Level 2 · Ages 8–11
Read it again any time, including while you work through the exercises.
So far, you have seen fractions as slices of pizza or pie. But a fraction is also a real number, with its exact place on a number line, just like 0, 1, 2 or 3. A number line is like an endless ruler: every point matches a number, called its coordinate.
To place a fraction, the denominator gives you the instructions: it tells you how many equal parts to cut each unit into (the space between two whole numbers). To place 3/4, I cut the unit between 0 and 1 into 4 equal parts, then I move 3 tick marks from 0: the numerator counts the steps.
What if the numerator is bigger than the denominator? No panic: the fraction simply goes past 1! For example 7/3 means 7 steps of one third each: 3 steps to reach 1, 3 more steps to reach 2, and 1 extra step. So 7/3 sits between 2 and 3, just after 2. Tip: find how many times the denominator fits into the numerator to know between which whole numbers you land.
One last magic link: the number line connects fractions and decimal numbers. Since 1/2 = 0.5 and 3/4 = 0.75, these notations name the same point on the line. Two different outfits, one single number! Practice switching between them, it will make all your calculations easier.
Place 3/4 on a number line between 0 and 1.
dénominateur = 4
The denominator tells me to cut the unit between 0 and 1 into 4 equal parts.
numérateur = 3
The numerator tells me to move 3 tick marks from 0.
0 → 1/4 → 2/4 → 3/4
I count the steps: 3/4 is on the third tick mark, just before 1.
Result: 3/4 sits three quarters of the way from 0 to 1.
Place 7/3 on a number line.
7/3 = 6/3 + 1/3
I split 7 thirds into groups: 6 thirds make 2 wholes, with 1 third left over.
7/3 = 2 + 1/3
So 7/3 is between 2 and 3, one third of the way past 2.
unité coupée en 3
I cut the unit between 2 and 3 into 3 equal parts and place the point on the first tick mark.
Result: 7/3 is between 2 and 3, on the first third tick mark after 2.