Fractions and Mixed Numbers
Name:
CH
Date:
APTER
6
Fractions and Mixed Numbers
PROBLEM SOLVING
Thinking Skills Solve. The figure is a square divided into many smaller pieces. What fraction of the square is the rectangle?
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
1.
Enrichment 4A
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Name:
Date:
Use the graph. Express the answers in simplest form. 2.
The graph shows the number of books sold by Mr. Harrods for the last 6 months. Book Sales
30
Number of Books
25 20 15 10 5 0
Jan.
Feb.
Mar.
Apr.
May
June
46
a.
14 of the books sold in May and June altogether were comic books. What fraction of the total number of books sold in May and June were comic books?
b.
Write the number of books sold in February, March, and April as a fraction of the total number of books sold during the 6 months.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Month
Chapter 6 Fractions and Mixed Numbers
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1/6/09 5:36:32 PM
Name:
Date:
Answer the questions. Express answers in simplest form. 3.
2 Raj poured 4_ 3 liters of water equally into identical cups.
2 liter of water. Each cup contained _ 9
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
How many cups did Raj use?
4.
In the figure, X and Y are identical overlapping squares. If the length of each side of the shaded region is half the length of square X, what fraction of the figure is not shaded? X
Y
Enrichment 4A
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Name:
Date:
PROBLEM SOLVING
Strategies Answer the question. Express the answers as mixed numbers or fractions in simplest form. 5.
A box contains six number cards. The six numbers form a pattern when ordered from least to greatest. Joanne draws these four cards from the box. 1 _ 2
1 6_ 2
1 1_ 4
1 _ 4
Solve. Express the answer in simplest form. 6.
The total mass of a basket, 4 large pebbles, and 2 small pebbles is 7 _ 12 kilogram. The total mass of the basket, 2 large pebbles and 1 small 5 pebble is _ 12 kilogram. Find the mass of the empty basket.
48
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
What number cards are likely to be left in the bag?
Chapter 6 Fractions and Mixed Numbers
MS_Enrich_4A_Ch06_45-53.indd 48
1/6/09 5:36:32 PM
Name:
Date:
Solve. Show your work. 7.
Two mystery fractions are both less than 1. 1 The sum of the fractions is 1_ 4.
1 The difference between the fractions is _ 4.
What are the two fractions?
8.
1 2 plates and 3 bowls weigh 2_ 5 pounds.
9 5 plates and 6 bowls weigh 4_ 10 pounds.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Find the weight of one plate.
9.
3 2 _ _ of Mr. Hussein’s money is equal to 5 of Ms. Lee’s money. Ms. Lee has $20 3
more than Mr. Hussein. How much money do they have altogether?
Enrichment 4A
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49 1/6/09 5:36:32 PM
Name:
Date:
PROBLEM SOLVING
Exploration Solve. Show your work. 10.
Jolene and Kathy had the same number of baseball cards after Jolene 2 gave _ 5 of her cards to Kathy. They had 42 cards in all. How many
baseball cards did Jolene have at first? Show two methods for solving this problem.
Method 2
50
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Method 1
Chapter 6 Fractions and Mixed Numbers
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9/29/09 9:14:32 AM
Name:
Date:
Solve. 11.
A box contains 5 number cards. The 5 numbers form a pattern when arranged in order. Lucy draws 3 cards from the box and she places them on the table as shown. 3 1_ 4
1 1_ 2
2
What two cards are likely to be left in the box? Show four different patterns.
a.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
b.
c.
d.
Enrichment 4A
MS_Enrich_4A_Ch06_45-53.indd 51
51 1/6/09 5:36:33 PM
Name:
Date:
Journal Writing Explain.
12.
3 4 1 _ _ _ ⫹ ⫽ 5 8 3
13.
5 4 9 _ _ ⫺_ 6⫽5 11
14.
2 2 _ _ ⫻ 21 ⫽ 21 7 7
52
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Jason made the following calculations. Explain the errors Jason made.
Chapter 6 Fractions and Mixed Numbers
MS_Enrich_4A_Ch06_45-53.indd 52
1/6/09 5:36:33 PM
Name:
15.
Date:
1 1 1 _ _ 1_ ⫹ 3 ⫽ 4 ⫹ 4 6 2 1 ⫽ 4_ 6
16. 3 The diagram shows _ 5 of a fraction strip shaded. Juliet erases some of the
3 3 _ shading to show _ 10 shaded. Explain the steps she took to shade 10 of the
fraction strip.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Step 1
Step 2
Step 3
Enrichment 4A
MS_Enrich_4A_Ch06_45-53.indd 53
53 1/6/09 5:36:33 PM
CH
Date:
APTER
6
Fractions and Mixed Numbers
PROBLEM SOLVING
Thinking Skills Solve. The figure is a square divided into many smaller pieces. What fraction of the square is the rectangle?
