Solve: (+7) × (+1⅚) Multiplication with Mixed Numbers

Q: Why can't I just multiply 7 times the whole number part and 7 times the fraction part?

While this method can work, it's much more confusing and error-prone! Converting to an improper fraction gives you one clean multiplication: $ 7 \times \frac{11}{6} $ instead of juggling multiple parts.

Q: How do I convert 1⅚ to an improper fraction?

Use the formula: (whole × denominator) + numerator over the same denominator. So $ 1\frac{5}{6} = \frac{(1×6)+5}{6} = \frac{11}{6} $

Q: Do I need to convert 7 to a fraction too?

Yes! Write 7 as $ \frac{7}{1} $ so you can multiply fraction by fraction: $ \frac{7}{1} \times \frac{11}{6} = \frac{77}{6} $

Q: How do I convert ⁷⁷⁄₆ back to a mixed number?

Divide the numerator by the denominator: 77 ÷ 6 = 12 remainder 5. So $ \frac{77}{6} = 12\frac{5}{6} $

Q: What if my final fraction needs to be simplified?

Always check if you can reduce your fraction! Find the greatest common factor of the numerator and denominator, then divide both by it. In this case, $ \frac{77}{6} $ is already in lowest terms.

Multiplying Whole Numbers with Mixed Numbers

Solve the following expression:

$(+7)\times(+1\frac{5}{6})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Convert mixed fraction to fraction

00:11 Convert whole number to fraction

00:15 Make sure to multiply numerator by numerator and denominator by denominator

00:20 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

Solve the following expression:

$(+7)\times(+1\frac{5}{6})=$

Step-by-step solution

Let's convert the mixed fraction to an improper fraction:

$1\frac{5}{6}=\frac{11}{6}$

Now let's write the exercise:

$7\times\frac{11}{6}=\frac{7}{1}\times\frac{11}{6}=$

We'll multiply numerator by numerator and denominator by denominator:

$\frac{7\times11}{1\times6}=\frac{77}{6}$

Let's convert the improper fraction to a mixed fraction:

$\frac{77}{6}=12\frac{5}{6}$

Final Answer

$12\frac{5}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to improper fractions before multiplying
Technique: Change $1\frac{5}{6}$ to $\frac{11}{6}$ , then multiply $7 \times \frac{11}{6}$
Check: Convert final answer back to mixed number: $\frac{77}{6} = 12\frac{5}{6}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying whole number with mixed number directly
Don't multiply 7 × 1 = 7 then add 7 × 5/6 separately = wrong method! This creates confusion and leads to incorrect calculations. Always convert the mixed number to an improper fraction first, then multiply normally.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why can't I just multiply 7 times the whole number part and 7 times the fraction part?

While this method can work, it's much more confusing and error-prone! Converting to an improper fraction gives you one clean multiplication: $7 \times \frac{11}{6}$ instead of juggling multiple parts.

How do I convert 1⅚ to an improper fraction?

Use the formula: (whole × denominator) + numerator over the same denominator. So $1\frac{5}{6} = \frac{(1×6)+5}{6} = \frac{11}{6}$

Do I need to convert 7 to a fraction too?

Yes! Write 7 as $\frac{7}{1}$ so you can multiply fraction by fraction: $\frac{7}{1} \times \frac{11}{6} = \frac{77}{6}$

How do I convert ⁷⁷⁄₆ back to a mixed number?

Divide the numerator by the denominator: 77 ÷ 6 = 12 remainder 5. So $\frac{77}{6} = 12\frac{5}{6}$

What if my final fraction needs to be simplified?

Always check if you can reduce your fraction! Find the greatest common factor of the numerator and denominator, then divide both by it. In this case, $\frac{77}{6}$ is already in lowest terms.

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