GCSE Maths - How to Convert Ratios into Fractions (2026/27 exams)

1. Formula
   Observation

   The ratio is written on screen as "3 : 5".

2. Audio
   Observation

   The narrator introduces the example as "ratios like three to five" and interprets it as apples to berries.

3 : 5

Ratio of apples to berries in the worked example.

Positive integer ratio terms; here 3 apples and 5 berries in the simplest version.

1. Audio
   Observation

   Narrator says the ratio represents "apples to berries" and that there are three apples.

2. Diagram
   Observation

   Three pink apple icons appear under the label "APPLES".

$\text{apples}$

Number of apples represented by the first term of the ratio.

In the simplified model used for conversion, $\text{apples}=3$.

1. Audio
   Observation

   Narrator says there are five berries for every three apples.

2. Diagram
   Observation

   Five purple berry icons appear under the label "BERRIES".

$\text{berries}$

Number of berries represented by the second term of the ratio.

In the simplified model used for conversion, $\text{berries}=5$.

1. Formula
   Observation

   The screen shows "TOTAL = 8" beneath the 3-apple and 5-berry grouping.

2. Audio
   Observation

   Narrator states that in the simple case there would be "a total of eight pieces of fruit".

$\text{total}$

Total number of fruit pieces in the chosen representative grouping.

For the simplest version shown, $\text{total}=3+5=8$.

1. Formula
   Observation

   The fraction $\frac{3}{8}$ is written on screen under the prompt about the fraction of fruit that are apples.

2. Audio
   Observation

   Narrator says, "we just do the number of apples, so three, over the total of eight."

$\frac{3}{8}$

Fraction of all fruit that are apples in the part-to-whole interpretation.

Proper fraction with numerator 3 and denominator 8.

1. Formula
   Observation

   The fraction $\frac{5}{8}$ is written on screen under the prompt about the fraction of fruit that are berries.

2. Audio
   Observation

   Narrator says, "this time we do five over eight" because five of every eight pieces are berries.

$\frac{5}{8}$

Fraction of all fruit that are berries in the part-to-whole interpretation.

Proper fraction with numerator 5 and denominator 8.

1. Formula
   Observation

   The fraction $\frac{3}{5}$ appears beside the text "AS MANY APPLES AS BERRIES".

2. Audio
   Observation

   Narrator says there are "three over five, or three fifths, as many apples as there are berries."

$\frac{3}{5}$

Part-to-part fraction comparing apples with berries.

Proper fraction with numerator 3 and denominator 5.

1. Formula
   Observation

   The fraction $\frac{5}{3}$ appears beside the text "AS MANY BERRIES AS APPLES".

2. Audio
   Observation

   Narrator says, "So five over three. So there's five thirds as many berries as there are apples."

$\frac{5}{3}$

Part-to-part fraction comparing berries with apples.

Improper fraction with numerator 5 and denominator 3.

1. Formula
   Observation

   The decimal "1.67" is shown below $\frac{5}{3}$.

2. Audio
   Observation

   Narrator says, "five thirds is exactly the same thing as one point six seven."

1. The displayed value is rounded; the exact decimal expansion of $5/3$ is repeating.

1.67

Rounded decimal representation of the improper fraction $\frac{5}{3}$.

Approximate decimal form of a rational number.

1. Diagram
   Observation

   The worked example shows 3 apples and labels the apple count as 3.

2. Audio
   Observation

   The narrator refers to “the number three, which is how many apples we have.”

3

Number of apples in the ratio example.

Count of apples

1. Diagram
   Observation

   The worked example shows 5 berries and labels the berry count as 5.

2. Audio
   Observation

   The narrator says multiplying by 1.67 gives 5, “which is what we expected because we know that for every three apples, we have five berries.”

5

Number of berries in the ratio example.

Count of berries

1. Diagram
   Observation

   The screen displays TOTAL = 8 beneath the apples and berries.

8

Total number of fruit pieces, obtained from $3 + 5$.

Total count of fruit

1. Audio
   Observation

   Narrator explains that the ratio represents apples to berries and says, "for every three apples, there are five berries."

2. Diagram
   Observation

   The screen labels the two terms as "APPLES" and "BERRIES" and shows 3 apple icons and 5 berry icons.

The video defines the ratio 3 : 5 as a relationship between two quantities: for every 3 apples there are 5 berries. The emphasis is on the paired relationship rather than on a fixed total count.

