Ratio
Ratio refers to a comparison between two similar things.
Ratio can be represented with a colon.
a:b
Ratio can also be represented as a fraction.
Ratio of yellow beads to green beads = 1 to 2 = 1:2 =
Ratio of yellow beads to green beads = 2 to 4 = 2:4 =
Ratio of yellow beads to green beads = 3 to 6 = 3:6 =
Proportion
Proportion refers to two equal ratios.
a:b = c:d
=
For ratios and
to be in proportion → ad = bc
To Prove Ratios are in Proportion, Cross-Multiply
In order to cross-multiply, it is helpful to understand algebraic equations.
It is also helpful to know your multiplication and division tables.
=
For ratios and
→
ad = 1 × 12
bc = 2 × 6
1 × 12 = 2 × 6
12 = 12
Because ad = bc, ratios and
are in proportion.
To Solve for an Unknown Variable in Proportionate Ratios, Cross-Multiply
In order to cross-multiply, it is helpful to understand algebraic equations.
It is also helpful to know your multiplication and division tables.
=
For ratios and
→
ad = bc
ad = 2 × d
bc = 4 × 5
2 × d = 4 × 5
2d = 20
=
d = 10
Question
Prove that the ratios of yellow to green beads in the image below are in proportion.
Answer
=
Answer Process
=
For ratios and
→
ad = 1 × 4
bc = 2 × 2
1 × 4 = 2 × 2
4 = 4
Because ad = bc, ratios and
are in proportion.
Question
In the image below, two ramps are in proportion. Find the length L of the larger ramp.
Answer
6
Answer Process
=
For ratios and
→
ad = 2 × L
bc = 3 × 4
2 × L = 3 × 4
2L = 12
=
L = 6
Question
In the image below, two ramps are in proportion. Find the length Q of the smaller ramp.
Answer
10
Answer Process
=
For ratios and
→
ad = 20 × Q
bc = 40 × 5
20 × Q = 40 × 5
20Q = 200
=
Q = 10
Practice – Questions
1. Prove that the ratios of yellow to green beads in the image below are in proportion.
2. In the image below, two ramps are in proportion. Find the length L of the larger ramp.
3. In the image below, two ramps are in proportion. Find the length Q of the smaller ramp.
4. In the image below, two rectangular boxes are in proportion. Find the length L of the larger box.
5. In the image below, two rectangular boxes are in proportion. Find the width W of the smaller box.
Practice – Answers
1. For ratios and
→
ad = 1 × 6
bc = 2 × 3
1 × 6 = 2 × 3
6 = 6
Because ad = bc, ratios and
are in proportion.
2. 21
3. 6
4. 21
5. 3