Ratios & Proportions: Find the Missing Value

Key Vocabulary:

• Ratios: Compare two or more quantities and can be written in three different ways.

  • Example:

    • 5:6 – using a colon

    • 5/6 – fraction form

    • 5 to 6 – typical way of reading a ratio

• Proportion: Shows that two or more ratios are equivalent.

  • Separated by an equal sign.

    • Example: 1/2=8/16

Key Points:

1. Proportions are the same as equivalent fractions.

   • Example: 34 is equivalent to 912

     • 3/4×3/3=912

2. Show proportions in fractional form to easily calculate and solve.

   • Example:

     • Solve for x:
       1 : 2 = 5 : x

     • Step 1: Turn the equation into fraction form.

       • 1 : 2 = 5 : x → 12=5𝑥

     • Step 2: Cross-multiply

       • 1/2=5/𝑥 1×𝑥=2×5𝑥=10

3. Use clear multiplication or division relationships to solve proportions.

   • Example: 3/5=𝑥2/5

     • 3/5×5/5=15/25

Practice Problems

Try solving each problem below, check your answer, and then play the video to see a step-by-step walkthrough of the solution.

Practice Problem #1

Complete the ratio: 12 to 15 is equal to X to 60.

12/15 = x/60

15x/15 = 720/15

x=48

Practice Problem #2

Complete the ratio: 6 to 8 is equal to X to 36.

6/8 = x/36

8x/8 = 216/8

x=27

Practice Problem #3

Complete the ratio: 0.75 to 120 is equal to X to 456.

0.75/120 = x/456

120x/120 = 342/120

x=2.85

Practice Problem #4

Complete the ratio: 36 to 56 is equal to 28.8 to X.

36/56 = 28.8/x

36x/36 = 1612.8/36

x=44.8