1. The ratio compares two categories, here apples and berries.

2. It states a relative relationship, not necessarily an absolute total.

1. Audio
   Observation

   Narrator says, "because it's only a ratio, we can't tell the total number of pieces of fruit."

2. Diagram
   Observation

   Multiple scaled examples are shown: 3 and 5 with TOTAL = 8, 6 and 10 with TOTAL = 16, and 9 and 15 with TOTAL = 24.

The video demonstrates that the same ratio can correspond to different totals. The ratio fixes the relative sizes of the parts, while the actual total depends on which equivalent multiple of the ratio is chosen.

1. The ratio is known.

2. No additional information fixes the scale factor or total.

1. Meaning of the ratio 3 : 5

1. Audio
   Observation

   Narrator says they can "act as though there's three apples, five berries, and eight pieces in total, because this is the most simple version."

2. Diagram
   Observation

   A box labeled "MOST SIMPLE VERSION" highlights the 3-apple, 5-berry grouping with TOTAL = 8.

To convert a ratio into fractions, the video chooses the smallest whole-number representative of the ratio. For 3 : 5, this means treating the situation as if there are exactly 3 apples, 5 berries, and 8 fruits in total.

1. The ratio terms are positive integers.

2. The goal is to form fractions from the ratio.

3. Using the simplest representative does not change the fractional relationships.

1. Meaning of the ratio 3 : 5
2. A ratio does not determine the total amount

1. Audio
   Observation

   Narrator says, "to find the fraction of fruit that are apples, we just do the number of apples ... over the total of eight," then repeats the method for berries.

2. Formula
   Observation

   The screen shows $\frac{3}{8}$ and $\frac{5}{8}$ under prompts asking for the fraction of fruit that are apples and berries.

A part-to-whole fraction is formed by placing one term of the ratio over the sum of all terms. In this example, apples over total gives $\frac{3}{8}$, and berries over total gives $\frac{5}{8}$.

1. The whole is the sum of the compared parts.

2. The ratio terms are treated as the numbers of parts in the simplest version.

1. Use the simplest equivalent version when converting a ratio to fractions

1. Audio
   Observation

   Narrator says they can write "how many apples there are as a fraction of how many berries there are, and vice versa."

2. Formula
   Observation

   The screen shows $\frac{3}{5}$ with "AS MANY APPLES AS BERRIES" and $\frac{5}{3}$ with "AS MANY BERRIES AS APPLES".

A part-to-part fraction compares one quantity directly with another quantity in the ratio. From 3 : 5, the video forms $\frac{3}{5}$ for apples compared with berries and $\frac{5}{3}$ for berries compared with apples.

1. The fraction compares two parts of the same ratio.

2. The order of numerator and denominator determines which quantity is being compared to which.

1. Meaning of the ratio 3 : 5

1. Audio
   Observation

   Narrator says, "fractions like five thirds just represent numbers" and identifies $\frac{5}{3}$ with 1.67.

2. Formula
   Observation

   The screen displays $\frac{5}{3}$ and then 1.67 below it.

1. The spoken phrase "exactly the same thing as one point six seven" should be understood as a rounded decimal representation, not an exact terminating decimal.

The video explains that a fraction such as $\frac{5}{3}$ is still a valid number even though it is larger than 1. It is used to express that one quantity is more than another in a part-to-part comparison.

1. The numerator is larger than the denominator.

2. The fraction is being interpreted as a numerical multiplier in a comparison.

1. Part-to-part fractions from a ratio

1. Diagram
   Observation

   The title reads HOW TO CONVERT RATIOS TO FRACTIONS.

2. Audio
   Observation

   The narrator demonstrates converting a ratio into fractions by using the ratio terms and their sum.

To convert a ratio into fractions, identify the two quantities being compared, use each quantity as a numerator when needed, and choose the denominator according to the question: the total of the ratio parts for a part-to-whole fraction, or the other quantity for a part-to-part fraction.

1. The ratio must compare two quantities.

2. The wording of the question determines whether the denominator is the total or the other quantity.

1. Diagram
   Observation

   The first example shows $3/8$ and $5/8$ after displaying TOTAL = 8.

2. Diagram
   Observation

   The second example computes TOTAL NUMBER: $4 + 3 = 7$ and then gives $4/7$.

A part-to-whole fraction compares one part of a ratio to the total of all parts. In the examples, the total is found by adding the ratio terms, so 3 : 5 gives total 8 and 4 : 3 gives total 7.

1. The denominator must represent the whole collection described by the ratio.

1. Method for converting a ratio into fractions

1. Diagram
   Observation

   The first example shows $3/5$ AS MANY APPLES AS BERRIES and $5/3$ AS MANY BERRIES AS APPLES.

