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Objective: Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. (5NS 1.2) Remind students about the names of the place values to the right of the decimal, how to verbally express decimals in word form, and how they are written as fractions. Decimal Say (Word Form) Fraction Fraction with Powers of 10 0.1 one tenth 0.01 one hundredth
one thousandth
Example 1: (Model with direct instruction) Express 0.8 as a fraction in simplest form. 1 8 10
2 i 2 i 2
2 i 5
÷
GCF = 2
Simplify with Prime Factorization Simplify with Greatest Common Factor Model with Base- Blocks
Converting decimals into fractions
ASK: “What do you notice about the number of decimal places and the denominators in each fraction?” [ The number of decimal places is the power of 10 in the denominator. i.e. two decimal places => 102 = 100 ]
Example 2: (Model with direct instruction) Express 0.08 as a fraction in simplest form. 1 8 100
2 i 2 i 2
2 i 2 i 5 i 5
÷
GCF = 4
Simplify with Prime Factorization Simplify with Greatest Common Factor Model with Base- Blocks Example 3: (You Try!) Express 0.5 as a fraction in simplest form. 1 5 10
2 i 5
÷
GCF = 5
Simplify with Prime Factorization Simplify with Greatest Common Factor Model with Base- Blocks ASK: What do you notice about the two different models for 0.8 and 0.08? [ Accept any reasonable responses. Sample: 0.08 is much smaller than 0.8. ]
Converting Fractions to Decimals
When the denominator is a 10, 100, or 1,000: 0.7 =
Remind students that when we convert decimals to fractions, the number of decimal places reveals the value of the denominator. The same is true when converting fractions to decimals. Therefore: 8 10
Making equivalent fractions: 2 5
i
= 1 , therefore according to the Identity Property of Multiplication the value of
remains the same.
i
i
i
i
Other examples: CST Released Test Question: What decimal is equal to
A) 0.
B) 0.
C) 0.
D) 1.
Solution: 3 5
i
The denominator informs us how many decimal places our number will contain. 1000 = 103 , therefore our answer has three (3) decimal places.
Using division: 5 8
= 5 ÷ 8 8 5.
So,
The Secret to Dividing with Decimals Adding zeros after (or to the right) of a decimal point does not change a number’s value! 15 9
3 i 5 3 i 3 = 5 ÷ 3 3 5.
So,
Other examples: So, 2
= 2 + ( 2 ÷ 5 )
