Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams
You already know what equivalent fractions are, and you know how to place fractions on a number line. Now put those two ideas together. If two fractions land on the exact same point on a number line, they are equivalent, even though they look different.
Maya cuts a paper strip into 6 equal parts and shades 3 of them. She cuts a same-size strip into 2 equal parts and shades 1. Both shaded parts cover the exact same length of the strip, so 3/6 and 1/2 are equivalent.
Cutting every step into smaller steps never moves the point. Halfway along 4 steps is step 2. Halfway along 6 steps is step 3. Halfway along 8 steps is step 4. The point stayed where it was, so 2/4, 3/6 and 4/8 are all names for 1/2.
There is a short way to write another name for the same point: multiply the top number and the bottom number by the same number. Starting from 1/2, times 3 gives 3/6. Then check it on the line, where 3/6 sits on the same point as 1/2.
Equivalent fractions are just different names for the same point on a number line.
Practice items adapted from WeBWorK Open Problem Library problems by Carl Yao (PCC) (CC BY-NC-SA 3.0).
At the Meadow Lane allotment the fence rail runs from the gate to the shed. You have walked it before, counting jumps from the gate at 0. Five posts hold the rail up, evenly spaced, so there are 4 equal gaps along it.
Leo starts at the gate and counts 2 jumps of 1/4. Which post does he stop at?
Jobs that lean on this skill. Follow one to see everything it is built on.
18 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.