2. Diagram
   Observation

   The second example shows PLAIN COOKIES over CHOCOLATE COOKIES and gives $3/4$.

A part-to-part fraction compares one quantity in a ratio directly to another quantity in the same ratio. The denominator is the quantity being compared against, not the total.

1. The question asks how many of one item there are as a fraction of another item.

1. Method for converting a ratio into fractions

1. Diagram
   Observation

   The video shows 3:5, 6:10, and 9:15 as different totals that preserve the same relationship.

2. Audio
   Observation

   Narrator says the total could be 8, 16, or 24, but all we know is that for every three apples there must also be five berries.

1. This claim is not stated as a formal theorem in the video; it is inferred from the worked demonstration.

If a ratio is multiplied by the same positive factor in both terms, the resulting part-to-whole and part-to-part fractions are unchanged.

1. The original ratio has positive integer terms.

2. Both terms are multiplied by the same positive factor.

For any common positive scaling factor applied to both terms of the ratio.

1. Audio
   Observation

   Narrator explicitly uses the total 8 as the denominator when finding the fraction of fruit that are apples and berries.

2. Formula
   Observation

   The displayed fractions are $\frac{3}{8}$ and $\frac{5}{8}$.

When converting a two-term ratio a : b into fractions of the whole, the denominator is $a+b$.

1. The ratio terms a and b represent the parts of a single whole.

2. The question asks for the fraction of the whole occupied by one part.

For the two-part ratio shown in the example.

1. Audio
   Observation

   Narrator contrasts "how many apples ... as a fraction of how many berries" with the reverse wording.

2. Formula
   Observation

   The screen pairs $\frac{3}{5}$ with "AS MANY APPLES AS BERRIES" and $\frac{5}{3}$ with "AS MANY BERRIES AS APPLES".

From a ratio a : b, the fraction $a/b$ expresses how many a there are per b, while $b/a$ expresses how many b there are per a.

1. a and b are the two quantities being compared.

2. The fractions are interpreted as part-to-part comparisons.

For the two quantities in the ratio.

1. Audio
   Observation

   Narrator walks through choosing the simplest version, computing the total, then forming $\frac{3}{8}$, $\frac{5}{8}$, $\frac{3}{5}$, and $\frac{5}{3}$.

2. Formula
   Observation

   The screen successively displays TOTAL = 8, $\frac{3}{8}$, $\frac{5}{8}$, $\frac{3}{5}$, and $\frac{5}{3}$.

1. Expression

   $$3 : 5$$
   Explanation

   Start with the given ratio of apples to berries.

   Justification

   This is the example introduced at the beginning of the clip.

   Shown in the video
2. Expression

   $$3 + 5 = 8$$
   Explanation

   Choose the simplest representative version and add the two parts to get the total number of fruit.

   Justification

   The video says we can act as though there are 3 apples, 5 berries, and 8 pieces in total.

   Shown in the video
3. Expression

   $$\frac{3}{8}$$
   Explanation

   Form the fraction of all fruit that are apples by putting the apple count over the total.

   Justification

   This is the part-to-whole rule demonstrated on screen and in narration.

   Shown in the video
4. Expression

   $$\frac{5}{8}$$
   Explanation

   Form the fraction of all fruit that are berries by putting the berry count over the total.

   Justification

   The same part-to-whole rule is applied to the other term.

   Shown in the video
5. Expression

   $$\frac{3}{5}$$
   Explanation

   Form the part-to-part fraction comparing apples with berries.

   Justification

   The narrator explicitly says there are three fifths as many apples as berries.

   Shown in the video
6. Expression

   $$\frac{5}{3}$$
   Explanation

   Reverse the comparison to express berries relative to apples.

   Justification

   The narrator says to show how many berries there are as a fraction of how many apples, do it the other way round.

   Shown in the video

The ratio 3 : 5 yields the part-to-whole fractions $\frac{3}{8}$ and $\frac{5}{8}$, and the part-to-part fractions $\frac{3}{5}$ and $\frac{5}{3}$.

1. Audio
   Observation

   Narrator says fractions like five thirds just represent numbers and equates $\frac{5}{3}$ with 1.67.

2. Formula
   Observation

   The screen shows $\frac{5}{3}$ and then 1.67.

1. The decimal is rounded; the exact value is the repeating decimal 1.666...

2. The final spoken sentence is cut off before the full multiplier statement is completed.

1. Expression

   $$\frac{5}{3}$$
   Explanation

   Begin with the part-to-part fraction comparing berries to apples.

