Frequently Asked Questions
Q: How can you express a mixed number as an improper
fraction?
A1: You can draw a picture and divide each whole number
part into sections that match the denominator of the
fraction part. Then count the total number of sections.
For example, for 3 15, show each of the 3 wholes as
fifths. There are 16 fifths, so 3 15 ⫽ 16
5.
A2: You can express the whole number part as a fraction
with the same denominator as the fraction part.
Then combine the two parts.
For example, for 3 15, each whole is 5 fifths.
There are 3 wholes plus 1 more fifth.
1
3 wholes is 15 fifths. So 3 5 ⫽ 16 fifths, or
16
5.
Q: What strategies can you use to put fractions and
mixed numbers in order?
A:
You can use equivalent fractions and whole numbers
to compare the numbers.
For example, put 94, 3 15,
0
1
4
9
12
8,
2
12
8
and 3 23 in order.
3
4
1
3
5
2
3
3
4
9 is the only value that is less than 1, so it
12
4
8 ⫽ 1 8 , which is less than 3, so it is next.
3 15 and 3 23 are both between 3 and 4.
Since 51 is less than 32, 3 15 is less than 3 23.
234
is least.
NEL
Practice
Lesson 1
1. Use pattern blocks to model improper fractions.
Use the yellow hexagon as one whole. Make an
improper fraction using 13 blocks of one other colour.
Sketch and name the fraction. Repeat, using another
colour of pattern block.
Lesson 2
2. Sketch a diagram for each fraction. Circle one whole
in each diagram.
12
4
a)
b)
3
5
䊏
3. For what values of ■ is 12 greater than 1?
Explain your thinking.
Lesson 3
4. After a party, there were 22 slices of pizza left. If each
pizza had 10 slices, how many whole pizzas were left?
5. Write each fraction as a mixed number. Sketch a
diagram to show why your answer is correct.
22
9
16
14
a)
b)
c)
d)
2
3
3
4
1
6. Riley can knit a square for a blanket in 2 h. How many
hours will it take her to knit 25 squares?
7. a) Choose three denominators that make 32
䊏 an
improper fraction.
b) Write a mixed number for each fraction in part a).
NEL
235
Lesson 5
8. a) Each cake in the diagram at the left has been
divided into four equal parts. What improper
fraction does this diagram show? What mixed
number does it show?
b) Sketch a similar diagram to show 1 35 cakes. What
improper fraction does your diagram show?
9. Use centimetre cubes and a number line to model
each mixed number. Write each mixed number as an
improper fraction.
2
4
a) 3
b) 2
5
5
10. Two improper fractions have a numerator of 17. The
䊏
equivalent mixed numbers are 3 䊏
䊏 and 1 䊏. What could
the mixed numbers be? Name one possibility for each.
Lesson 6
11. Order these numbers from least to greatest using the
11
5
number line: 2 34, 23
8 , 8 , 18
0
Reading Strategy
Synthesizing
Use reasoning and
insight to determine
what the fraction
could be.
1
2
3
12. Give an example of two mixed numbers that you think
are easy to compare. Explain your thinking.
13. How do you know that 2 37 ⬍ 3 68?
Lesson 7
14. The sum of the numerator and the denominator of an
improper fraction is 17. The fraction is between 2 and 3.
What could the fraction be?
Look back at What Do You Think? on page 209. How have your
answers and explanations changed?
236
NEL