Math worksheet for dividing mixed fractions with step-by-step instructions and examples.

Let’s solve each problem step by step, following the rules given in the worksheet:

Rule Recap:
1. Convert mixed fractions to improper fractions.
2. Invert the divisor (second fraction) and change to ×.
- If dividing by a whole number, write it as over 1 first, then invert.
3. Multiply the two fractions.

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Problem 1:

Already solved on sheet:
$1 \frac{1}{3} \div \frac{1}{2} = \frac{4}{3} \div \frac{1}{2} = \frac{4}{3} \times \frac{2}{1} = \frac{8}{3}$
*(Note: The sheet says “= ___ / 3” — so answer is 8/3)*

But since it’s already filled, we’ll skip to next.

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Problem 2:

$2 \frac{3}{5} \div 3$

Step 1: Convert $2 \frac{3}{5}$ → $\frac{(2×5 + 3)}{5} = \frac{13}{5}$
Wait — hold on! The sheet shows:
“= $\frac{12}{5} \div \frac{3}{1}$” — that’s wrong.

Let me recalculate carefully:

$2 \frac{3}{5} = \frac{2×5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}$ — NOT 12/5.

So the sheet has an error here? But let’s check what they wrote:

They wrote:
$2 \frac{3}{5} \div 3 = \frac{12}{5} \div \frac{3}{1} = \_\_ \times \_\_ = \_\_/15$

That suggests they think $2 \frac{3}{5} = \frac{12}{5}$ — which is incorrect.

Actually, $2 \frac{2}{5} = \frac{12}{5}$, but this is $2 \frac{3}{5}$.

Hmm — maybe typo in the sheet? Or did I misread?

Looking back at image:
Problem 2 says:
“2) $2 \frac{3}{5} \div 3 = \frac{12}{5} \div \frac{3}{1} = \_\_ \times \_\_ = \_\_/15$”

This must be a mistake in the worksheet. Because $2 \frac{3}{5} = \frac{13}{5}$, not 12/5.

But perhaps for consistency with the worksheet’s own setup, we should follow their lead? No — better to do it correctly.

Wait — let me double-check the original image description.

User provided image text:

> 2) $2 \frac{3}{5} \div 3 = \frac{12}{5} \div \frac{3}{1} = \_\_ \times \_\_ = \_\_/15$

This is clearly wrong. $2 \frac{3}{5} = \frac{13}{5}$, not 12/5.

But maybe it's a trick? Or perhaps I’m misreading the mixed number?

No — standard conversion: whole × denominator + numerator.

2 × 5 = 10 + 3 = 13 → 13/5.

However, looking ahead — if we proceed with 12/5 as written, then:

$\frac{12}{5} \div \frac{3}{1} = \frac{12}{5} \times \frac{1}{3} = \frac{12}{15}$

Which matches the blank “___ /15”.

So even though it’s mathematically incorrect, the worksheet expects us to use 12/5.

Perhaps it’s a typo and meant to be $2 \frac{2}{5}$? But we have to go with what’s written.

Alternatively — maybe the student is supposed to catch the error? Unlikely for this level.

Given the context — this is a practice sheet with guided steps, and they’ve already filled in $\frac{12}{5}$, so we’ll continue with that for consistency.

So:

Problem 2:
$\frac{12}{5} \div \frac{3}{1} = \frac{12}{5} \times \frac{1}{3} = \frac{12 \times 1}{5 \times 3} = \frac{12}{15}$

Answer: $\frac{12}{15}$

(We can leave as improper fraction, no need to simplify per instructions.)

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Problem 3:

$4 \frac{1}{2} \div \frac{2}{5}$

Step 1: Convert $4 \frac{1}{2}$ → $\frac{4×2 + 1}{2} = \frac{9}{2}$

Step 2: Invert divisor $\frac{2}{5}$ → becomes $\frac{5}{2}$, and change ÷ to ×

So: $\frac{9}{2} \times \frac{5}{2} = \frac{9×5}{2×2} = \frac{45}{4}$

Fill in blanks:

$4 \frac{1}{2} \div \frac{2}{5} = \frac{9}{2} \div \frac{2}{5} = \frac{9}{2} \times \frac{5}{2} = \frac{45}{4}$

Blanks:
First blank after = : 9
Second blank: 2
Then: 9 x 5 = 45; 2 x 2 = 4 → so last blank: 45/4

Wait — format is:

“= ____ ÷ ____ = ____ x ____ = ____”

So:

= $\frac{9}{2}$ ÷ $\frac{2}{5}$ = $\frac{9}{2}$ x $\frac{5}{2}$ = $\frac{45}{4}$

So blanks:

First line: 9 over 2 → so first blank: 9, second blank: 2? Wait no — look at structure.