   Justification

   This fraction was derived directly from the ratio 3 : 5.

   Shown in the video
2. Expression

   $$\frac{5}{3} \approx 1.67$$
   Explanation

   Rewrite the fraction in decimal form to interpret it as a number.

   Justification

   The video states that five thirds is the same thing as 1.67, using a rounded decimal display.

   Shown in the video
3. Expression

   $$\text{berries} \approx 1.67 \times \text{apples}$$
   Explanation

   Read the decimal as a multiplier telling how many times as many berries there are compared with apples.

   Justification

   This follows from the preceding part-to-part comparison; the clip ends before the narrator finishes the sentence.

   Derived from the video

The fraction $\frac{5}{3}$ means that the number of berries is about 1.67 times the number of apples.

1. Audio
   Observation

   The narrator says: if we take the number three, which is how many apples we have, and multiply it by 1.67, we get five.

2. Diagram
   Observation

   The screen writes $3 x 1.67 = 5$.

1. The equality $3 x 1.67 = 5$ is presented as a check using the rounded decimal 1.67 rather than the exact fraction $5/3$.

1. Expression

   $$3 \times 1.67 = 5$$
   Explanation

   The video multiplies the number of apples by the displayed decimal multiplier to recover the number of berries.

   Justification

   This checks the statement that there are 1.67 times as many berries as apples.

   Shown in the video

Using the rounded multiplier 1.67, the example verifies that 3 apples correspond to 5 berries.

1. Diagram
   Observation

   The screen shows TOTAL NUMBER: $4 + 3 = 7$.

2. Audio
   Observation

   The narrator says to add together four and three to get a total of seven cookies.

1. Expression

   $$4 + 3 = 7$$
   Explanation

   The ratio parts for chocolate and plain cookies are added to obtain the whole number of cookies represented by the ratio.

   Justification

   A part-to-whole fraction requires the total of all parts.

   Shown in the video

The total corresponding to the ratio 4 : 3 is 7.

1. Diagram
   Observation

   The solution writes $4/7$ for part 1 and $3/4$ for part 2.

2. Audio
   Observation

   The narrator explains putting 4 over the total 7, then putting 3 over 4 for the second part.

1. Expression

   $$\frac{4}{7}$$
   Explanation

   For the fraction of total cookies that are chocolate, the number of chocolate cookies is placed over the total number of cookies.

   Justification

   This matches a part-to-whole interpretation of the ratio.

   Shown in the video
2. Expression

   $$\frac{3}{4}$$
   Explanation

   For the number of plain cookies as a fraction of the number of chocolate cookies, the number of plain cookies is placed over the number of chocolate cookies.

   Justification

   This matches a part-to-part comparison between the two quantities in the ratio.

   Shown in the video

From the ratio 4 : 3, the video obtains $4/7$ for chocolate out of total and $3/4$ for plain as many as chocolate.

1. Audio
   Observation

   The entire clip works through the example of converting the ratio of apples to berries into fractions.

2. Diagram
   Observation

   The screen repeatedly shows 3 apples, 5 berries, TOTAL = 8, and the resulting fractions.

Given the ratio 3 : 5 representing apples to berries, express the relationship using fractions.

1. Ratio: 3 : 5

2. Interpretation: apples : berries

3. Simplest representative totals: 3 apples, 5 berries, 8 total fruit

Find (i) the fraction of all fruit that are apples, (ii) the fraction of all fruit that are berries, (iii) apples as a fraction of berries, and (iv) berries as a fraction of apples.

1. Expression

   $$3 + 5 = 8$$
   Explanation

   Use the simplest version of the ratio and compute the total number of fruit.

   Justification

   The video says this is enough for converting the ratio into fractions.

   Shown in the video
2. Expression

   $$\frac{3}{8}$$
   Explanation

   The fraction of fruit that are apples is 3 over 8.

   Justification

   Part-to-whole fraction: number of apples divided by total fruit.

   Shown in the video
3. Expression

   $$\frac{5}{8}$$
   Explanation

   The fraction of fruit that are berries is 5 over 8.

   Justification

   Part-to-whole fraction: number of berries divided by total fruit.

   Shown in the video
4. Expression

   $$\frac{3}{5}$$
   Explanation

   There are three fifths as many apples as berries.

   Justification

   Part-to-part fraction: apples compared with berries.

