Solve: 7/8 × 2⅞ × ¼ Fraction Multiplication Problem

Fraction Multiplication with Mixed Numbers

78×278×14= \frac{7}{8}\times2\frac{7}{8}\times\frac{1}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to convert from a mixed number to a fraction only
00:07 We'll do this by multiplying the whole number by the denominator
00:10 and adding it to the numerator
00:14 This is the fraction, now let's continue to solve multiplication of fractions
00:27 Make sure to multiply numerator by numerator and denominator by denominator
00:36 We'll solve one multiplication at a time and then continue
00:57 We'll use long multiplication to find the numerator multiplication
01:00 This is the numerator multiplication
01:07 We'll use long multiplication to find the denominator multiplication
01:10 This is the denominator multiplication
01:13 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

78×278×14= \frac{7}{8}\times2\frac{7}{8}\times\frac{1}{4}=

2

Step-by-step solution

First, let's convert the mixed fraction to a simple fraction as follows:

78×8×2+78×14= \frac{7}{8}\times\frac{8\times2+7}{8}\times\frac{1}{4}=

Let's solve the exercise in the numerator:

78×16+78×14= \frac{7}{8}\times\frac{16+7}{8}\times\frac{1}{4}=

78×238×14= \frac{7}{8}\times\frac{23}{8}\times\frac{1}{4}=

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

7×23×18×8×4= \frac{7\times23\times1}{8\times8\times4}=

Let's solve the exercises in the numerator and denominator:

7×2364×4=161256 \frac{7\times23}{64\times4}=\frac{161}{256}

3

Final Answer

161256 \frac{161}{256}

Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Convert mixed numbers to improper fractions first
  • Technique: Combine all fractions: 7×23×18×8×4 \frac{7 \times 23 \times 1}{8 \times 8 \times 4}
  • Check: Multiply numerators together and denominators together separately ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying whole and fractional parts separately
    Don't multiply 2 × ¼ = ½ then add 7/8 × ¼ = wrong approach! This treats the mixed number as separate parts instead of one value. Always convert mixed numbers to improper fractions before multiplying.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number first?

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A mixed number like 278 2\frac{7}{8} represents one complete value. To multiply fractions correctly, you need to work with single fractions, not mixed parts.

How do I convert 2⅞ to an improper fraction?

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Use the formula: (whole×denominator)+numeratordenominator \frac{(whole \times denominator) + numerator}{denominator} . So 278=(2×8)+78=238 2\frac{7}{8} = \frac{(2 \times 8) + 7}{8} = \frac{23}{8}

Can I simplify before multiplying?

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Yes! Look for common factors you can cancel. For example, if you see 8 in a numerator and 8 in a denominator, you can cancel them to make calculations easier.

Why is my answer a fraction smaller than 1?

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When you multiply by fractions less than 1 (like 14 \frac{1}{4} ), the result gets smaller. Think of it as taking "a quarter of" the previous result!

Do I need to convert my answer back to a mixed number?

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Not necessarily! Improper fractions are perfectly valid answers. However, if the problem asks for a mixed number or if it's more practical, you can convert 161256 \frac{161}{256} back.

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