In problem 1:
“= $\frac{4}{3}$ $\frac{1}{2}$ = $\frac{4}{3}$ x $\frac{2}{1}$ = $\frac{8}{3}$”

And blanks are under numerators/denominators? Actually in printed version, it’s:

For problem 3:
“= ____ ÷ ____ = ____ x ____ = ____”

With lines under where numbers go.

From example, it seems they want the improper fraction written as numerator over denominator, but in blanks, probably just the numbers.

Looking at problem 1:
It shows:
“= $\frac{4}{3}$ ÷ $\frac{1}{2}$ = $\frac{4}{3}$ x $\frac{2}{1}$ = $\frac{8}{3}$”

And in the blank spaces below, for problem 1, it’s already filled: 4, 3, 1, 2, etc.? No — in the user’s image transcription, for problem 1 it’s shown as completed.

For problem 3, it’s:

“3) $4 \frac{1}{2} \div \frac{2}{5} = \_\_\_ \div \_\_\_ = \_\_\_ \times \_\_\_ = \_\_\_$”

Based on pattern, likely:

First blank: numerator of first improper fraction → 9
Second blank: denominator of first improper fraction → 2
Third blank: numerator of inverted divisor → 5
Fourth blank: denominator of inverted divisor → 2
Fifth blank: result numerator over denominator? Or just the fraction?

In problem 1, final answer is written as $\frac{8}{3}$, so probably fifth blank is "45/4" or just the value.

But in the layout, for problem 2, it ends with “= ___ /15”, so for problem 3, likely “= ___ / ___” but it’s written as single blank.

Looking back at user’s text:

For problem 3: “= ____ ÷ ____ = ____ x ____ = ____”

And in problem 2: “= ____ x ____ = ____ /15”

Ah — in problem 2, the last part specifies denominator 15, so answer is numerator only? No — it says “= ___ /15”, so blank is numerator.

Similarly, for problem 3, no such specification, so probably write full fraction.

But to match format, let’s see:

In problem 1: ends with “= ___ / 3” — and they put 8, meaning 8/3.

In problem 2: “= ___ /15” — so blank is 12.

For problem 3: no denominator specified, so likely write the entire fraction in the last blank.

But in the visual, it might be structured differently. Since we don’t have image, based on text:

I think safest is to fill as:

After “= ____ ÷ ____” → these are the improper fraction parts: so 9 and 2 (meaning 9/2)

Then “= ____ x ____” → the multiplication: 9 and 5? No — it’s $\frac{9}{2} \times \frac{5}{2}$, so numerators and denominators.

Actually, looking at problem 1:
“= $\frac{4}{3}$ ÷ $\frac{1}{2}$ = $\frac{4}{3}$ x $\frac{2}{1}$ = $\frac{8}{3}$”

So in the blanks for problem 3:

First pair: 9 and 2 (for 9/2)

Second pair: 5 and 2 (for 5/2) — because inverted divisor is 5/2

Then result: 45/4

But how to write in blanks? Probably:

Blank1: 9
Blank2: 2
Blank3: 5
Blank4: 2
Blank5: 45/4

But in problem 2, they have “= ___ x ___ = ___ /15”, so for multiplication step, they put the numerators? Let’s see problem 2:

“= $\frac{12}{5}$ x $\frac{1}{3}$ = ___ /15”

So in the multiplication step, they didn’t fill blanks for the fractions, but directly to the result with denominator 15.

In the user’s text for problem 2:
“= ____ x ____ = ____ /15”

So blanks before “x” are for the two fractions being multiplied.

In problem 2: $\frac{12}{5} \times \frac{1}{3}$, so first blank: 12/5? But it’s written as separate blanks.

Perhaps each blank is for a number, and the fraction bar is implied.

To avoid confusion, let’s calculate all and present clearly.

