CLUSTER:
Build fractions from unit fractions by
applying and extending previous
understandings of operations on
whole numbers.
4.NF.4 STANDARDS
a. Understand Fractions as Multiples of Unit
Fractions
b. Understand Fractions as Multiples of Unit
Fractions
c. Multiply Fractions by Whole Numbers in Word
Problems
4NF.4A - UNDERSTAND FRACTIONS AS
MULTIPLES OF UNIT FRACTIONS
Understand a fraction a/b as a multiple of 1/b.
For example, use a visual fraction model to
represent 5/4 as the product 5 × (1/4),
recording the conclusion by the equation 5/4 =
5 × (1/4). (4.NF footnote: Grade 4 expectations
in this domain are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.)
PROBLEM 1:
Each day Debbie reads ⅛ of her new book.
Which number sentence best represents the fraction of her book that
Debbie has read after 7 days?
A. 1/8 × 1/7 = 1/56
B. 1/8 × 1/7 = 7/8
C. 1/8 × 7 = 1/56
D. 1/8× 7 = 7/8
PROBLEM 2:
Which multiplication sentence can be used to calculate
the total shaded area shown in the model below?
A.
B.
C.
D.
4x⅛
8x¼
4x⅙
6x¼
PROBLEM 3:
WRITE AN EXPRESSION TO SHOW:
4x⅜
PROBLEM 4:
TRUE OR FALSE??
4x⅓=
PROBLEM 5:
For each of the expressions below, circle either “Less than 1” or “Greater
than 1” to show whether the expression is less than or greater than 1.
4NF.4B - UNDERSTAND MULTIPLICATION OF
FRACTIONS BY WHOLE NUMBERS
Understand a multiple of a/b as a multiple of 1/b,
and use this understanding to multiply a fraction by
a whole number. For example, use a visual fraction
model to express 3 × (2/5) as 6 × (1/5), recognizing
this product as 6/5. (In general, n × (a/b) = (n ×
a)/b.) (4.NF footnote: Grade 4 expectations in this
domain are limited to fractions with denominators 2,
3, 4, 5, 6, 8, 10, 12 and 100.)
PROBLEM 1:
Which expression is equivalent to 6 × ⅔ ?
A. 12 × ½
B. 12 × ⅓
C. 6 × ⅓
D. 3 × ⅔
PROBLEM 2:
True or False?
5x
1
5
=
PROBLEM 3:
Kara wrote an expression that has a value of 12/5.
For parts (a)-(c), circle YES or NO to indicate whether each expression has a value
of 12/5.
YES or NO (a) 12 × ⅕
YES or NO (b) 12 × 5/5
YES or NO (c) 3 × ⅘
PROBLEM 4:
Rewrite:
3 x 6/8 as the product of a unit fraction and a whole number. Solve.
Rewrite:
4 x 2/3 as the product of a unit fraction and a whole number. Solve
4NF.4C - MULTIPLY FRACTIONS BY WHOLE
NUMBERS IN WORD PROBLEMS
Solve word problems involving multiplication of a fraction
by a whole number, e.g., by using visual fraction models
and equations to represent the problem. For example, if
each person at a party will eat 3/8 of a pound of roast
beef, and there will be 5 people at the party, how many
pounds of roast beef will be needed? Between what two
whole numbers does your answer lie? (4.NF footnote:
Grade 4 expectations in this domain are limited to
fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and
100.)
PROBLEM 1:
Jasmine makes 6 purses. She uses ¾ yard
of cloth to make each purse. What is the
total amount of cloth, in yards, Jasmine
uses to make all 6 purses?
PROBLEM 2:
What is the ?
5x?
=
1
5
1
5
1
5
1
5
+ + + +
1
5
PROBLEM 3:
In a relay race, each runner runs ½ of a lap. If
there are 4 team members, how long is the race
altogether?
A.
B.
C.
D.
⅛ lap
1 lap
2 laps
4½ laps
PROBLEM 4:
A builder planned to build houses.
Each house will be built on ⅚
of an acre. How much land will be
needed for 7 houses? Show your
work.