Express a ratio in simplest form

Amber : violet

\(\displaystyle 45:63\)

Which is the simplest whole-number ratio?

You group 42 items and 70 items, using the same number of items in every group. Which exact group size should give the smallest whole-number group counts?

Each row starts with a fixed number of items. Use the same group size for both rows. The Groups column shows complete groups; Left shows leftover items. Find the largest size with no leftovers

Which group size is the largest that fits both sets exactly?

Use one common factor

An equivalent ratio keeps the same comparison. Make the terms whole numbers in a common unit, then divide every term by their highest common factor

1. 1Keep the order The names determine which term comes first
2. 2Match units Convert like quantities to the same unit before comparing their numbers \(\displaystyle 1.7\text{ m}=170\text{ cm}\)
3. 3Change every term Use the same multiplier to clear decimals or fraction denominators. Then remove any common factor

Ratio

\(\displaystyle 54:81\)

Write the simplest whole-number ratio

Find the highest common factor of both terms

First : second

\(\displaystyle 1.6\text{ m}:72\text{ cm}\)

Write the lengths as a simplest whole-number ratio

Convert the first length to centimetres before simplifying

Ratio

\(\displaystyle 0.45:1.05\)

Write the simplest whole-number ratio

Multiply both terms by one hundred, then simplify

Ratio

\(\displaystyle \frac{5}{6}:\frac{7}{9}\)

Write the simplest whole-number ratio

Use a common multiple of both denominators

The task asks for simplest form. What should the student do next?