   Shown in the video
5. Expression

   $$\frac{5}{3} \approx 1.67$$
   Explanation

   There are five thirds as many berries as apples, which is about 1.67 times as many.

   Justification

   Part-to-part fraction reversed, then interpreted as a decimal multiplier.

   Shown in the video

Apples are $\frac{3}{8}$ of the fruit, berries are $\frac{5}{8}$ of the fruit, there are $\frac{3}{5}$ as many apples as berries, and there are $\frac{5}{3} \approx 1.67$ times as many berries as apples.

The two part-to-whole fractions add to 1 because $\frac{3}{8}+\frac{5}{8}=1$, and the two part-to-part fractions are reciprocals because $\frac{3}{5}$ and $\frac{5}{3}$ invert one another.

1. Diagram
   Observation

   The screen shows APPLES : BERRIES = 3 : 5, TOTAL = 8, and four resulting fraction statements.

2. Audio
   Observation

   The narrator explains that 3 times 1.67 gives 5 because for every three apples there are five berries.

1. The decimal 1.67 is visibly rounded; the exact fraction form $5/3$ is also shown separately.

Given 3 apples and 5 berries, find the fraction of fruit that are apples, the fraction of fruit that are berries, how many apples there are as a fraction of how many berries there are, and how many berries there are as a fraction of how many apples there are.

1. Apples : Berries = 3 : 5

2. Total fruit = 8

Express the given ratio as both part-to-whole and part-to-part fractions.

1. Expression

   $$\frac{3}{8}$$
   Explanation

   The number of apples is placed over the total number of fruit.

   Justification

   This answers the part-to-whole question for apples.

   Shown in the video
2. Expression

   $$\frac{5}{8}$$
   Explanation

   The number of berries is placed over the total number of fruit.

   Justification

   This answers the part-to-whole question for berries.

   Shown in the video
3. Expression

   $$\frac{3}{5}$$
   Explanation

   The number of apples is placed over the number of berries.

   Justification

   This answers how many apples there are as a fraction of how many berries there are.

   Shown in the video
4. Expression

   $$\frac{5}{3}$$
   Explanation

   The number of berries is placed over the number of apples.

   Justification

   This answers how many berries there are as a fraction of how many apples there are.

   Shown in the video
5. Expression

   $$3 \times 1.67 = 5$$
   Explanation

   The video checks the last relationship using the rounded decimal 1.67.

   Justification

   This verifies the statement that there are 1.67 times as many berries as apples.

   Shown in the video

$\frac{3}{8}$, $\frac{5}{8}$, $\frac{3}{5}$, $\frac{5}{3}$; equivalently 1.67 times as many berries as apples.

The video verifies the decimal relationship by computing $3 x 1.67 = 5$.

1. Diagram
   Observation

   The problem text reads BEN HAS A BAG OF CHOCOLATE AND PLAIN COOKIES IN THE RATIO OF 4 : 3.

2. Diagram
   Observation

   The worked solution shows CHOCOLATE : PLAIN = 4 : 3, TOTAL NUMBER: $4 + 3 = 7$, then $4/7$ and $3/4$ with green check marks.

3. Audio
   Observation

   The narrator reads the question and explains both parts step by step.

Ben has a bag of chocolate and plain cookies in the ratio of 4 : 3. Part 1 asks for the fraction of total cookies that are chocolate. Part 2 asks to express the number of plain cookies as a fraction of the number of chocolate cookies.

1. Chocolate : Plain = 4 : 3

Find (1) the fraction of total cookies that are chocolate and (2) the number of plain cookies as a fraction of the number of chocolate cookies.

1. Expression

   $$\text{CHOCOLATE} : \text{PLAIN} = 4 : 3$$
   Explanation

   Write down the known ratio with labels for each quantity.

   Justification

   This identifies which number belongs to chocolate and which belongs to plain.

   Shown in the video
2. Expression

   $$4 + 3 = 7$$
   Explanation

   Add the two parts of the ratio to get the total number represented by the ratio.

   Justification

   A part-to-whole fraction needs the total of all parts.

   Shown in the video
3. Expression

   $$\frac{4}{7}$$
   Explanation

   Place the number of chocolate cookies over the total number of cookies.

   Justification

   This answers part 1, the fraction of total cookies that are chocolate.

   Shown in the video
4. Expression

   $$\frac{3}{4}$$
   Explanation

   Place the number of plain cookies over the number of chocolate cookies.

   Justification

   This answers part 2, expressing plain cookies as a fraction of chocolate cookies.

