Unit 4 · Topic 02 · Fractions
Kabir was given 2/4 of a chocolate bar and Anaya was given 1/2 of an identical one.
Kabir was delighted — he had two pieces and she only had one.
Then they put the bars side by side.
Ms. Rao handed out two identical chocolate bars. She snapped Kabir's into four equal pieces and gave him two. She snapped Anaya's into two equal pieces and gave her one.
Kabir counted his pieces. Two. Anaya had one. He was pleased with the arrangement.
"Put them next to each other," said Ms. Rao.
Kabir laid his two quarters end to end beside Anaya's single half. They were exactly the same length.
He tried it again with the pieces the other way round. Still the same.
"But I've got MORE pieces."
"You have more pieces and each one is smaller," said Ms. Rao. "Twice as many, each half the size. Those two changes cancel each other out exactly."
She wrote 1/2 = 2/4 on the board, then continued: 3/6, 4/8, 5/10.
"Every one of these is the same amount of chocolate. I made each by multiplying the top and the bottom by the same number. Multiply the top by 3 and the bottom by 3, and you have cut every piece into three — more pieces, smaller each, same total."
Anaya asked how to go the other way, from 24/36 down to something simpler.
"Divide both by something they share. What divides 24 and 36?"
"Two," said Kabir. "Gives 12/18."
"Two again," said Anaya. "6/9. Then three. 2/3."
"Three steps," said Ms. Rao. "Or one, if you spot that the biggest number dividing both is 12. Twenty-four divided by twelve is two, thirty-six divided by twelve is three. Straight to 2/3."
Kabir tried to simplify 12/16 and stopped at 6/8, pleased.
"Can you still divide both by something?"
He could. Both by two again, giving 3/4.
"Simplest form means you have kept going until nothing divides both except one. Six eighths is correct but it is not finished."
Two fractions are EQUIVALENT when they represent the same amount, even though the numbers look different. 1/2, 2/4 and 5/10 are all the same amount.
To make an equivalent fraction, multiply the numerator AND the denominator by the same number. You are cutting every piece into smaller pieces — more of them, each smaller, so the total is unchanged.
To simplify, DIVIDE the numerator and denominator by a common factor. Dividing by the HIGHEST common factor gets you there in one step; dividing by a smaller one works too but takes several.
A fraction is in SIMPLEST FORM when the only number dividing both top and bottom is 1. 6/8 is correct but unfinished — it still simplifies to 3/4. Adding the same number to top and bottom does NOT work; only multiplying or dividing preserves the value.
Draw circles split into 2, 4, 6, and 8 parts; shade half each time and write all four fractions.
Find the missing number: 1/2 = ?/16 and 5/6 = 35/?.
Use cross multiplication to solve 8/9 = x/15.
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