Solve proportions
key notes :-
1. Definition of Proportions
- A proportion is an equation that states that two ratios or fractions are equal.
- It is expressed in the form:
- The numbers a, b, c, and d are called terms of the proportion. a and d are called extremes, and b and c are called means.
2. Cross Multiplication Method
- To solve proportions, we can use the cross-multiplication method.
- Cross-multiply the extremes and the means: a×d=b×c
- Then, solve for the unknown term.
3. Example of Solving Proportions
- Problem: Solve the proportion
- Step 1: Cross-multiply: 3×8 = 4×x.
- Step 2: Simplify: 24 = 4x.
- Step 3: Solve for x:
- So, x=6.
Learn with an example
✈️ Solve for w in the proportion.
4/6 = 6/w
w = ____
- Solve for w in the proportion.
- 4/6 = 6/w
- 4/6 ( 6w ) = 6/w ( 6w ) ——-> Multiply both sides by 6w
- 4w = 6 · 6 ——–>Simplify
- 4w = 36 ——-> Simplify
- w = 9 —–>Divide both sides by 4
✈️ Solve for d in the proportion.
1/4 = 2/d
d = ____
- Solve for d in the proportion.
- 1/4 = 2/d
- 1/4 ( 4d ) = 2/d ( 4d ) ——->Multiply both sides by 4d
- d = 4 · 2 ——> Simplify
- d = 8 ——-> Simplify
✈️ Solve for t in the proportion.
10/t = 8/12
t= __
- Solve for t in the proportion.
- 10/t = 8/12
- 10/t ( 12t ) = 8/12 ( 12t ) ——> Multiply both sides by 12t
- 12 · 10 = 8t ——> Simplify
- 120 = 8t ——> Simplify
- 15 = t ——> Divide both sides by 8
Let’s practice! 🖊️
