Evaluate the Expression: Converting Ratio 19:8 to Standard Form

Q: Why do we decompose 19 as (20-1) instead of other combinations?

We choose 20-1 because 20 divides evenly by 8, making the calculation simpler! This gives us $ 20:8 = \frac{20}{8} = 2\frac{1}{2} $, which is much easier to work with.

Q: How do I know when to write the answer as a fraction?

When you have a division like 1:8, always convert it to fraction form $ \frac{1}{8} $. This makes the final expression clearer and follows standard mathematical notation.

Q: Can I decompose ratios in other ways?

Yes! You could write 19:8 as (18+1):8 or (15+4):8. However, choose decompositions that make calculations easier - usually involving round numbers that divide evenly.

Q: Why can't I just calculate 19÷8 directly?

You absolutely can! But this exercise teaches decomposition skills that help with more complex problems. It shows you how to break down ratios systematically using known facts.

Ratio Decomposition with Fraction Subtraction

What expression does the 19:8 exercise equal?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the equivalent expression

00:03 Use the distribution law

00:07 Break down 19 into 20 minus 1

00:12 Divide each factor and then subtract

00:23 Solve the division and find the expression

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What expression does the 19:8 exercise equal?

Step-by-step solution

Let us begin by decomposing 19 into a subtraction exercise:

$(20-1):8=$

Next we divide each term inside of the parentheses by 8:

$20:8-1:8=$

We can see that answers C+D can be discarded since we divided 20 by 8.

Now we write the division exercise on the right as a fraction and we get:

$20:8-\frac{1}{8}$

Final Answer

20:8 and we subtract $\frac{1}{8}$

Key Points to Remember

Essential concepts to master this topic

Decomposition Rule: Break ratios into simpler parts using addition or subtraction
Technique: Convert 19:8 to (20-1):8, then distribute: 20:8 - 1:8
Check: Verify 20:8 - $\frac{1}{8}$ equals original 19:8 ratio ✓

Common Mistakes

Avoid these frequent errors

Not converting division to fraction form
Don't leave 1:8 as division notation = confusing expression! This makes it unclear what mathematical operation you're performing. Always convert division ratios to fraction form: 1:8 = $\frac{1}{8}$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why do we decompose 19 as (20-1) instead of other combinations?

We choose 20-1 because 20 divides evenly by 8, making the calculation simpler! This gives us $20:8 = \frac{20}{8} = 2\frac{1}{2}$ , which is much easier to work with.

How do I know when to write the answer as a fraction?

When you have a division like 1:8, always convert it to fraction form $\frac{1}{8}$ . This makes the final expression clearer and follows standard mathematical notation.

Can I decompose ratios in other ways?

Yes! You could write 19:8 as (18+1):8 or (15+4):8. However, choose decompositions that make calculations easier - usually involving round numbers that divide evenly.

What if the second number in the ratio isn't 8?

The same method works! For example, 23:5 becomes (25-2):5 = 25:5 - 2:5 = $5 - \frac{2}{5}$ . Always look for the nearest multiple of your denominator.

Why can't I just calculate 19÷8 directly?

You absolutely can! But this exercise teaches decomposition skills that help with more complex problems. It shows you how to break down ratios systematically using known facts.

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