standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Problem 1
Look at your yardstick and 12-inch ruler again.
Ms. Cole says that 1 foot is equivalent to
$$\frac{1}{3}$$
yard. Do you agree or disagree? Explain.
Using similar reasoning, determine what fraction of a foot an inch is.
Use your reasoning from Part (a) to solve the following conversions.
$$\frac{2}{3}$$
yard = ______ feet
$$2\frac{1}{3}$$
yards = ______ feet
$$\frac{5}{12}$$
foot = ______ inches
$$3\frac{1}{4}$$
feet = ______ inches
$$4\frac{1}{2}$$
yards = ______ inches
Problem 2
a.  Show or explain how you know
$${{1\over16}}$$
pound =
$$1$$
ounce.
b.  Show or explain how you know
$${1\over4}$$
pound =
$$4$$
ounces.
c.  Show or explain how you know
$$4{3\over8}$$
pounds =
$${67}$$
ounces.
Problem 3
Solve.
a.
$${{1\over4}}$$
gallon = ________ quart
b.
$${{3\over2}}$$
quarts = ________ pints
c.
$${4{1\over2}}$$
pints = ________ cups
d.
$${7{3\over4}}$$
cups = ________ fluid ounces
Problem 4
Solve.
a.
$${{1\over24}}$$
day = ________ hour
b.
$${{13\over60}}$$
hour = ________ minutes
c.
$${2{1\over4}}$$
minutes = ________ seconds
d.
$${3{1\over2}}$$
days = ________ minutes


aligns: no