Solve: Multiplying 2 Times the Fraction 5/7

Whole Number Multiplication with Proper Fractions

2×57= 2\times\frac{5}{7}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Move the multiplication to the numerator
00:06 Calculate the multiplication
00:10 Now convert to a mixed fraction
00:14 Break down 10 into 7 plus 3
00:21 Split the fraction into a whole number and remainder
00:26 Convert from improper fraction to whole number, and combine with mixed fraction
00:34 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

2×57= 2\times\frac{5}{7}=

2

Step-by-step solution

To solve this problem, we'll multiply the whole number 2 by the fraction 57\frac{5}{7}:

  • Step 1: Multiply the numerator 5 by the whole number 2:

2×5=10 2 \times 5 = 10

  • Step 2: Write the result over the original denominator 7:

107 \frac{10}{7}

  • Step 3: Convert 107\frac{10}{7} to a mixed number:

Since 10 divided by 7 is 1 with a remainder of 3, we can express this as:

137 1\frac{3}{7}

Therefore, the solution to the problem is 137\textbf{1}\frac{\textbf{3}}{\textbf{7}}.

3

Final Answer

137 1\frac{3}{7}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply whole number by numerator, keep denominator unchanged
  • Technique: Convert 2×57 2 \times \frac{5}{7} to 107 \frac{10}{7} by calculating 2 × 5 = 10
  • Check: Convert improper fraction to mixed number: 10 ÷ 7 = 1 remainder 3 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying both numerator and denominator by the whole number
    Don't multiply 2 × 5 AND 2 × 7 to get 10/14! This changes the fraction's value completely. The denominator stays the same when multiplying by a whole number. Always multiply only the numerator by the whole number.

Practice Quiz

Test your knowledge with interactive questions

\( 5:\frac{2}{5}= \)

FAQ

Everything you need to know about this question

Why don't I multiply the denominator by 2?

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When multiplying a fraction by a whole number, only the numerator changes. Think of it like this: 57 \frac{5}{7} means 5 parts out of 7, so 2 times that means 10 parts out of 7, not 10 parts out of 14!

Do I always need to convert to a mixed number?

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Not always! It depends on what the problem asks for. Improper fractions like 107 \frac{10}{7} and mixed numbers like 137 1\frac{3}{7} are both correct - they're just different ways to write the same value.

How do I convert an improper fraction to a mixed number?

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Divide the numerator by the denominator! For 107 \frac{10}{7} :

  • 10 ÷ 7 = 1 with remainder 3
  • So you get 1 (whole number) and 37 \frac{3}{7} (leftover fraction)

Can I write 2 as a fraction to make this easier?

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Absolutely! Writing 2=21 2 = \frac{2}{1} lets you multiply fractions: 21×57=107 \frac{2}{1} \times \frac{5}{7} = \frac{10}{7} . Both methods give the same answer!

What if my whole number is larger, like 15?

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Same process! For 15×57 15 \times \frac{5}{7} , you'd calculate 15 × 5 = 75, giving you 757 \frac{75}{7} . Just remember to multiply only the numerator!

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