Math.5.NF.5a 5.NF.B.5.A Math.5.NF.5b 5.NF.B.5.B

Common Core Standards Factors & Products
Grade:	5th Grade
Standard:	Math.5.NF.5a or 5.NF.B.5.A
Description:	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.
Standard:	Math.5.NF.5b or 5.NF.B.5.B
Description:	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.

EFFECTS OF MULTIPLICATION

Does the operation of multiplication on a number result in a larger number?
The answer is sometimes. Let's look at some cases.

When a number is multiplied by a fraction equivalent to 1,
the product is equal to the number.

Example:	$3$ × $\frac{2}{2}$ = $\frac{6}{2}$ = $3$
Example:	$\frac{1}{3}$ × $\frac{4}{4}$ = $\frac{4}{12}$ = $\frac{1}{3}$

When a positive whole number is multiplied by a fraction greater than 1,
the product is greater than the whole number.

Example:

3

1 \frac{1}{4}

3

\frac{5}{4}

\frac{15}{4}

3 \frac{3}{4}

When a positive whole number is multiplied by a fraction between 0 and 1,
the product is less than the whole number.

Example:	$3$ × $\frac{1}{3}$ = $\frac{3}{3}$ = $1$
Example:	$3$ × $\frac{1}{6}$ = $\frac{3}{6}$ = $\frac{1}{2}$

When a number greater than 1 is multiplied by a number greater than 1,
the product is greater than both numbers.

Common Core Standards