Find the Ratio: Converting 400g Flour and 200g Sugar to Simplest Form

Q: Why is the ratio 2:1 and not 400:200?

Ratios should always be in simplest form! Since 400 and 200 both divide by 200, we get $ 400 ÷ 200 = 2 $ and $ 200 ÷ 200 = 1 $, giving us 2:1.

Q: How do I know which number comes first in the ratio?

The order matches the question! Since it asks for flour to sugar, flour comes first. Always read carefully: 'A to B' means A:B.

Q: What does 2:1 actually mean in this recipe?

It means for every 2 parts flour, you need 1 part sugar. So flour is exactly twice the amount of sugar in this recipe!

Q: Can I write this as a fraction instead?

Yes! The ratio 2:1 can also be written as the fraction $ \frac{2}{1} = 2 $. Both show that flour is 2 times the amount of sugar.

Q: What if the numbers don't divide evenly?

Find the Greatest Common Divisor (GCD) of both numbers, then divide each number by the GCD. This always gives you the simplest form!

Ratio Simplification with Common Factors

A recipe calls for 400g of flour and 200g of sugar. What is the ratio of flour to sugar in the recipe?

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Step-by-step written solution

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Understand the problem

A recipe calls for 400g of flour and 200g of sugar. What is the ratio of flour to sugar in the recipe?

Step-by-step solution

To find the ratio of flour to sugar, divide the amount of flour by the amount of sugar.
Thus, we have $\text{flour:sugar} = \frac{400}{200} = 2:1$ .
Therefore, the ratio of flour to sugar is $2:1$ .

Final Answer

$3:2$

Key Points to Remember

Essential concepts to master this topic

Rule: Ratios compare quantities by dividing one by another
Technique: Find GCD of 400 and 200, then divide both by 200
Check: Verify 2:1 means flour is double the sugar amount ✓

Common Mistakes

Avoid these frequent errors

Writing ratios in wrong order
Don't write sugar:flour when asked for flour:sugar = backwards answer! This flips the relationship completely and shows sugar as the larger quantity. Always match the order requested in the question.

Practice Quiz

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What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

Why is the ratio 2:1 and not 400:200?

Ratios should always be in simplest form! Since 400 and 200 both divide by 200, we get $400 ÷ 200 = 2$ and $200 ÷ 200 = 1$ , giving us 2:1.

How do I know which number comes first in the ratio?

The order matches the question! Since it asks for flour to sugar, flour comes first. Always read carefully: 'A to B' means A:B.

What does 2:1 actually mean in this recipe?

It means for every 2 parts flour, you need 1 part sugar. So flour is exactly twice the amount of sugar in this recipe!

Can I write this as a fraction instead?

Yes! The ratio 2:1 can also be written as the fraction $\frac{2}{1} = 2$ . Both show that flour is 2 times the amount of sugar.

What if the numbers don't divide evenly?

Find the Greatest Common Divisor (GCD) of both numbers, then divide each number by the GCD. This always gives you the simplest form!

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