This lesson plan contains solutions to ratio and proportion problems: 1) The ratio of the sides of a rectangle is 4:5. To make it a square, the shorter side must be increased by 1/4 and the longer side must be decreased by 1/5. 2) The original ratio of two quantities is 3:5. If the smaller is made 4 times as large, the new ratio is 12:5. If the smaller is doubled and the larger halved, the new ratio is 12:5.

1. LESSON PLAN
Submitted by
Greeshma George

2. WELCOME

3. The sides of a rectangle are in the ratio 4 ∶ 5
(1)By what fraction should the shorter be increased to
make it a square?
(2)By what fraction should be longer side be decreased
to make it a square?

4. Ratio of sides = 𝟒 ∶ 𝟓
Shorter side = 𝟒𝒙
Larger side = 𝟓𝒙
(i) Let k part of the shorter side be increased
k part of shorter side = 𝒌 × 𝟒𝒙
= 𝟒𝒌𝒙
New shorter side = 𝟒𝒙 + 𝟒𝒌𝒙

5. 𝟒𝒙 + 𝟒𝒌𝒙 : 𝟓 = 𝟏 ∶ 𝟏
𝟒𝒙 + 𝟒𝒌𝒙/𝟓𝒙 = 𝟏/𝟏
𝟒𝒙 + 𝟒𝒌𝒙 = 𝟓𝒙
𝟒𝒌 = 𝟓𝒙 − 𝟒𝒙
𝟒𝒌𝒙 = 𝒙
𝒌 = 𝒙/𝟒𝒙
𝒌 = 𝟏/𝟒 , the required fraction

6. Let k part of the longer side be decreased.
k part of the longer side = 𝑘 × 5𝑥
= 5𝑘𝑥
New longer side = 5𝑥 – 5𝑘𝑥
4𝑥 ∶ (5𝑥 – 5𝑘𝑥) = 1 : 1

7. 𝟒𝒙
(𝟓𝒙 – 𝟓𝒌𝒙)
=
𝟏
𝟏
𝟒𝒙 = 𝟓𝒙 – 𝟓𝒌𝒙
𝟓𝒌𝒙 = 𝟓𝒙 – 𝟒𝒙
𝟓𝒌𝒙 = 𝒙
𝒌 =
𝒙
𝟓𝒙
𝒌 =
𝟏
𝟓
, is the required fraction

8. Two quantities are in the ratio 3 : 5.
(1)If the smaller alone is made four times the
original, what would the ratio be?
(2)If the smaller is doubled and the larger is halved,
what would the ratio be?

9. Ratio of quantities = 𝟑 ∶ 𝟓
Smaller quantity = 𝟑𝒙
Larger quantity = 𝟓𝒙
New smaller quantity = 𝟒 × 𝟑𝒙
= 𝟏𝟐𝒙
Larger quantity = 𝟓𝒙
New ratio = 𝟏𝟐𝒙 ∶ 𝟓𝒙
= 𝟏𝟐 ∶ 𝟓

10. New smaller quantity = 𝟐 × 𝟑𝒙 = 𝟔𝒙
New larger quantity =
𝟓𝒙
𝟐
New ratio = 𝟔𝒙 ∶
𝟓𝒙
𝟐
= 𝟔 ∶
𝟓
𝟐
= 𝟔 × 𝟐 ∶
𝟓
𝟐
× 𝟐
= 𝟏𝟐 ∶ 𝟓