Grade 6Math

Writing Ratios in Three Notations

This Grade 6 math skill from Pengi Math (Grade 6) teaches students to write ratios using all three standard notations: as a fraction (a/b), with a colon (a:b), and in words (a to b). Students practice recognizing and converting between these forms to communicate ratios clearly in any context.

Key Concepts

Property A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$, $\frac{a}{b}$, or $a:b$.

Examples The ratio 20 to 36 can be written as $20\ \text{to}\ 36$, $20:36$, and $\frac{20}{36}$.

The ratio 45 to 18 can be written as $45\ \text{to}\ 18$, $45:18$, and $\frac{45}{18}$.

Common Questions

What are the three ways to write a ratio?

A ratio can be written as a fraction (3/4), with a colon (3:4), or in words (3 to 4). All three forms represent the same relationship.

Which notation for ratios is most common in school math?

The colon notation (a:b) is very common in ratio problems, but fraction notation is used when performing calculations and percent notation is used for part-to-whole relationships.

Can ratios be simplified like fractions?

Yes. Ratios can be simplified by dividing both terms by their greatest common factor. For example, 6:9 simplifies to 2:3.

Is the order of numbers in a ratio important?

Yes. The order of terms in a ratio matters. A ratio of 3:5 is different from 5:3 because they represent different comparisons.

Where is writing ratios in three notations taught?

This skill is covered in the Grade 6 Pengi Math textbook as part of the introduction to ratios.