   Shown in the video

Part 1: $\frac{4}{7}$. Part 2: $\frac{3}{4}$.

Both final answers are marked with green check marks on screen.

1. Diagram
   Observation

   The title "HOW TO CONVERT RATIOS TO FRACTIONS" appears, followed by the centered ratio "3 : 5".

1. Title text

2. Ratio 3 : 5

1. The screen changes from a blank white background to the lesson title.

2. The ratio 3 : 5 is then added beneath the title.

1. No numerical manipulation occurs yet.

2. The ratio remains the central object on screen.

This opening establishes the topic and the specific example ratio that will be converted into fractions.

1. Diagram
   Observation

   The words "APPLES" and "BERRIES" appear above the two terms, and 3 pink apple icons plus 5 purple berry icons appear below them.

1. Label APPLES

2. Label BERRIES

3. 3 apple icons

4. 5 berry icons

1. The abstract ratio is assigned category labels.

2. Icon counts are added to visualize the terms.

1. The ratio remains 3 : 5.

2. The left term corresponds to apples and the right term to berries.

The animation turns the symbolic ratio into a concrete comparison of two counted collections.

1. Diagram
   Observation

   Three groupings are shown side by side: 3 and 5 with TOTAL = 8, 6 and 10 with TOTAL = 16, and 9 and 15 with TOTAL = 24.

1. Group 1: 3 apples, 5 berries, TOTAL = 8

2. Group 2: 6 apples, 10 berries, TOTAL = 16

3. Group 3: 9 apples, 15 berries, TOTAL = 24

1. Additional scaled examples appear one after another.

2. The totals increase while the ratio relationship stays the same.

1. Each grouping preserves the proportion 3 : 5.

2. The visual message is that the total is not uniquely determined by the ratio alone.

This sequence demonstrates that a ratio fixes relative amounts, not the absolute total.

1. Diagram
   Observation

   A blue box labeled "MOST SIMPLE VERSION" points to the 3-apple, 5-berry grouping with TOTAL = 8.

1. Blue box

2. Label MOST SIMPLE VERSION

3. 3-apple / 5-berry grouping

1. Attention is narrowed from multiple possible totals to one chosen representative case.

2. The selected grouping is visually emphasized.

1. The underlying ratio remains 3 : 5.

2. The chosen case is the smallest whole-number version.

The video signals that for conversion purposes it is sufficient to work with the simplest equivalent form.

1. Diagram
   Observation

   Fractions are written one by one: $\frac{3}{8}$, $\frac{5}{8}$, $\frac{3}{5}$, and $\frac{5}{3}$, each paired with explanatory text.

1. Prompt about fraction of fruit that are apples

2. Prompt about fraction of fruit that are berries

3. Prompt about apples as a fraction of berries

4. Prompt about berries as a fraction of apples

5. Fractions $3/8$, $5/8$, $3/5$, $5/3$

1. The screen moves from part-to-whole fractions to part-to-part fractions.

2. Each new fraction is introduced with matching verbal wording.

1. All fractions are derived from the same base ratio 3 : 5.

2. The counts 3, 5, and total 8 remain the source values.

The visual progression distinguishes two different ways of turning a ratio into fractions.

1. Diagram
   Observation

   The fraction $\frac{5}{3}$ is boxed and the decimal 1.67 is written below it.

1. The clip ends before the narrator completes the final explanatory sentence.

1. Fraction $5/3$

2. Decimal 1.67

1. The part-to-part fraction is reframed as a decimal number.

2. The visual focus shifts from ratio language to multiplier language.

1. The quantity being represented is still the comparison of berries to apples.

This ending clarifies that an improper fraction can be read as a numerical multiplier greater than 1.

1. Diagram
   Observation

   The screen is divided into labeled regions showing apples, berries, total, and four fraction prompts.

2. Animation
   Observation

   The equation $3 x 1.67 = 5$ appears progressively at the bottom right.

1. 3 apple icons

2. 5 berry icons

3. TOTAL = 8

4. fraction labels $3/8$, $5/8$, $3/5$, $5/3$

5. decimal label 1.67 x

1. The multiplication check $3 x 1.67 = 5$ is written onto the board.

2. The board then clears before the next example.

1. The ratio remains 3 : 5 throughout this segment.

2. The total remains 8 throughout this segment.

The visual layout separates part-to-whole fractions from part-to-part fractions and uses the multiplication check to connect $5/3$ with the rounded decimal 1.67.

1. Diagram
   Observation

   A new whiteboard-style page presents the cookie problem and then fills in the solution line by line.