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
1.
Enrichment 4A
MS_Enrich_4A_Ch06_45-53.indd 45
45 1/6/09 5:36:31 PM
Name:
Date:
Use the graph. Express the answers in simplest form. 2.
The graph shows the number of books sold by Mr. Harrods for the last 6 months. Book Sales
30
Number of Books
25 20 15 10 5 0
Jan.
Feb.
Mar.
Apr.
May
June
46
a.
14 of the books sold in May and June altogether were comic books. What fraction of the total number of books sold in May and June were comic books?
b.
Write the number of books sold in February, March, and April as a fraction of the total number of books sold during the 6 months.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Month
Chapter 6 Fractions and Mixed Numbers
MS_Enrich_4A_Ch06_45-53.indd 46
1/6/09 5:36:32 PM
Name:
Date:
Answer the questions. Express answers in simplest form. 3.
2 Raj poured 4_ 3 liters of water equally into identical cups.
2 liter of water. Each cup contained _ 9
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
How many cups did Raj use?
4.
In the figure, X and Y are identical overlapping squares. If the length of each side of the shaded region is half the length of square X, what fraction of the figure is not shaded? X
Y
Enrichment 4A
MS_Enrich_4A_Ch06_45-53.indd 47
47 1/10/09 1:00:29 PM
Name:
Date:
PROBLEM SOLVING
Strategies Answer the question. Express the answers as mixed numbers or fractions in simplest form. 5.
A box contains six number cards. The six numbers form a pattern when ordered from least to greatest. Joanne draws these four cards from the box. 1 _ 2
1 6_ 2
1 1_ 4
1 _ 4
Solve. Express the answer in simplest form. 6.
The total mass of a basket, 4 large pebbles, and 2 small pebbles is 7 _ 12 kilogram. The total mass of the basket, 2 large pebbles and 1 small 5 pebble is _ 12 kilogram. Find the mass of the empty basket.
48
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
What number cards are likely to be left in the bag?
Chapter 6 Fractions and Mixed Numbers
MS_Enrich_4A_Ch06_45-53.indd 48
1/6/09 5:36:32 PM
Name:
Date:
Solve. Show your work. 7.
Two mystery fractions are both less than 1. 1 The sum of the fractions is 1_ 4.
1 The difference between the fractions is _ 4.
What are the two fractions?
8.
1 2 plates and 3 bowls weigh 2_ 5 pounds.
9 5 plates and 6 bowls weigh 4_ 10 pounds.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Find the weight of one plate.
9.
3 2 _ _ of Mr. Hussein’s money is equal to 5 of Ms. Lee’s money. Ms. Lee has $20 3
more than Mr. Hussein. How much money do they have altogether?
Enrichment 4A
MS_Enrich_4A_Ch06_45-53.indd 49
49 1/6/09 5:36:32 PM
Name:
Date:
PROBLEM SOLVING
Exploration Solve. Show your work. 10.
Jolene and Kathy had the same number of baseball cards after Jolene 2 gave _ 5 of her cards to Kathy. They had 42 cards in all. How many
baseball cards did Jolene have at first? Show two methods for solving this problem.
Method 2
50
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Method 1
Chapter 6 Fractions and Mixed Numbers
MS_Enrich_4A_Ch06_45-53.indd 50
9/29/09 9:14:32 AM
Name:
Date:
Solve. 11.
A box contains 5 number cards. The 5 numbers form a pattern when arranged in order. Lucy draws 3 cards from the box and she places them on the table as shown. 3 1_ 4
1 1_ 2
2
What two cards are likely to be left in the box? Show four different patterns.
a.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
b.
c.
d.
Enrichment 4A
MS_Enrich_4A_Ch06_45-53.indd 51
51 1/6/09 5:36:33 PM
Name:
Date:
Journal Writing Explain.
12.
3 4 1 _ _ _ ⫹ ⫽ 5 8 3
13.
5 4 9 _ _ ⫺_ 6⫽5 11
14.
2 2 _ _ ⫻ 21 ⫽ 21 7 7
52
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Jason made the following calculations. Explain the errors Jason made.
Chapter 6 Fractions and Mixed Numbers
MS_Enrich_4A_Ch06_45-53.indd 52
1/6/09 5:36:33 PM
Name:
15.
Date:
1 1 1 _ _ 1_ ⫹ 3 ⫽ 4 ⫹ 4 6 2 1 ⫽ 4_ 6
16. 3 The diagram shows _ 5 of a fraction strip shaded. Juliet erases some of the
3 3 _ shading to show _ 10 shaded. Explain the steps she took to shade 10 of the
fraction strip.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
Step 1
Step 2
Step 3
Enrichment 4A
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