Use one known part of a ratio to find the others

A ratio is 2:5. The two-part share is 24 g. What should you divide 24 by to find one part?

A, B and C have masses in the ratio 3:5:2. If A increases from 18 g to 36 g and the ratio stays fixed, what happens to the total?

The ratio of masses A:B:C is 3:5:2. Change the known mass of A. Each mass is its Parts value times one equal part. Compare masses of 18 g and 36 g for A, then find the total when A has a mass of 36 g

When A is 36 g, what is the total mass?

Start with the known share

The divisor depends on what the given amount represents. Divide a total by all the parts, but divide one known share by its own term

1. 1Match The known amount is one share, not the total. Match it to its ratio term
2. 2Divide Divide the known amount by its own term to find one equal part
3. 3Multiply Multiply one part by the requested term. For the total, use the sum of all terms

A : B : C

\(\displaystyle 4:7:3\)

Known mass of A

\(\displaystyle 52\text{ g}\)

Find B’s mass

The 52 g is four parts, not fourteen parts

Red : blue : green

\(\displaystyle 3:2:5\)

Blue counters

\(\displaystyle 18\)

Find the total number of counters

Find one part from the blue counters, then count all the parts

A : B

\(\displaystyle 3:5\)

Known amount for B

\(\displaystyle 40\text{ L}\)

Which first step is appropriate?

A plan uses scale 1:200. An actual wall is 12 m long. Should its plan length be larger or smaller than 12 m?

At scale 1:200, the table shows a 3 cm plan length represents 6 m. How long would an actual 12 m wall be on the same plan?

Use the scale in the right direction

A 1:200 drawing represents each 200 cm of actual length by 1 cm on the drawing. Keep the units the same when applying the scale

1. 1Same unit first A scale of 1:n compares drawing and actual lengths in the same unit
2. 2Drawing to actual Multiply the drawn length by n, then convert units if needed \(\displaystyle 3\text{ cm}\times200=600\text{ cm}=6\text{ m}\)
3. 3Actual to drawing Convert the actual length to the drawing unit, then divide by n \(\displaystyle 600\text{ cm}\div200=3\text{ cm}\)

Model scale

\(\displaystyle 1:50\)

Actual length

\(\displaystyle 9\text{ m}\)

Find the model length in cm

Convert 9 m to cm before dividing by 50

A 1:100 plan shows a 4 cm wall. Which method finds the actual length?