student learning goal chart handout pre-algebra learning goal student will understand rational and...
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Student Learning Goal Chart
Handout
Pre-Algebra Learning Goal
Student will understand rational and real numbers.
Students will understand rational and real numbers by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)
Pre-Algebra
3-1 Rational Numbers
Today’s Learning Goal Assignment
Learn to write rational numbers in equivalent forms.
Pre-Algebra
3-1 Rational Numbers
rationalonumber
relativelyoprime
Vocabulary
Pre-Algebra
3-1 Rational Numbers
A rational number is any number that can be written as a fraction , where n and d are integers and d 0.
nd
Decimals that terminate or repeat are rational numbers.
Pre-Algebra
3-1 Rational Numbers
Numerator nd Denominator
Pre-Algebra
3-1 Rational Numbers
The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.
Pre-Algebra
3-1 Rational Numbers
12 of the 15 boxes are shaded.
4 of the 5 boxes are
shaded.
The same total area is shaded.
You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3.
1215
45
=1215
45
Pre-Algebra
3-1 Rational Numbers
Lesson Quiz: Part 1
Simplify.
1. 2.
Write each decimal as a fraction in simplest form.
3. 0.27 4. –0.625
5. Write as a decimal 2.16
18 42
3 7
15 21
5 7
27 100
– 5 8
13 6
Pre-Algebra
3-1 Rational Numbers
Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.)
Lesson Quiz: Part 2
6.
0.325
Pre-Algebra
3-1 Rational Numbers
Are you ready for the FAST Track?
If YES, prepare for Ch. 3 Section 2 along with Ch. 3 Section 5!
If NO, continue with the Ch. 3 Section 1 lesson!
Pre-Algebra
3-1 Rational Numbers
Pre-Algebra HW: page ?? #?-??
Page ??
#?-??
Pre-Algebra
3-1 Rational Numbers3-1 Rational Numbers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
3-1 Rational Numbers
Warm UpDivide.
Pre-Algebra
3-1 Rational Numbers
12 24
34
16
1. 36 3 2. 144 6
3. 68 17 4. 345 115
5. 1024 64
Pre-Algebra
3-1 Rational Numbers
Problem of the Day
An ice cream parlor has 6 flavors of ice cream. A dish with two scoops can have any two flavors, including the same flavor twice. How many different double-scoop combinations are possible? 21
Pre-Algebra
3-1 Rational Numbers
Today’s Learning Goal Assignment
Learn to write rational numbers in equivalent forms.
Pre-Algebra
3-1 Rational Numbers
rationalonumber
relativelyoprime
Vocabulary
Pre-Algebra
3-1 Rational Numbers
A rational number is any number that can be written as a fraction , where n and d are integers and d 0.
nd
Decimals that terminate or repeat are rational numbers.
Pre-Algebra
3-1 Rational Numbers
Numerator nd Denominator
Pre-Algebra
3-1 Rational Numbers
The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.
Pre-Algebra
3-1 Rational Numbers
12 of the 15 boxes are shaded.
4 of the 5 boxes are
shaded.
The same total area is shaded.
You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3.
1215
45
=1215
45
Pre-Algebra
3-1 Rational Numbers
Additional Example 1A: Simplifying Fractions
5 10
5 = 1 • 5 10 = 2 • 5
;5 is a common factor.
Divide the numerator and denominator by 5.
1 2
=
510
Simplify.
= 5 ÷ 5 10 ÷ 5
A.
Pre-Algebra
3-1 Rational Numbers
Additional Example 1B: Simplifying Fractions
16
80
16 = 1 • 16 80 = 5 • 16
;16 is a common factor.
1 5
=
1680
Divide the numerator and denominator by 16.= 16 ÷
16 80 ÷ 16
B.
Simplify.
Pre-Algebra
3-1 Rational Numbers
= –18 29
–18 29
18 = 2 • 9 29 = 1 • 29
;There are no common factors.
–18 and 29 are relatively prime.–18 29
C.
Simplify.
Additional Example 1C: Simplifying Fractions
Pre-Algebra
3-1 Rational Numbers
Try This: Example 1A
6 30
6 = 1 • 630 = 5 • 6
;6 is a common factor.
Divide the numerator and denominator by 6.
