Grades45
Fractions and percentages run through Grades 4 and 5: adding, subtracting and multiplying fractions, and seeing one fraction three ways — as a circle, a bar and a percent. The real difficulty is rarely the arithmetic; it is that a fraction does not yet feel like a concrete amount. Every lesson on this page builds the fraction as an animated picture first and lets the formula follow, with worked examples parents can follow along.
Spot this family when a problem works with parts of a whole: adding or subtracting fractions with unlike denominators, taking a fraction of an amount (fraction multiplication), or asking what percent one amount is of another. The common sign: the answer is a part of something, not a whole counting number.
A pizza is cut into 8 equal slices. You eat 2 slices. What fraction of the pizza did you eat? (Enter the numerator)
Key idea: A fraction is parts taken over total equal parts.
A pizza cut into 8 equal slices with 2 eaten — the numerator is asked for.
Count the eaten slices over the total slices.
Eaten = 2 slices out of 8: the fraction 2/8.
The numerator (the top number) is 2.
So: So the numerator is 2.
Warm-up with matching pieces: 1/4 + 2/4 = ___
Key idea: Same denominators: add the tops, keep the bottom.
So: So 1/4 + 2/4 = 3/4.
What is 2/3 × 3/4?
Key idea: Multiply the tops, multiply the bottoms.
So: So 2/3 × 3/4 = 6/12.
A library has 300 books. 10% of them are comic books. How many comic books are there?
Key idea: Find 1% first (divide by 100), then scale up.
So: So there are 30 comic books.
A pizza is cut into 8 equal slices and 3 slices are eaten. What fraction was eaten? If you change the view to a tape and then to a percent, does the amount change?
Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)
A pizza is cut into 8 equal slices, and 3 of them are eaten. Look at that same amount as a pie, as a tape, as a percent — does the amount itself change?
Keep that question in mind — the whole lesson answers it. The lesson mantra: change the view, keep the amount.
Change the numbers and watch the diagram redraw itself:
They add numerators and denominators straight across — but only pieces of the same size can be added. A common denominator re-slices both fractions into one shared piece size so they can be counted; seeing that re-slicing once usually fixes the habit for good.
No — a percent is simply a fraction whose denominator is fixed at 100. Seeing the two notations as one amount (3/8 and 37.5% covering exactly the same region) is the foundation under every Grade 5 percent problem: discounts, interest and percentage change.
They are among the most heavily tested families in Grades 4–5 and appear in most olympiad papers and selective Grade 6 entrance exams, from direct computation through to advanced percentage problems.