I’ll solve each properly.

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Let me redo all problems carefully, ignoring any potential errors in the worksheet’s pre-filled parts, and do them correctly.

The instruction says: “Work out these fraction divisions.” So we should do them right.

Also, in problem 2, if we use correct value, it won’t match their “/15”, but that’s okay — we provide correct answer.

But to be safe, since the worksheet might expect their version, but I think as educational assistant, we should teach correct math.

Decision: Solve correctly, note discrepancy if needed, but for final answer, give correct values.

Start over.

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Problem 1: Already done: $1 \frac{1}{3} \div \frac{1}{2} = \frac{4}{3} \times \frac{2}{1} = \frac{8}{3}$

Problem 2: $2 \frac{3}{5} \div 3$

Correctly: $2 \frac{3}{5} = \frac{13}{5}$

Divide by 3 = divide by $\frac{3}{1}$, so multiply by $\frac{1}{3}$

$\frac{13}{5} \times \frac{1}{3} = \frac{13}{15}$

But worksheet has $\frac{12}{5}$ leading to $\frac{12}{15}$, which simplifies to $\frac{4}{5}$, while correct is $\frac{13}{15}$.

Since the problem is to "work out", and worksheet may have typo, I'll use correct calculation.

But let's check the other problems.

Problem 3: $4 \frac{1}{2} \div \frac{2}{5} = \frac{9}{2} \div \frac{2}{5} = \frac{9}{2} \times \frac{5}{2} = \frac{45}{4}$

Problem 4: $2 \frac{4}{5} \div \frac{1}{3}$

Convert: $2 \frac{4}{5} = \frac{2*5 + 4}{5} = \frac{14}{5}$

Divide by $\frac{1}{3}$ = multiply by $\frac{3}{1}$

$\frac{14}{5} \times \frac{3}{1} = \frac{42}{5}$

Problem 5: $1 \frac{1}{4} \div \frac{2}{7}$

Convert: $1 \frac{1}{4} = \frac{5}{4}$

Divide by $\frac{2}{7}$ = multiply by $\frac{7}{2}$

$\frac{5}{4} \times \frac{7}{2} = \frac{35}{8}$

Problem 6: $3 \frac{2}{3} \div \frac{3}{5}$

Convert: $3 \frac{2}{3} = \frac{11}{3}$

Divide by $\frac{3}{5}$ = multiply by $\frac{5}{3}$

$\frac{11}{3} \times \frac{5}{3} = \frac{55}{9}$

Now, for the blanks in the worksheet, we need to fill according to the format.

From the examples:

Example 1:
$2 \frac{3}{4} \div 1 \frac{2}{5} = \frac{11}{4} \div \frac{7}{5} = \frac{11}{4} \times \frac{5}{7} = \frac{55}{28}$

So in the steps, they show the improper fractions, then the multiplication.

For the problems, the format is:

For problem n:
[mixed] ÷ [fraction or integer] = [improper] ÷ [divisor as fraction] = [improper] x [inverted divisor] = [result]

And blanks are for the numbers in those positions.

Specifically, for problem 3:
“4 \frac{1}{2} \div \frac{2}{5} = \_\_\_ \div \_\_\_ = \_\_\_ \times \_\_\_ = \_\_\_”

Based on example, the first "=" after the division is for the improper fraction form of the dividend and the divisor as fraction.

So for problem 3:
= $\frac{9}{2}$ ÷ $\frac{2}{5}$

So blanks: first blank is 9 (numerator of first), second blank is 2 (denominator of first)? But it's "____ ÷ ____", which might mean the entire fraction, but in context, likely they want the numerator and denominator separately for each fraction.

Looking at problem 1 in the sheet: it's written as "= \frac{4}{3} \div \frac{1}{2}", so in the blank version, for problem 1, it's already filled, but for others, the blanks are where the numbers go.

Perhaps each "____" represents a number, and the fraction is formed by consecutive blanks.

For instance, in problem 3:
"= ____ ÷ ____ " — this might be for the first fraction's numerator and denominator, but that doesn't make sense because there are two fractions.

Another possibility: "____ ÷ ____" means the first improper fraction and the divisor fraction, but since they are fractions, perhaps the blanks are for the values like "9/2" but that's not a single number.

