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Evaluating Algebraic Expressions

Warm Up
California Standards
Lesson Presentation
5-1 Ratios

Evaluating Algebraic Expressions
Warm Up
Write each fraction in lowest terms.

1. 14   7          2. 24   3
16   8             64   8

3. 9    1          4. 45   3
72    8            120   8
5-1 Ratios

Evaluating Algebraic Expressions
California
Standards
Preparation for MG1.1 Compare
weights, capacities, geometric
measures, times, and temperatures
within and between measurement
systems (e.g., miles per hour and feet
per second, cubic inches to cubic
centimeters).
5-1 Ratios

Vocabulary
Evaluating Algebraic Expressions
ratio
equivalent ratios
5-1 Ratios

Evaluating Algebraic Expressions
A ratio is a comparison of two quantities.

Ratios can be written in several ways. 7
to 5, 7:5, and 7 name the same ratio.
5
5-1 Ratios
Additional Example 1: Writing Ratios in Simplest
Form
Evaluating Algebraic Expressions
Write the ratio 15 bikes to 9 skateboards in
simplest form.

bikes    = 15                Write the ratio
skateboards   9                 as a fraction.

15 ÷ 3
=        = 5       Simplify.
9÷3      3

5
The ratio of bikes to skateboards is     , 5:3, or 5 to 3.
3
5-1 Ratios
Check It Out! Example 1

Evaluating Algebraic Expressions
Write the ratio 24 shirts to 9 jeans in
simplest form.

shirts = 24                 Write the ratio as
jeans    9                  a fraction.

24 ÷ 3
=            = 8    Simplify.
9÷3        3

8
The ratio of shirts to jeans is     , 8:3, or 8 to 3.
3
5-1 Ratios

Evaluating Algebraic Expressions

When simplifying ratios based on
measurements, write the quantities
with the same units, if possible.
5-1 Ratios
Additional Example 2: Writing Ratios Based on
Measurement
Evaluating yards to 12 feet in simplest
Write the ratio 3 Algebraic Expressions
form.
First convert yards to feet.
3 yards = 3 ● 3 feet   There are 3 feet in each yard.
= 9 feet      Multiply.

Now write the ratio.
3 yards = 9 feet          9÷3=3
=              Simplify.
12 feet      12 feet      12 ÷ 3 4
The ratio is 3 , 3:4, or 3 to 4.
4
5-1 Ratios
Check It Out! Example 2
Write the ratio 36 inches to 4 feet in
Evaluating Algebraic Expressions
simplest form.
First convert feet to inches.
4 feet = 4 ● 12 inches   There are 12 inches in each
foot.
= 48 inches        Multiply.
Now write the ratio.
36 inches = 36 inches = 36 ÷ 12 = 3     Simplify.
4 feet     48 inches     48 ÷ 12 4
The ratio is 3 , 3:4, or 3 to 4.
4
5-1 Ratios

Evaluating Algebraic Expressions
Ratios that make the same comparison
are equivalent ratios. Equivalent
ratios represent the same point on the
number line. To check whether two
ratios are equivalent, you can write both
in simplest form.
5-1 Ratios
Additional Example 3: Determining Whether Two
Ratios Are Equivalent
Evaluating Algebraic Expressions
Simplify to tell whether the ratios are
equivalent.

A. 3 and 2     3   3 ÷ 3 =1          1= 1
=             Since       ,
27    18    27 27 ÷ 3 9           9 9
the ratios are
2   2 ÷ 2 =1
=             equivalent.
18 18 ÷ 2 9

B. 12 and 27 12 = 12 ÷ 3 = 4   Since 4  3 ,
15     36 15 15 ÷ 3 5             5 4
the ratios are not
27 = 27 ÷ 9 3
equivalent.
36 36 ÷ 9 = 4
5-1 Ratios
Check It Out! Example 3

Simplify to tell whether the ratios are
Evaluating Algebraic Expressions
equivalent.

A. 3 and 9     3   3÷3= 1            1= 1
=             Since       ,
15    45    15 15 ÷ 3 5           5 5
the ratios are
9   9÷9= 1
=             equivalent.
45 45 ÷ 9 5

14 = 14 ÷ 7 2
B. 14 and 16                   Since 2  4 ,
49 49 ÷ 7 = 7         7 9
49     36                   the ratios are not
16 = 16 ÷ 4 4
equivalent.
36 36 ÷ 4 = 9
5-1 Ratios
Additional Example 4: Earth Science Application

At 4°C, four cubic feet of silver has the same
Evaluating Algebraic Expressions
mass as 42 cubic feet of water. At 4°C,
would 20 cubic feet of silver have the same
mass as 210 cubic feet of water?
Since 2 = 2 ,
4    ? 20       ft3 silver        21      21
=
42     210      ft3 water
210 cubic feet of water
4÷2                            would have the same
= 20 ÷ 10 Divide.
?
42 ÷ 2     210 ÷ 10            mass at 4°C as 20 cubic
feet of silver.
2     =  2
21       21       Simplify.
5-1 Ratios
Check It Out! Example 4

At 4°C, two cubic feet of silver has the same
Evaluating Algebraic Expressions
mass as 21 cubic feet of water. At 4°C,
would 105 cubic feet of water have the same
mass as 10 cubic feet of silver?

2 = 10
?            ft3 silver Since 2 = 2 ,
21   105        ft3 water        21  21

2 = 10 ÷ 5
?                    105 cubic feet of water
Divide.    would have the same
21   105 ÷ 5
mass at 4°C as 10 cubic
2 = 2          Simplify. feet of silver.
21  21
5-1 Ratios
Lesson Quiz: Part I
Write each ratio in simplest form.
Evaluating Algebraic Expressions
1
1. 22 tigers to 44 lions
2
2. 5 feet to 14 inches    30
7
Find two ratios that are equivalent to each
given ratio.

3. 4   Possible answer: 8 , 12
15                    30 45

4. 8   Possible answer: 16 , 24
21                    42 63
5-1 Ratios
Lesson Quiz: Part II
Simplify to tell whether the ratios are
Evaluating Algebraic Expressions
equivalent.
5. 16 and 32 8 = 8; yes
10     20 5 5

6. 36 and 28    3 14 ; no
24     18    2 9
7. Kate poured 8 oz of juice from a 64 oz bottle.
Brian poured 16 oz of juice from a 128 oz bottle.
Are the ratios of poured juice to starting amount
of juice equivalent?
8 and 16 ; yes, both equal 1
64      128                    8

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