Ratio Tables and Graphs - Basic Number Systems and Operations Within Them (Pre-Algebra)

	Fraction Form	Greatest Common Factor	Rewrite	Simplify
Tearrik	$\frac{2 7}{1 5}$	$GCF (27, 15) = 3$	$\frac{9 \cdot 3}{5 \cdot 3}$	$\frac{9}{5}$
Zain	$\frac{4 5}{2 5}$	$GCF (45, 25) = 5$	$\frac{9 \cdot 5}{5 \cdot 5}$	$\frac{9}{5}$

Fraction Form

Greatest Common Factor

Rewrite

Simplify

Tearrik

\frac{2 7}{1 5}

GCF (27, 15) = 3

\frac{9 \cdot 3}{5 \cdot 3}

\frac{9}{5}

Zain

\frac{4 5}{2 5}

GCF (45, 25) = 5

\frac{9 \cdot 5}{5 \cdot 5}

\frac{9}{5}

$\frac{1 4}{6}$
Scaling Back	Scaling Forward
$\frac{1 4 \div 2}{6 \div 2}$	$\frac{7 \times 3}{3 \times 3}$
$\frac{7}{3}$	$\frac{2 1}{9}$

\frac{1 4}{6}

Scaling Back

Scaling Forward

\frac{1 4 \div 2}{6 \div 2}

\frac{7 \times 3}{3 \times 3}

\frac{7}{3}

\frac{2 1}{9}

Distance Run (Miles)	$1$	$2$	$3$	$4$
Time (Minutes)	$10$	$20$	$30$	$40$

Distance Run (Miles)

1

2

3

4

Time (Minutes)

10

20

30

40

Height	$2$	$A$	$6$	$18$
Width	$3$	$6$	$9$	$B$

Height

2

A

6

18

Width

3

6

9

B

Height	$2$	$A$	$6$	$18$
Width	$3$	$6$	$9$	$B$

Height

2

A

6

18

Width

3

6

9

B

Height, $x$	$2$	$4$	$6$	$18$
Width, $y$	$3$	$6$	$9$	$27$

Height,

x

2

4

6

18

Width,

y

3

6

9

27

Maya	Mark
Days	Photos	Days	Photos
$1$	$5$	$1$	$7$
$2$	$10$	$2$	$14$
$3$	$15$	$3$	$21$
$4$	$20$	$4$	$28$
$5$	$25$	$5$	$35$

Maya

Mark

Days

Photos

Days

Photos

1

5

1

7

2

10

2

14

3

15

3

21

4

20

4

28

5

25

5

35

a The tables will be graphed one by one on a coordinate plane. The

x -

axis will indicate the days, while the

y -

axis will show the number of photos taken. Begin by writing the ordered pair

(x, y)

for each column of the table recorded by Maya.

Maya
Days	Photos	$(x, y)$
$1$	$5$	$(1, 5)$
$2$	$10$	$(2, 10)$
$3$	$15$	$(3, 15)$
$4$	$20$	$(4, 20)$
$5$	$25$	$(5, 25)$

To graph the data, begin at the origin and move along the $x -$ axis the number of units specified by the day. Then, move the number of units specified by the photos taken vertically to graph each ordered pair.

Before adding Mark's data to the graph, write each column of the table as an ordered pair.

Mark
Days	Photos	$(x, y)$
$1$	$7$	$(1, 7)$
$2$	$14$	$(2, 14)$
$3$	$21$	$(3, 21)$
$4$	$28$	$(4, 28)$
$5$	$35$	$(5, 35)$

Each ordered pair can now be added to the graph.

The graph corresponds to the one given in option B.

b In this part, the ratios of photos taken to days passed for Mark and Maya will be compared. Consider the first column of both tables to see their unit ratios.

	Maya	Mark
Day, $x$	$1$	$1$
Photos, $y$	$5$	$7$

Maya's photo-to-day ratio is $5 : 1$ and Mark's is $7 : 1 .$ Now, look at the graph drawn in Part A.

Notice that both sets of points appear to fit in straight lines. However, the line for Mark is steeper than the line for Maya. The statements that are true about the ratios of photos taken to days passed have been identified.

Statement	True?
The ratio of photos to days for Maya is $5 : 1 .$	$✓$
The ratio of photos to days for Mark is $7 : 1 .$	$✓$
The line for Mark's data is steeper than the line for Maya's.	$✓$
The ratio of days to photos for Maya is $5 : 1 .$	$\times$
The ratio of days to photos for Mark is $7 : 1 .$	$\times$
The line for Maya's data is steeper than the line for Mark's.	$\times$

Photos	$4$	$8$	$12$
Time (minutes)	$5$	$10$	$15$

Photos

4

8

12

Time (minutes)

5

10

15

Photos	$20$	$24$	$28$
Time (minutes)	$25$	$30$	$35$

Photos

20

24

28

Time (minutes)

25

30

35

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Catch-Up and Review

Comparing the Simplest Forms of a Pair of Ratios

Equivalent Ratios

Scaling Ratios

Determining if Two Ratios Are Equivalent

Mark's Favorite Shot

Hint

Solution

Ratio Table

Exploring the Aspect Ratio of Mark's New Phone Camera

Hint

Solution

Mark and Maya's Five-Day Photo Challenge

Hint

Solution

How Much Money Will Mark Earn?

Hint

Solution

Graphing Ratio Tables on a Coordinate Plane

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