2. Animation
   Observation

   Text appears sequentially: CHOCOLATE : PLAIN, 4 : 3, TOTAL NUMBER: $4 + 3 = 7$, then $4/7$, then PLAIN COOKIES / CHOCOLATE COOKIES, then $3/4$.

1. Problem statement about Ben's cookies

2. CHOCOLATE : PLAIN = 4 : 3

3. TOTAL NUMBER: $4 + 3 = 7$

4. Answer $4/7$

5. Answer $3/4$

6. Green check marks

1. The solution is constructed step by step from the given ratio.

2. Each final answer is confirmed with a green check mark.

1. The given ratio stays 4 : 3 throughout the worked solution.

2. The total derived from the ratio stays 7 once computed.

The animation makes explicit that the denominator changes depending on whether the question asks for a fraction of the total or a fraction of the other quantity.

1. Diagram
   Observation

   The math content disappears and an outro card appears with WE ALSO DO..., speech bubbles, empty boxes, and credits.

2. Audio
   Observation

   The narrator says the video is finished and thanks the viewer.

1. WE ALSO DO... heading

2. two empty rectangular boxes

3. speech bubbles

4. credits text

1. The instructional content is replaced by promotional and credit information.

1. No further mathematical content is introduced.

This segment functions as the closing card rather than part of the lesson.

1. Audio
   Observation

   Narrator warns, "because it's only a ratio, we can't tell the total number of pieces of fruit."

2. Diagram
   Observation

   Several different totals are shown for the same ratio.

A ratio such as 3 : 5 tells you the exact total number of items.

The video shows that the same ratio can correspond to totals of 8, 16, 24, and so on; only the relative relationship is fixed.

1. Audio
   Observation

   The narrator separately introduces fractions of the total fruit and fractions comparing apples with berries.

2. Formula
   Observation

   The screen distinguishes $\frac{3}{8}$, $\frac{5}{8}$ from $\frac{3}{5}$, $\frac{5}{3}$.

All fractions made from a ratio mean the same thing.

The video distinguishes fractions of the whole, using the total 8 as denominator, from direct comparisons between the two parts, using 3 and 5 as numerator and denominator.

1. Audio
   Observation

   Narrator says, "This might seem a bit weird, but remember that fractions like five thirds just represent numbers."

2. Formula
   Observation

   The screen shows $\frac{5}{3}$ and 1.67.

A fraction larger than 1 cannot correctly describe how many of one thing there are compared with another.

The video explains that $\frac{5}{3}$ is a legitimate number and corresponds to about 1.67 times as many berries as apples.

1. Diagram
   Observation

   The same ratio 4 : 3 leads to two different denominators: 7 for the fraction of total cookies and 4 for plain as a fraction of chocolate.

2. Audio
   Observation

   The narrator explicitly distinguishes part 1 from part 2 and changes the denominator accordingly.

Assuming that every fraction made from a ratio must use the total of the ratio parts as the denominator.

The denominator depends on the wording of the question: use the total when asking for a fraction of the whole collection, but use the other quantity when asking how many of one item there are as a fraction of another item.

1. Diagram
   Observation

   The screen shows both $5/3$ and 1.67 x AS MANY BERRIES AS APPLES.

2. Audio
   Observation

   The narrator uses 1.67 in the check $3 x 1.67 = 5$.

1. This clarification is inferred from the contrast between the exact fraction and the rounded decimal shown on screen.

Thinking that the displayed decimal 1.67 is the exact ratio value rather than a rounded approximation.

In this example, $5/3$ is the exact fraction and 1.67 is a rounded decimal representation used for a quick numerical check.

1. Audio
   Observation

   The narrator first defines the ratio and then says they can use the most simple version for conversion.

2. Diagram
   Observation

   The 3 : 5 example is reduced to a highlighted simplest grouping with TOTAL = 8.

Understanding what the ratio means is required before choosing the simplest representative version for conversion.

1. Audio
   Observation

   After selecting the simplest version, the narrator immediately computes $\frac{3}{8}$ and $\frac{5}{8}$.

2. Formula
   Observation

   TOTAL = 8 is used as the denominator in the next displayed fractions.

The part-to-whole fractions depend on first fixing a representative total, here 8, from the simplest version of the ratio.

1. Audio
   Observation

   The narrator moves from the basic ratio meaning to comparing apples with berries and berries with apples.

2. Formula
   Observation

   The fractions $\frac{3}{5}$ and $\frac{5}{3}$ are built directly from the two ratio terms.

