Solve: 1/5 × 7/8 × 2⅔ Fraction Multiplication with Mixed Numbers

Fraction Multiplication with Mixed Number Conversion

Solve the following problem:

15×78×223= \frac{1}{5}\times\frac{7}{8}\times2\frac{2}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:03 We want to convert from a number and fraction to just a fraction
00:06 We'll do this by multiplying the whole number by the denominator
00:09 and raising it to the numerator
00:13 Make sure to multiply numerator by numerator and denominator by denominator
00:22 We'll reduce what we can
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

15×78×223= \frac{1}{5}\times\frac{7}{8}\times2\frac{2}{3}=

2

Step-by-step solution

First, let's convert the mixed fraction to an improper fraction as follows:

15×78×3×2+23= \frac{1}{5}\times\frac{7}{8}\times\frac{3\times2+2}{3}=

Let's solve the equation in the numerator:

15×78×6+23= \frac{1}{5}\times\frac{7}{8}\times\frac{6+2}{3}=

15×78×83= \frac{1}{5}\times\frac{7}{8}\times\frac{8}{3}=

Since the only operation in the equation is multiplication, we'll combine everything into one equation:

1×7×85×8×3= \frac{1\times7\times8}{5\times8\times3}=

Let's simplify the 8 in the numerator and denominator of the fraction:

1×75×3= \frac{1\times7}{5\times3}=

Let's solve the equations in the numerator and denominator and we should obtain the following:

715 \frac{7}{15}

3

Final Answer

715 \frac{7}{15}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert mixed numbers to improper fractions before multiplying
  • Technique: 223=83 2\frac{2}{3} = \frac{8}{3} since 3×2+2=8 3 \times 2 + 2 = 8
  • Check: Simplify by canceling common factors: 8 cancels in numerator and denominator ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying mixed numbers without converting to improper fractions
    Don't try to multiply 15×78×223 \frac{1}{5} \times \frac{7}{8} \times 2\frac{2}{3} with the mixed number as-is = confusing calculations and wrong answers! This makes the multiplication process complicated and error-prone. Always convert mixed numbers to improper fractions first, then multiply straight across.

Practice Quiz

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\( 94+12+6= \)

FAQ

Everything you need to know about this question

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

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Use the formula: improper fraction = (whole × denominator) + numerator / denominator. For 223 2\frac{2}{3} : (2 × 3) + 2 = 8, so it becomes 83 \frac{8}{3} .

Can I simplify before multiplying all the fractions?

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Yes! It's actually easier to cancel common factors first. In this problem, the 8 in the numerator cancels with the 8 in the denominator, making the math simpler.

Why did we get two correct answers in the choices?

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Both 715 \frac{7}{15} and 1516 \frac{15}{16} might be listed as correct due to different problem interpretations or answer key errors. Always work through the problem step-by-step to find the true answer.

What if I forget to convert the mixed number?

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You'll likely get confused trying to multiply the whole number part separately. Always convert first! It makes the entire multiplication process much cleaner and reduces errors.

How do I know when my final fraction is fully simplified?

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Check if the numerator and denominator share any common factors. In 715 \frac{7}{15} , since 7 is prime and doesn't divide 15, it's already in lowest terms.

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