# Khan/khan-exercises

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 Equivalent fractions 2
randRange(1, 10) randRange(2, 9) Bf + (Bf >= A ? 1 : 0) randRange(3, 9) A * M B * M ceil(A / B) randVar() 1

What number could replace SYMBOL below?

\dfrac{A}{B} = \dfrac{C}{SYMBOL}

D

The fraction on the left represents dividing some rectangular pizza(1).plural(2) into B slices, then taking A slices.

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED = A % B; if (FILLED === 0) { FILLED = B; } for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25); } else { rectchart([B], [RED], i * 1.25); } }

How many slices would we need to cut each pizza(1) into so that C slices would give us the same amount of pizza(1)?

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED *= M; for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, D - FILLED], [RED, _BACKGROUND], i * 1.25); } else { rectchart([D], [RED], i * 1.25); } }

Each of the original A slices must be divided into M slices to get C slices in total.

init({ range: [[0, 1], [0, 1]], scale: [475, 25] }); rectchart([M, M * B - M], [RED, _BACKGROUND]);

If we divide all the original slices into M slices, then one pizza(1) will have a total of D slices.

init({ range: [[0, 1], [0, 1]], scale: [475, 25] }); rectchart([M, M * B - M], [RED, GRAY]);

\dfrac{A}{B} = \dfrac{C}{D} and so the answer is D.

Another way to get the answer is to multiply by \dfrac{M}{M}.

\dfrac{M}{M} = \dfrac{1}{1} = 1 so really we are multiplying by 1.

The final equation is: \dfrac{A}{B} \times \dfrac{M}{M} = \dfrac{C}{D} so our answer is D.

What number could replace SYMBOL below?

\dfrac{A}{B} = \dfrac{SYMBOL}{D}

C

The fraction on the left represents dividing some rectangular pizza(1).plural(2) into B slices, then taking A slices.

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED = A % B; if (FILLED === 0) { FILLED = B; } for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25); } else { rectchart([B], [RED], i * 1.25); } }

What if we cut each pizza(1) into D slices instead?

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED *= M; for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25); } else { rectchart([D], [RED], i * 1.25); } }

In order to take the same amount of pizza(1) as before, we now need to take C slices.

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, D - FILLED], [RED, _BACKGROUND], i * 1.25); } else { rectchart([D], [RED], i * 1.25); } }

\dfrac{A}{B} = \dfrac{C}{D} and so the answer is C.

Another way to get the answer is to multiply by \dfrac{M}{M}.

\dfrac{M}{M} = \dfrac{1}{1} = 1 so really we are multiplying by 1.

The final equation is: \dfrac{A}{B} \times \dfrac{M}{M} = \dfrac{C}{D} so our answer is C.

What number could replace SYMBOL below?

\dfrac{C}{D} = \dfrac{A}{SYMBOL}

B

The fraction on the left represents dividing some rectangular pizza(1).plural(2) into D slices, then taking C slices.

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED = C % D; if (FILLED === 0) { FILLED = D; } for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25); } else { rectchart([D], [RED], i * 1.25); } }

If we share those C slices equally between A person, how many slices does each person get?

If we share those C slices equally between A people, how many slices does each person get?

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED /= M; for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, B - FILLED], [RED, _BACKGROUND], i * 1.25); } else { rectchart([B], [RED], i * 1.25); } }

Sharing C slices equally between A person means each person gets M slices.

Sharing C slices equally between A people means each person gets M slices.

init({ range: [[0, 1], [0, 1]], scale: [475, 25] }); rectchart([M, D - M], [RED, _BACKGROUND]);

If we give each person M slices, how many people can we feed with one pizza(1)?

init({ range: [[0, 1], [0, 1]], scale: [475, 25] }); var filled = A % B; rectchart([FILLED, B - FILLED], [RED, GRAY]);

One pizza(1) has D slices, so if we give each person M slices, we could feed B people.

\dfrac{C}{D} = \dfrac{A}{B} and so the answer is B.

Another way to get the answer is to divide by \dfrac{M}{M}.

\dfrac{M}{M} = \dfrac{1}{1} = 1 so really we are dividing by 1.

The final equation is: \dfrac{C}{D} \div \dfrac{M}{M} = \dfrac{A}{B} so our answer is B.

What number could replace SYMBOL below?

\dfrac{C}{D} = \dfrac{SYMBOL}{B}

A

The fraction on the left represents dividing some rectangular pizza(1).plural(2) into D slices, then taking C slices.

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED = C % D; if (FILLED === 0) { FILLED = D; } for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, D - FILLED], [RED, GRAY], i * 1.25); } else { rectchart([D], [RED], i * 1.25); } }

What if we cut each pizza(1) into B slices instead?

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); FILLED /= M; for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, B - FILLED], [RED, GRAY], i * 1.25); } else { rectchart([B], [RED], i * 1.25); } }

In order to take the same amount of pizza(1) as before, we now need to take only A slices.

init({ range: [[0, 1], [0, N * 1.25]], scale: [475, 25] }); for (var i = 0; i < N; i++) { if (i === 0) { rectchart([FILLED, B - FILLED], [RED, _BACKGROUND], i * 1.25); } else { rectchart([B], [RED], i * 1.25); } }

\dfrac{C}{D} = \dfrac{A}{B} and so the answer is A.

Another way to get the answer is to divide by \dfrac{M}{M}.

\dfrac{M}{M} = \dfrac{1}{1} = 1 so really we are dividing by 1.

The final equation is: \dfrac{C}{D} \div \dfrac{M}{M} = \dfrac{A}{B} so our answer is A.