Solve: 5.25 × 2/3 × 7/21 - Decimal and Fraction Multiplication

Q: Why convert 5.25 to a fraction instead of converting fractions to decimals?

Converting to fractions allows cancellation! Notice how the 21 in $ \frac{21}{4} $ cancels with 21 in the denominator. This makes calculations much easier than working with long decimals.

Q: How do I convert 5.25 to a mixed number?

5.25 means 5 and 25 hundredths. Since $ \frac{25}{100} = \frac{1}{4} $, we get $ 5\frac{1}{4} $. Always simplify the fractional part!

Q: Can I simplify 7/21 before multiplying?

Yes! $ \frac{7}{21} = \frac{1}{3} $ since both 7 and 21 divide by 7. Simplifying fractions early makes multiplication much easier.

Q: Why does the explanation cancel 21 with 21?

When multiplying fractions, you can cancel any numerator with any denominator if they have common factors. Here, 21 in the numerator of $ \frac{21}{4} $ cancels with 21 in the denominator of $ \frac{7}{21} $.

Q: How do I know when to stop simplifying?

Keep simplifying until the numerator and denominator have no common factors except 1. In our final answer $ 1\frac{1}{6} $, since 1 and 6 share no common factors, we're done!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this problem together.

00:11 First, convert the number from its numeric form to a mixed number.

00:20 Next, change the mixed number into a fraction.

00:24 Multiply the whole number by the denominator. Then, add the numerator. This is your fraction.

00:30 This fraction shows the whole number.

00:44 Let's simplify the problem to make it easier.

00:48 Reduce any numbers you can.

00:56 Remember, multiply the numerators together and the denominators together.

01:05 Break fourteen into twelve plus two.

01:09 Split the fraction into a whole number and the remainder.

01:15 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$5.25\cdot\frac{2}{3}\cdot\frac{7}{21}=\text{?}$

2

Step-by-step solution

We first rewrite the decimal fraction in the form of a mixed fraction:

$5.25=5\frac{1}{4}$

We obtain the following exercise:

$5\frac{1}{4}\cdot\frac{2}{3}\cdot\frac{7}{21}=$

We write the mixed fraction as a simple fraction:

$5\frac{1}{4}=\frac{4\times5+1}{4}=\frac{20+1}{4}=\frac{21}{4}$

We obtain the following:

$\frac{21}{4}\cdot\frac{2}{3}\cdot\frac{7}{21}=$

We simplify the 21 and obtain:

$\frac{7}{4}\cdot\frac{2}{3}=\frac{14}{12}=\frac{12+2}{12}=1\frac{2}{12}=1\frac{1}{6}$

3

Final Answer

$1\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change decimals to fractions before multiplying fractions
Technique: Cancel common factors like $\frac{21}{4} \cdot \frac{7}{21} = \frac{7}{4}$
Check: Convert final answer to decimal: $1\frac{1}{6} = 1.167...$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying decimals and fractions directly without conversion
Don't multiply 5.25 × 2/3 directly = confusing mixed operations! This makes cancellation impossible and leads to calculation errors. Always convert decimals to fractions first, then multiply all fractions together.

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

Why convert 5.25 to a fraction instead of converting fractions to decimals?

+

Converting to fractions allows cancellation! Notice how the 21 in $\frac{21}{4}$ cancels with 21 in the denominator. This makes calculations much easier than working with long decimals.

How do I convert 5.25 to a mixed number?

+

5.25 means 5 and 25 hundredths. Since $\frac{25}{100} = \frac{1}{4}$ , we get $5\frac{1}{4}$ . Always simplify the fractional part!

Can I simplify 7/21 before multiplying?

+

Yes! $\frac{7}{21} = \frac{1}{3}$ since both 7 and 21 divide by 7. Simplifying fractions early makes multiplication much easier.

Why does the explanation cancel 21 with 21?

+

When multiplying fractions, you can cancel any numerator with any denominator if they have common factors. Here, 21 in the numerator of $\frac{21}{4}$ cancels with 21 in the denominator of $\frac{7}{21}$ .

How do I know when to stop simplifying?

+

Keep simplifying until the numerator and denominator have no common factors except 1. In our final answer $1\frac{1}{6}$ , since 1 and 6 share no common factors, we're done!

Should I leave my answer as an improper fraction?

+

For mixed number problems, it's usually better to express your final answer as a mixed number like $1\frac{1}{6}$ rather than the improper fraction $\frac{7}{6}$ .

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Solve: 5.25 × 2/3 × 7/21 - Decimal and Fraction Multiplication

Mixed Number Multiplication with Fraction Simplification

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