Calculate 3/7 and 1/3 of 210g: Finding Cake Ingredient Quantities

Q: Why do I multiply the fraction by 210 instead of dividing?

Fractions tell us what part to take! When you see $ \frac{3}{7} $ of 210g, it means "3 out of every 7 parts." Multiplying gives you exactly that portion.

Q: Can I convert the fractions to decimals first?

Yes! $ \frac{3}{7} \approx 0.429 $ and $ \frac{1}{3} \approx 0.333 $. Then multiply: 0.429 × 210 = 90g and 0.333 × 210 = 70g. Just be careful with rounding!

Q: How do I know if 160g makes sense as an answer?

Check that your answer is less than the total (210g) but more than either individual part (90g or 70g). Since 70

Q: What if the fractions add up to more than 1?

That would mean you have more ingredients than the total cake, which is impossible! Always check: \( \frac{3}{7} + \frac{1}{3} = \frac{16}{21} ✓

Q: Do I need to simplify fractions before calculating?

Not necessary for this problem! $ \frac{3}{7} $ and $ \frac{1}{3} $ are already in lowest terms. Just multiply directly by 210.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

A chocolate cake has 210 grams of ingredients.

$\frac{3}{7}$ of the ingredients are chocolate cookies and $\frac{1}{3}$ of the cake's ingredients are coconut.

How many grams of chocolate cookies and coconut are there in the cake?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the weight of the chocolate cookies.
Step 2: Calculate the weight of the coconut.
Step 3: Add these two weights to find the total weight of both components.

Step 1: Calculate the weight of the chocolate cookies:
The fraction of the total ingredients that are chocolate cookies is $\frac{3}{7}$ . Thus, the weight of the chocolate cookies is:

\text{Weight of chocolate cookies} = \frac{3}{7} \times 210 = 90 \text{ grams}

Step 2: Calculate the weight of the coconut:
The fraction of the total ingredients that are coconut is $\frac{1}{3}$ . Thus, the weight of the coconut is:

\text{Weight of coconut} = \frac{1}{3} \times 210 = 70 \text{ grams}

Step 3: Add these two weights together:
To find the total weight of the chocolate cookies and coconut, we sum the individual weights:

90 \text{ grams (chocolate cookies)} + 70 \text{ grams (coconut)} = 160 \text{ grams}

Therefore, the total weight of chocolate cookies and coconut in the cake is 160 grams.

3

Final Answer

160

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply the fraction by the whole amount to find parts
Technique: $\frac{3}{7} \times 210 = \frac{3 \times 210}{7} = \frac{630}{7} = 90$
Check: Sum individual parts: 90g + 70g = 160g total ingredients ✓

Common Mistakes

Avoid these frequent errors

Adding fractions instead of multiplying by the total
Don't add 3/7 + 1/3 = 16/21 then multiply by 210! This gives 160g for one ingredient, not the total. The fractions represent parts of the whole 210g. Always multiply each fraction by 210 separately, then add the results.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why do I multiply the fraction by 210 instead of dividing?

+

Fractions tell us what part to take! When you see $\frac{3}{7}$ of 210g, it means "3 out of every 7 parts." Multiplying gives you exactly that portion.

Can I convert the fractions to decimals first?

+

Yes! $\frac{3}{7} \approx 0.429$ and $\frac{1}{3} \approx 0.333$ . Then multiply: 0.429 × 210 = 90g and 0.333 × 210 = 70g. Just be careful with rounding!

How do I know if 160g makes sense as an answer?

+

Check that your answer is less than the total (210g) but more than either individual part (90g or 70g). Since 70 < 160 < 210, it's reasonable!

What if the fractions add up to more than 1?

+

That would mean you have more ingredients than the total cake, which is impossible! Always check: $\frac{3}{7} + \frac{1}{3} = \frac{16}{21} < 1$ ✓

Do I need to simplify fractions before calculating?

+

Not necessary for this problem! $\frac{3}{7}$ and $\frac{1}{3}$ are already in lowest terms. Just multiply directly by 210.

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Calculate 3/7 and 1/3 of 210g: Finding Cake Ingredient Quantities

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Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I multiply the fraction by 210 instead of dividing?

Can I convert the fractions to decimals first?

How do I know if 160g makes sense as an answer?

What if the fractions add up to more than 1?

Do I need to simplify fractions before calculating?

🌟 Unlock Your Math Potential

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