A ratio is how a story compares two amounts, and a proportion is what lets you scale it. These free printable word problems share a total in a given ratio and scale recipes and rates up and down, with the numbers kept friendly so the reasoning stays visible.
Sharing in a ratio is the gentle start: twenty sweets split three-to-one is four equal parts, three of them one child's and one the other's. Seeing the ratio as a number of equal parts, rather than as two separate numbers, is what makes the sharing obvious and what carries over to every later proportion.
Why this sheet works
Scaling comes next. If three apples cost ninety cents, one costs thirty, and any number costs thirty times as many — the unit rate is the hinge every proportion turns on. A child who finds the per-one amount first can answer any version of the question without setting up a formal proportion at all.
How this one works
One question from this sheet, worked through a step at a time.
At that rate, how long will it take to move 135 liters?
A pump moves 180 liters every 4 minutes.
180 ÷ 4 = 45
180 ÷ 4 = 45
135 ÷ 45 = 3 minutes
asked:At that rate, how long will it take to move 135 liters?
3 minutes
Read it through once. Two things change TOGETHER at a fixed rate, so the trick is to find the rate for ONE unit first — everything the question asks scales from that.
Find the rate for one: 180 ÷ 4 = 45. That is how much goes with a single unit.
Now scale that rate of 45 to what the question asks: 135 ÷ 45 = 3 minutes.
Answer the question that was asked — "At that rate, how long will it take to move 135 liters?" — 3 minutes.