1 5
=
630 = 6 ÷ 6
30 ÷ 6
A.
Simplify.
Pre-Algebra
3-1 Rational Numbers
18
27
;9 is a common factor.
2 3
=
1827 =18 ÷ 9
27 ÷ 9
B.
Divide the numerator and denominator by 9.
Try This: Example 1B
Simplify.
18 = 3 • 3 • 227 = 3 • 3 • 3
Pre-Algebra
3-1 Rational Numbers
= – 17 35
17 –35
17 = 1 • 17 35 = 5 • 7
;There are no common factors.
17 and –35 are relatively prime.
17 –35
C.
Try This: Example 1C
Simplify.
Pre-Algebra
3-1 Rational Numbers
To write a finite decimal as a fraction, identify the place value of the farthest digit to the right. Then write all of the digits after the decimal points as the numerator with the place value as the denominator.
Pre-Algebra
3-1 Rational Numbers
–0.8
A. –0.8 –8 is in the tenths place.
Simplify by dividing by the common factor 2.
–8 10
=
= – 45
Additional Example 2A: Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
Pre-Algebra
3-1 Rational Numbers
5.37
B. 5.37 7 is in the hundredths place.
37 100
= 5
Additional Example 2B: Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
Pre-Algebra
3-1 Rational Numbers
0.622
C. 0.622 2 is in the thousandths place.
622 1000
=
= 311 500
Simplify by dividing by the common factor 2.
Additional Example 2C: Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
Pre-Algebra
3-1 Rational Numbers
–0.4
A. –0.4 –4 is in the tenths place.
Simplify by dividing by the common factor 2.
–4 10
=
Write the decimal as a fraction in simplest form.
Try This: Example 2A
= – 25
Pre-Algebra
3-1 Rational Numbers
8.75
B. 8.75 5 is in the hundredths place.
75 100
= 8
= 8 3 4
Simplify by dividing by the common factor 25.
Write the decimal as a fraction in simplest form.
Try This: Example 2B
Pre-Algebra
3-1 Rational Numbers
0.2625
0.2625 5 is in the ten-thousandths place.
2625 10,000
=
= 21 80
Simplify by dividing by the common factor 125.
C.
Write each decimal as a fraction in simplest form.
Try This: Example 2C
Pre-Algebra
3-1 Rational Numbers
denominator numerator
To write a fraction as a decimal, divide the numerator by the denominator. You can use long division.
When writing a long division problem from a fraction, put the numerator inside the “box,” or division symbol. It may help to write the numerator first and then say “divided by” to yourself as you write the division symbol.
numeratordenominator
Pre-Algebra
3-1 Rational Numbers
9 11 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal.
1
–9
.2
2
0
.0
2
11 9
–1 8
Additional Example 3A: Writing Fractions as Decimals
A.
Write the fraction as a decimal.
The fraction is equivalent to the decimal 1.2.11 9
Pre-Algebra
3-1 Rational Numbers
This is a terminating decimal.20 7
.30 5
The remainder is 0.
7 20
–07
1 0
0
0
0
.0
0–6 0
–1 0 0
B.
Additional Example 3B: Writing Fractions as Decimals
Write the fraction as a decimal.
The fraction is equivalent to the decimal 0.35.7 20
Pre-Algebra
3-1 Rational Numbers
9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal.
1
–9
.6
6
0
.0
6
15 9
–5 4
Write the fraction as a decimal.
Try This: Example 3A
A.
The fraction is equivalent to the decimal 1.6.15 9
Pre-Algebra
3-1 Rational Numbers
40 9 This is a terminating decimal..20 2
The remainder is 0.
9 40
–09
1 0
0
0
.0
0–8 0
– 8 02 0
0
0
5
0– 2 00
B.
Write the fraction as a decimal.
Try This: Example 3B
The fraction is equivalent to the decimal 0.225.9 40
Pre-Algebra
3-1 Rational Numbers
Lesson Quiz: Part 1
Simplify.
1. 2.
Write each decimal as a fraction in simplest form.
3. 0.27 4. –0.625
5. Write as a decimal 2.16
18 42
3 7
15 21
5 7
27 100
– 5 8
13 6
Pre-Algebra
3-1 Rational Numbers
Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.)
Lesson Quiz: Part 2
6.
0.325