Solve the Fraction Equation: Finding 'a' in a/6 = 6/7

Q: Why do I get a mixed number as the answer?

Mixed numbers like $ 5\frac{1}{7} $ are perfectly normal! When you divide 36 by 7, it goes in 5 times with remainder 1, giving you 5 and 1/7. Both $ \frac{36}{7} $ and $ 5\frac{1}{7} $ are correct forms of the same answer.

Q: Can I just multiply both sides by 6 instead of cross-multiplying?

Yes! Multiplying both sides by 6 gives you $ a = 6 \times \frac{6}{7} = \frac{36}{7} $. Cross-multiplication is just a shortcut method that gets you to the same answer faster.

Q: How do I convert 36/7 to a mixed number?

Divide 36 by 7: 36 ÷ 7 = 5 remainder 1. This means 36/7 = 5 + 1/7 = $ 5\frac{1}{7} $. The quotient becomes the whole number, and the remainder goes over the original divisor.

Q: What if I chose answer choice a = 6 by mistake?

Let's check: $ \frac{6}{6} = 1 $, but $ \frac{6}{7} $ is less than 1. Since 1 ≠ 6/7, this answer is incorrect. Always verify your answer!

Q: Is there a pattern when cross-multiplying fractions?

Left fraction: numerator × right denominatorRight fraction: numerator × left denominatorSet equal: These two products are equalFor $ \frac{a}{6} = \frac{6}{7} $: a×7 = 6×6

Cross-Multiplication with Mixed Number Results

$\frac{a}{6}=\frac{6}{7}$

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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 isolate the unknown A

00:06 We'll multiply by denominators to eliminate fractions

00:10 We'll isolate the unknown A

00:18 We'll break down one fraction into a whole number and remainder

00:24 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

$\frac{a}{6}=\frac{6}{7}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Start with the given equation.
Step 2: Use cross-multiplication to eliminate the fractions.
Step 3: Simplify the resulting expression.
Step 4: Solve for the variable $a$ .

Now, let's work through each step:
Step 1: The equation given is $\frac{a}{6} = \frac{6}{7}$ .
Step 2: We apply cross-multiplication: Multiply both sides to get $a \times 7 = 6 \times 6$ .
Step 3: Simplify the equation: $7a = 36$ .
Step 4: Solve for $a$ by dividing both sides by 7:
$a = \frac{36}{7}$ .
This fraction can be converted to a mixed number: $a = 5\frac{1}{7}$ .

Therefore, the solution to the problem is $a = 5\frac{1}{7}$ .

Final Answer

$a=5\frac{1}{7}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: When a/b = c/d, then a×d = b×c
Technique: For a/6 = 6/7, multiply: a×7 = 6×6 = 36
Check: Substitute back: 36/7 ÷ 6 = 36/42 = 6/7 ✓

Common Mistakes

Avoid these frequent errors

Multiplying straight across instead of cross-multiplying
Don't multiply a×6 = 6×7 = a×6 = 42! This ignores the fraction structure and gives a = 7 instead of the correct 36/7. Always cross-multiply: multiply the numerator of each fraction by the denominator of the other fraction.

Practice Quiz

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Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I get a mixed number as the answer?

Mixed numbers like $5\frac{1}{7}$ are perfectly normal! When you divide 36 by 7, it goes in 5 times with remainder 1, giving you 5 and 1/7. Both $\frac{36}{7}$ and $5\frac{1}{7}$ are correct forms of the same answer.

Can I just multiply both sides by 6 instead of cross-multiplying?

Yes! Multiplying both sides by 6 gives you $a = 6 \times \frac{6}{7} = \frac{36}{7}$ . Cross-multiplication is just a shortcut method that gets you to the same answer faster.

How do I convert 36/7 to a mixed number?

Divide 36 by 7: 36 ÷ 7 = 5 remainder 1. This means 36/7 = 5 + 1/7 = $5\frac{1}{7}$ . The quotient becomes the whole number, and the remainder goes over the original divisor.

What if I chose answer choice a = 6 by mistake?

Let's check: $\frac{6}{6} = 1$ , but $\frac{6}{7}$ is less than 1. Since 1 ≠ 6/7, this answer is incorrect. Always verify your answer!

Is there a pattern when cross-multiplying fractions?

Left fraction: numerator × right denominator
Right fraction: numerator × left denominator
Set equal: These two products are equal

For $\frac{a}{6} = \frac{6}{7}$ : a×7 = 6×6

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