many fifths are in 1 whole?
How many ninths are in 1 whole?
Pull
113 - 2
3
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3
3 5
=
2 5 5
2 8 5
To borrow a whole number:
Take one from the whole number and write it as a fraction.
+
3 3 5
=
(Click the denominator)
Then, add the new mixed # and the fraction.
5 5
+2So, 3 3
5 = 2 8 5
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5 1 4
3 7 12
5 3 12
3 7 12
4 1212
3 7 12
3 12
4 1512
3 7 12
1 8 12
1 2 3
Click
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9
4 5 8
8
4 5 8
8 8
4 3 8
Click
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58 Can this problem be solved without borrowing?
Yes or No
3 1 2
1 4
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59 Can this problem be solved without borrowing?
Yes or No
7 2 3
3 4
6
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60What does 17 become when borrowing? 3
10
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61What does 9 become when borrowing? 2
5
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62
2 1 12
A
1 2224
B
4 1 6
2 1 4
=
1 1112
C
1 1 12
D
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63
A
3 1321
B
6 2 7
3 2 3
=
3 8 21
2 2 3
C
2 1321
D
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64
A
6 1 6
B
15 8 1012
=
7 5 6
7 1 6
C
6 2 12
D
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65 Two items in a package have a combined
weight of pounds. If one item weighs
pounds, how much does the other
item weigh?
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66 My brother is years old. My sister is
years younger than my brother. How
old is my sister?
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67 Keith bought pounds of dried fruit.
He ate pounds of it. How much dried
fruit is left?
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68 A board is 8 feet long. If you cut off feet of it, how much is left?