Generate simple equivalent fractions and explain why they are equivalent using visual fraction models
Two fractions are equivalent when they cover the same amount, even though they look different. You have seen that two names can mark the same point on a number line. Now you make the extra names yourself. Split every part of a bar the same way and the shaded amount stays put: more parts, smaller parts, same space.
Leo chalks the bed by the shed into 8 equal rows and plants onions in 4 of them: 4/8. He rubs out every second line, so the rows join in pairs. Now the bed is 4 strips with 2 planted, which reads 2/4. Two more lines go and it reads 1/2. Same onions the whole time.
You can travel the other way too. Join the parts back into equal groups and both numbers get smaller, while the shaded space stays exactly where it is. Pairs, threes, any size, as long as every group is the same. When there is no group left to make, that last name has the smallest numbers. Finding it is called simplifying.
To make an equivalent fraction, multiply the top and bottom by the same number, or divide the top and bottom by the same number. The shaded amount never changes, only how many pieces it's split into.
Equivalent fractions cover the same amount of space, no matter how many pieces you cut it into, as long as you multiply or divide the top and bottom by the same number.
You have seen that two names can mark the same point on a number line. Making the extra names is the whole job this year. Start at the bed by the shed: 8 equal rows, onions in 4 of them, chalked on the door as 4/8. Leo rubs out every second line, so the rows join in pairs.
The bed is 4 wide strips now, and 2 of them are onion. Has the amount of onion changed?
Jobs that lean on this skill. Follow one to see everything it is built on.
14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.