Solve the Multiplication: 7 × 3/8 Step by Step

Whole Number-Fraction Multiplication with Mixed Numbers

Solve:

7×38= 7\times\frac{3}{8}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together.
00:08 We'll start by moving the product to the top.
00:12 Next, let's calculate the product.
00:17 Now, we'll change it into a mixed fraction.
00:21 We'll break down 21 into 16 plus 5.
00:26 Next, let's separate the fraction into a whole number and the rem ainder.
00:31 Convert from the improper fraction to a whole number, then combine it with the mixed fraction .
00:38 And that's how we find the solution! Great job.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve:

7×38= 7\times\frac{3}{8}=

2

Step-by-step solution

To solve this problem, we will start by multiplying the whole number 7 by the fraction 38 \frac{3}{8} using the rule for multiplying a whole number by a fraction.

Calculate the product:

  • 7×38=7×38 7 \times \frac{3}{8} = \frac{7 \times 3}{8}
  • =218 = \frac{21}{8}

The fraction 218 \frac{21}{8} is an improper fraction, meaning the numerator is greater than the denominator. To convert it to a mixed number, we divide 21 by 8:

  • 21 divided by 8 equals 2 with a remainder of 5.
  • This gives us the mixed number: 258 2\frac{5}{8}

The remainder becomes the numerator of the fraction part, and the denominator remains the same as in the original fraction.

Therefore, the solution to the problem is 258 2\frac{5}{8} .

3

Final Answer

258 2\frac{5}{8}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply whole number by numerator, keep denominator unchanged
  • Technique: Convert 7×38=218 7 \times \frac{3}{8} = \frac{21}{8} then to mixed number
  • Check: Convert back: 258=218=2.625 2\frac{5}{8} = \frac{21}{8} = 2.625

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying with fractions
    Don't add 7 + 3/8 = 10 3/8! This gives a completely wrong answer because addition and multiplication are different operations. Always multiply the whole number by the numerator: 7 × 3 = 21, then place over the denominator.

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 7 by both the numerator and denominator?

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When multiplying by a whole number, you only multiply the numerator! Think of 7 as 71 \frac{7}{1} , so 71×38=7×31×8=218 \frac{7}{1} \times \frac{3}{8} = \frac{7 \times 3}{1 \times 8} = \frac{21}{8} .

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

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Divide the numerator by the denominator! For 218 \frac{21}{8} : 21 ÷ 8 = 2 remainder 5, so the answer is 258 2\frac{5}{8} .

What if my fraction is already proper after multiplying?

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That's great! If your numerator is smaller than the denominator, you already have your final answer. Just check if you can simplify the fraction further.

Can I leave my answer as an improper fraction?

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Usually mixed numbers are preferred for final answers because they're easier to understand. 258 2\frac{5}{8} is clearer than 218 \frac{21}{8} for most people!

Why is 21 ÷ 8 = 2 remainder 5, not 2.625?

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For mixed numbers, we want the whole number part and the remaining fraction! The remainder 5 becomes the new numerator: 258 2\frac{5}{8} .

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