A part-to-part fraction applies the ratio terms directly to one another without using the total.

1. Diagram
   Observation

   The screen presents $\frac{3}{8}$, $\frac{5}{8}$ under prompts about fractions of fruit, then $\frac{3}{5}$, $\frac{5}{3}$ under prompts about how many of one type compared with the other.

The video contrasts fractions of the whole with direct comparisons between the two parts of the ratio.

1. Audio
   Observation

   After introducing $\frac{5}{3}$, the narrator comments that such fractions just represent numbers and gives the decimal 1.67.

2. Formula
   Observation

   The improper fraction $\frac{5}{3}$ is followed by the decimal 1.67.

The discussion of part-to-part fractions includes the special case of an improper fraction, here $\frac{5}{3}$.

1. Diagram
   Observation

   The method is demonstrated by first finding totals such as 8 and 7 before writing fractions like $3/8$ and $4/7$.

The general conversion method includes the special case where one ratio part is compared to the total of all parts.

1. Diagram
   Observation

   The same method is also used to write $3/5$, $5/3$, and $3/4$ by comparing one quantity directly to another.

The general conversion method also includes the case where one ratio term is compared directly to the other ratio term.

1. Diagram
   Observation

   The apple-berry board displays several fraction forms derived from the ratio 3 : 5.

The apple and berry example applies the ratio-to-fraction method to both part-to-whole and part-to-part cases.

1. Diagram
   Observation

   The cookie problem explicitly asks for one part-to-whole fraction and one part-to-part fraction from the ratio 4 : 3.

Ben's cookie problem applies the same method in a word-problem setting.

1. Diagram
   Observation

   The cookie solution contrasts $4/7$ with $3/4$ from the same ratio 4 : 3.

Both come from the same ratio, but they differ in what the denominator represents: the whole collection versus the other quantity.

1. Audio
   Observation

   Narrator explains the ratio as apples to berries.

2. Diagram
   Observation

   Labels APPLES and BERRIES are attached to 3 : 5.

1. Meaning of the ratio 3 : 5

1. Audio
   Observation

   Narrator says a ratio alone does not tell the total number of fruit.

2. Diagram
   Observation

   Totals 8, 16, and 24 are shown for the same ratio.

1. A ratio does not determine the total amount

1. Audio
   Observation

   Narrator says they can act as though there are 3 apples, 5 berries, and 8 pieces in total.

2. Formula
   Observation

   TOTAL = 8 is displayed and then used in $\frac{3}{8}$ and $\frac{5}{8}$.

1. Use the simplest equivalent version when converting a ratio to fractions
2. Part-to-whole fractions from a ratio

1. Formula
   Observation

   The screen shows both $\frac{3}{8}$ and $\frac{3}{5}$ with different wording.

2. Audio
   Observation

   Narrator distinguishes fraction of fruit that are apples from apples as a fraction of berries.

1. Part-to-whole fractions from a ratio
2. Part-to-part fractions from a ratio

1. Audio
   Observation

   Narrator says there are five thirds as many berries as apples and links this to 1.67.

2. Formula
   Observation

   $\frac{5}{3}$ and 1.67 are shown together.

1. The final sentence is truncated in the clip.

1. Part-to-part fractions from a ratio
2. Improper fractions represent numbers greater than 1

1. Audio
   Observation

   Narrator says fractions like five thirds just represent numbers.

2. Formula
   Observation

   The decimal 1.67 is shown below $\frac{5}{3}$.

1. Improper fractions represent numbers greater than 1

1. Diagram
   Observation

   Title: HOW TO CONVERT RATIOS TO FRACTIONS.

1. Method for converting a ratio into fractions

1. Diagram
   Observation

   The cookie example adds $4 + 3 = 7$ before giving $4/7$.

1. Part-to-whole fraction from a ratio
2. Finding the total number of cookies from the ratio

1. Diagram
   Observation

   The second cookie answer uses $3/4$ rather than a denominator of 7.

1. Part-to-part fraction from a ratio
2. Confusing part-to-whole with part-to-part denominators

1. Diagram
   Observation

   The board shows 1.67 x AS MANY BERRIES AS APPLES and $3 x 1.67 = 5$.

1. 1.67
2. Verification that 1.67 expresses berries relative to apples
3. Treating 1.67 as the exact value of $5/3$

1. Diagram
   Observation

   The worked solution ends with $4/7$ and $3/4$ marked correct.

1. Ben's bag of chocolate and plain cookies in the ratio 4 : 3