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RATIOS
MATH IS
FUN!!!

•Compare the number of boys
to girls currently sitting in
this classroom.
• The number of boys =
• The number of girls =
• If we compare boys to girls we get
___ boys to _____ girls.
What do we call a comparison
between two quantities?
RATIO
We just found the
RATIO of boys to
girls.
Is the ratio of
girls to boys
the same ?
No, when writing a ratio, ORDER matters.
What is a ratio?
• A ratio is a comparison of
two numbers by division.
• Part-to-whole ratios
Example: girls to all
students in the class.
• Part-to-part ratios
Example: number of girls in
the class compared to the
number of boys.
It’s Friday night and your friends are having
a party……
The ratio of girls to guys is 2 to 12.
Would you want to attend the
party?
How many basketballs to footballs
are there?
• For every 4 basketballs
there are 6 footballs.
• The ratio is 4 to 6.
What are some other ways we
can write the ratio of
basketballs to footballs?
Every ratio can be written in 3 ways:
Careful !
• 4 to 6
First quantity to Second quantity
• 4:6
First quantity : Second quantity
•
4
6
First quantity divided by the
second quantity (as a fraction).
Order matters in a
ratio.
4 to 6
Is NOT the same as
6 to 4
Write the ratio of sandwiches to coke
bottles 3 different ways.
6:8 , 6 to 8, and 6
8
Since a fraction can be simplified, We can simplify the
ratio 6*
to 3$
. The ratio of
sandwiches to coke bottles can also be expressed as
3 : 4 or 3 to 4.
In other words, ratios can be simplified 6 = 3
to form equivalent ratios.
8
4
6 sandwiches to 8 cokes
EQUALS
6
8
3 sandwiches for every 4 cokes
3
=
4
Why don’t we try one more…
•
Kathy has a bag with 3 videocassettes, 4
marbles, 7 books, and 1 orange.
1) What is the ratio of books to marbles?
Answer: 7 to 4 7:4 7$
1) What is the ratio of videocassettes to the
total number of items in the bag?
Answer: 3 to 15 3:15 3! %
OR 1 to 5 1:5
1%
Simplifying Ratios
• Simplify the following ratios:
– 4 to 8
– 10 to 8
– 8 to 10
4 ÷4
=1
8 ÷4
2
= 1 to 2
Step 1 – Write the ratio as a fraction.
Step 2 – Simplify the fraction.
Step 3 – Write the equivalent ratio in the same form as the question.
10 ÷ 2
8 ÷2
= 5 = 5 to 4
4
8 ÷2 =4
10 ÷ 2
5
= 4 to 5
Are the following ratios equivalent?
3
18
1
6
2
and
12
4
10
and
5
15
Simplify both fractions.
1
6
2
5
1
3
But there are a few more ways to
tell if ratios are equivalent……