Grade 7 Complex Fractions and Unit Rates
Complex fractions and unit rates for grade 7 — simplify the stacked fraction, then divide to find the rate. Sixteen problems with a full answer key.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Simplify each complex fraction. For the word problems, divide to find the unit rate.
- 1.(1/2) ÷ (1/4) =
- 2.(3/4) ÷ (1/8) =
- 3.(2/3) ÷ (1/6) =
- 4.(1/2) ÷ (3/4) =
- 5.(5/6) ÷ (2/3) =
- 6.(3/8) ÷ (1/2) =
- 7.(7/10) ÷ (1/5) =
- 8.(2/5) ÷ (4/15) =
- 9.A runner covers 1/2 mile in 1/4 hour. What is the unit rate in miles per hour?
- 10.A snail travels 1/8 foot in 1/2 minute. What is the unit rate in feet per minute?
- 11.A recipe uses 3/4 cup of flour for 1/2 of a batch. What is the unit rate in cups per batch?
- 12.A hose delivers 2/3 gallon in 1/6 minute. What is the unit rate in gallons per minute?
- 13.2/3 of a can of paint covers 1/2 of a wall. What is the unit rate in walls per can?
- 14.A cyclist rides 3 1/2 miles in 1/4 hour. What is the unit rate in miles per hour?
- 15.A machine finishes 5/8 of a part in 1/4 hour. What is the unit rate in parts per hour?
- 16.A pipe leaks 3/10 liter in 3/4 hour. What is the unit rate in liters per hour?
What this worksheet covers
Sixteen fractions problems fill this drill page; problem 6 asks "(3/8) ÷ (1/2)", and the sheet stays at that level throughout. Within that, each problem arrives as a few sentences of context rather than a bare expression and several problems use mixed numbers, which have to be handled without dropping the whole-number part. Further down, problem 11 asks "A recipe uses 3/4 cup of flour for 1/2 of a batch. What is…". Common Core 7.RP.1 is the slot this page fills.
Skills practised
The grade 7 fractions sequence covers complex fractions, signed fractions, and fractions as terminating and repeating decimals; this page sits inside it. What a student is asked to do here is grade 7 Complex Fractions and Unit Rates. Concretely, the sheet tests whether a student can read a situation and choose an operation before computing and work in fractional units and give the answer in lowest terms.
About the drill format
This drill runs 16 problems in a steady layout, so the eye never has to hunt for the next one; problem 6, "(3/8) ÷ (1/2)" shows the level it holds. A page of one fraction operation lets the renaming step become routine before anything else is layered on.
Set A, Set B and Set C
Set A is the original MathSheetLab worksheet; Sets B and C keep its structure and redraw the numbers, with each answer recomputed rather than copied. Where Set A's problem 9 is "A runner covers 1/2 mile in 1/4 hour. What is the unit rate…", Set B's is "A machine finishes 7/8 of a part in 3/4 hour. What is the…".
8 story problem(s) drawn from the 7.RP.1 context family (unit rates from ratios of fractions) — parameters inferred from the standard and grade
How to use this worksheet
Have the student estimate before computing, then compare. At grade 7 an fractions answer that is wildly off should announce itself, and building that reflex matters as much as the sixteen answers. Ask the student to re-work one missed fractions problem from scratch on Set B rather than correcting it in place; the second attempt shows whether the method changed.
One mistake to watch for
Answers are left unsimplified or as improper fractions when the sheet asks for lowest terms. Watch problem 11 of this drill — "A recipe uses 3/4 cup of flour for 1/2 of a batch. What is…" — for this one.
Simplifying is seen as an optional extra step rather than part of the answer.
Add a checking step: is there a number that divides both parts? Is the top bigger than the bottom?
Other grade 7 fractions formats
The same skill in the other formats available at this grade.
- Timed Drill — Grade 7 Fractions Timed Drill, 60 problems
- Missing Number — Grade 7 Fractions Missing Number, 24 problems
- Mixed Review — Grade 7 Fractions Mixed Review, 30 problems
- Word Problems — Grade 7 Fractions Word Problems, 10 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 6 Dividing Fractions — grade 6, 16 problems
Drill sheets in other grade 7 topics
Six PDFs, no sign-up: three versions of this grade 7 fractions drill and three answer keys, each sixteen problems long.