I think the intended format is:

For the step "= A B = C x D = E", where A, B, C, D, E are fractions, but in the blanks, they want the numerators and denominators listed.

But in the user's text, for problem 2: " = ____ x ____ = ____ /15" , and from earlier, it's \frac{12}{5} x \frac{1}{3} = \frac{12}{15}, so the "____ x ____" likely corresponds to the numerators of the two fractions being multiplied, and the denominator is handled separately.

In problem 2: \frac{12}{5} x \frac{1}{3} = \frac{12 \times 1}{5 \times 3} = \frac{12}{15}, so they have "____ x ____" for the numerators 12 and 1, and then "/15" for the denominator product.

Similarly, for problem 3: \frac{9}{2} x \frac{5}{2} = \frac{45}{4}, so "____ x ____" would be 9 and 5 (numerators), and then the result is 45/4, so last blank might be "45/4" or just 45 with denominator implied.

But in problem 3, no denominator specified, so likely write the full fraction.

To resolve, let's look at the number of blanks.

For problem 3: " = ____ ÷ ____ = ____ x ____ = ____ "

Five blanks.

From example 1:
- After first = : \frac{11}{4} ÷ \frac{7}{5} — so two fractions
- Then = \frac{11}{4} x \frac{5}{7} — two fractions
- Then = \frac{55}{28} — one fraction

So in blanks, perhaps:

Blank1: numerator of first improper fraction (9)
Blank2: denominator of first improper fraction (2) — but then "÷ ____" would be for the divisor fraction.

Perhaps "____ ÷ ____" means the first fraction's value and the second fraction's value, but again, not single numbers.

I recall that in some worksheets, they have:

For "a/b ÷ c/d = a/b x d/c = (a*d)/(b*c)"

And in blanks, for the multiplication step, they ask for a, b, d, c or something.

For problem 3:
\frac{9}{2} ÷ \frac{2}{5} = \frac{9}{2} x \frac{5}{2} = \frac{45}{4}

So in the sequence:

" = [9/2] ÷ [2/5] = [9/2] x [5/2] = [45/4] "

If the blanks are for the numbers in order, perhaps:

First blank: 9 (num of first)
Second blank: 2 (den of first) — but then "÷ ____" might be for the divisor's num and den.

This is ambiguous.

Perhaps "____ ÷ ____" is for the two fractions as entities, but since it's text, likely they expect the numerator of the first fraction in first blank, denominator in second, but that doesn't fit.

Another idea: in the worksheet, for problem 1, it's shown with fractions, so for the blank versions, the "____" are where you write the numbers for the fractions.

For example, in problem 3:

"4 \frac{1}{2} \div \frac{2}{5} = \frac{9}{2} \div \frac{2}{5} = \frac{9}{2} \times \frac{5}{2} = \frac{45}{4}"

So in the blanks:

- First "____" after = : 9 (for num of 9/2)
- Second "____" : 2 (for den of 9/2) — but then "÷ ____" would be for the next fraction.

The expression is " = ____ ÷ ____ ", which suggests two things separated by ÷, so likely the first ____ is the first fraction (9/2), but that's not a single number.

I think the best way is to assume that for " = A ÷ B = C x D = E ", the blanks are for A, B, C, D, E as the fractional expressions, but since it's text, perhaps write the values.

For the sake of completing, I'll provide the numerical values for the blanks as per common interpretation.

From online sources or standard practice, in such sheets, for " = ____ ÷ ____ ", it often means the improper fraction of the dividend and the divisor as fraction, so for problem 3, first blank is "9/2", second blank is "2/5", but that might not fit.

Perhaps the blanks are for the numerators only, with denominators implied by position.

Let's count the blanks in the user's text:

For problem 3: " = ____ ____ = ____ x ____ = ____ " — 5 blanks.

In the multiplication step, for problem 2, they have " = ____ x ____ = ____ /15 ", and from context, the first two blanks are the numerators of the two fractions being multiplied, and the last is the numerator of the result, with denominator given.

In problem 2: \frac{12}{5} x \frac{1}{3} = \frac{12}{15}, so "____ x ____" is 12 and 1, and "____ /15" is 12.

For problem 3: \frac{9}{2} x \frac{5}{2} = \frac{45}{4}, so "____ x ____" should be 9 and 5 (numerators), and then " = ____ " should be 45/4 or just 45 with denominator 4 implied, but not specified.

In problem 3, no denominator specified, so likely the last blank is "45/4".

For the " = ____ ÷ ____ " part, in problem 2, it's " = \frac{12}{5} ÷ \frac{3}{1} ", so for problem 3, " = \frac{9}{2} ÷ \frac{2}{5} ", so perhaps the first blank is 9/2, second is 2/5, but again, not single numbers.

Perhaps the worksheet intends for the student to write the numbers in the fraction bars.

Given the constraints, I'll provide the answers for the final results, and for the intermediate blanks, I'll infer from the pattern.

For problem 3:
- After " = ": first blank: 9 (num of first improper)
- Second blank: 2 (den of first improper) — but then "÷ ____" might be for the divisor's num and den.

I think it's safer to output the final answers for each problem, as the main goal is to solve the divisions.

The user asked to "solve the problem accurately", and the problems are the six divisions.

So for each, the final answer is the result of the division.

Also, in the worksheet, for problem 1, answer is 8/3, for problem 2, if we follow their lead, 12/15, but correctly 13/15.

To be accurate, I'll use correct calculations.

Moreover, in the initial instruction, "CRITICAL: First work through the problem step by step, check your calculations carefully, and ONLY THEN provide the final answer."

So let's list the correct final answers for each problem.

Problem 1: 1 1/3 ÷ 1/2 = 4/3 * 2/1 = 8/3

Problem 2: 2 3/5 ÷ 3 = 13/5 * 1/3 = 13/15

Problem 3: 4 1/2 ÷ 2/5 = 9/2 * 5/2 = 45/4

Problem 4: 2 4/5 ÷ 1/3 = 14/5 * 3/1 = 42/5

Problem 5: 1 1/4 ÷ 2/7 = 5/4 * 7/2 = 35/8

Problem 6: 3 2/3 ÷ 3/5 = 11/3 * 5/3 = 55/9

Now, for the blanks in the worksheet, since the user may need to fill them, but the request is to "solve the problem", and the problems are the divisions, so the final answers are these fractions.

Perhaps the "problem" refers to filling the blanks, but the ultimate goal is the result of each division.

Given that, and to comply with the response format, I'll provide the final answers for each numbered problem.

Also, in the worksheet, for problem 2, they have "= ___ /15", so if we use correct 13/15, it fits, whereas their 12/5 is wrong.

So I'll go with correct math.

Final Answers:

1) 8/3
2) 13/15
3) 45/4
4) 42/5
5) 35/8
6) 55/9

But let's verify each calculation once more.

Problem 1:
1 1/3 = 4/3
4/3 ÷ 1/2 = 4/3 * 2/1 = 8/3 ✓

Problem 2:
2 3/5 = (2*5 + 3)/5 = 13/5
13/5 ÷ 3 = 13/5 * 1/3 = 13/15 ✓

Problem 3:
4 1/2 = 9/2
9/2 ÷ 2/5 = 9/2 * 5/2 = 45/4 ✓

Problem 4:
2 4/5 = (2*5 + 4)/5 = 14/5
14/5 ÷ 1/3 = 14/5 * 3/1 = 42/5 ✓

Problem 5:
1 1/4 = 5/4
5/4 ÷ 2/7 = 5/4 * 7/2 = 35/8 ✓

Problem 6:
3 2/3 = (3*3 + 2)/3 = 11/3
11/3 ÷ 3/5 = 11/3 * 5/3 = 55/9 ✓

All correct.

Now, for the response, since ExplainAnswer is false, TeachTopic is false, GeneratePractice is false, we only provide Final Answer.

But the Final Answer should be for the task, which is to solve the six problems.

So I'll list them.

Perhaps box each or list clearly.

Since it's a sheet with 6 problems, provide answers for 1 to 6.

Final Answer:
1) \frac{8}{3}
2) \frac{13}{15}
3) \frac{45}{4}
4) \frac{42}{5}
5) \frac{35}{8}
6) \frac{55}{9}

To match the worksheet's style, leave as improper fractions, no simplification needed.

Note: For problem 2, although the worksheet shows 12/5, the correct value is 13/5, so answer is 13/15, not 12/15. This is important for accuracy.

I think that's it.